diff --git a/apps/interactive-calibration/frameProcessor.cpp b/apps/interactive-calibration/frameProcessor.cpp index 217f03c8d1..18d0d87c94 100644 --- a/apps/interactive-calibration/frameProcessor.cpp +++ b/apps/interactive-calibration/frameProcessor.cpp @@ -79,7 +79,7 @@ bool CalibProcessor::detectAndParseChAruco(const cv::Mat &frame) std::vector > corners, rejected; std::vector ids; - cv::aruco::detectMarkers(frame, mArucoDictionary, corners, ids, cv::aruco::DetectorParameters::create(), rejected); + cv::aruco::detectMarkers(frame, cv::makePtr(mArucoDictionary), corners, ids, cv::makePtr(), rejected); cv::aruco::refineDetectedMarkers(frame, board, corners, ids, rejected); cv::Mat currentCharucoCorners, currentCharucoIds; if(ids.size() > 0) @@ -266,8 +266,8 @@ bool CalibProcessor::checkLastFrame() allObjPoints.reserve(mCurrentCharucoIds.total()); for(size_t i = 0; i < mCurrentCharucoIds.total(); i++) { int pointID = mCurrentCharucoIds.at((int)i); - CV_Assert(pointID >= 0 && pointID < (int)mCharucoBoard->chessboardCorners.size()); - allObjPoints.push_back(mCharucoBoard->chessboardCorners[pointID]); + CV_Assert(pointID >= 0 && pointID < (int)mCharucoBoard->getChessboardCorners().size()); + allObjPoints.push_back(mCharucoBoard->getChessboardCorners()[pointID]); } cv::solvePnP(allObjPoints, mCurrentCharucoCorners, tmpCamMatrix, mCalibData->distCoeffs, r, t); @@ -300,8 +300,7 @@ CalibProcessor::CalibProcessor(cv::Ptr data, captureParameters { case chAruco: #ifdef HAVE_OPENCV_ARUCO - mArucoDictionary = cv::aruco::getPredefinedDictionary( - cv::aruco::PREDEFINED_DICTIONARY_NAME(capParams.charucoDictName)); + mArucoDictionary = cv::aruco::getPredefinedDictionary(cv::aruco::PredefinedDictionaryType(capParams.charucoDictName)); mCharucoBoard = cv::aruco::CharucoBoard::create(mBoardSize.width, mBoardSize.height, capParams.charucoSquareLength, capParams.charucoMarkerSize, mArucoDictionary); #endif diff --git a/apps/interactive-calibration/frameProcessor.hpp b/apps/interactive-calibration/frameProcessor.hpp index bae79f930f..51c2906c8e 100644 --- a/apps/interactive-calibration/frameProcessor.hpp +++ b/apps/interactive-calibration/frameProcessor.hpp @@ -40,7 +40,7 @@ protected: cv::Ptr mBlobDetectorPtr; #ifdef HAVE_OPENCV_ARUCO - cv::Ptr mArucoDictionary; + cv::aruco::Dictionary mArucoDictionary; cv::Ptr mCharucoBoard; #endif diff --git a/apps/interactive-calibration/main.cpp b/apps/interactive-calibration/main.cpp index 3bf4a0776e..d83ef95aad 100644 --- a/apps/interactive-calibration/main.cpp +++ b/apps/interactive-calibration/main.cpp @@ -180,8 +180,8 @@ int main(int argc, char** argv) } else { #ifdef HAVE_OPENCV_ARUCO - cv::Ptr dictionary = - cv::aruco::getPredefinedDictionary(cv::aruco::PREDEFINED_DICTIONARY_NAME(capParams.charucoDictName)); + cv::aruco::Dictionary dictionary = + cv::aruco::getPredefinedDictionary(cv::aruco::PredefinedDictionaryType(capParams.charucoDictName)); cv::Ptr charucoboard = cv::aruco::CharucoBoard::create(capParams.boardSize.width, capParams.boardSize.height, capParams.charucoSquareLength, capParams.charucoMarkerSize, dictionary); diff --git a/doc/py_tutorials/py_calib3d/py_pose/py_pose.markdown b/doc/py_tutorials/py_calib3d/py_pose/py_pose.markdown index a1a612d6f6..15dd8584fa 100644 --- a/doc/py_tutorials/py_calib3d/py_pose/py_pose.markdown +++ b/doc/py_tutorials/py_calib3d/py_pose/py_pose.markdown @@ -59,7 +59,7 @@ pixels. Then to calculate the rotation and translation, we use the function, **cv.solvePnPRansac()**. Once we those transformation matrices, we use them to project our **axis points** to the image plane. In simple words, we find the points on image plane corresponding to each of (3,0,0),(0,3,0),(0,0,3) in 3D space. Once we get them, we draw lines from the first corner -to each of these points using our draw() function. Done !!! +to each of these points using our generateImage() function. Done !!! @code{.py} for fname in glob.glob('left*.jpg'): img = cv.imread(fname) @@ -89,9 +89,9 @@ See some results below. Notice that each axis is 3 squares long.: ### Render a Cube -If you want to draw a cube, modify the draw() function and axis points as follows. +If you want to draw a cube, modify the generateImage() function and axis points as follows. -Modified draw() function: +Modified generateImage() function: @code{.py} def draw(img, corners, imgpts): imgpts = np.int32(imgpts).reshape(-1,2) diff --git a/modules/objdetect/doc/objdetect.bib b/modules/objdetect/doc/objdetect.bib new file mode 100644 index 0000000000..394eff8537 --- /dev/null +++ b/modules/objdetect/doc/objdetect.bib @@ -0,0 +1,20 @@ +@article{Aruco2014, + author = {S. Garrido-Jurado and R. Mu\~noz-Salinas and F.J. Madrid-Cuevas and M.J. Mar\'in-Jim\'enez} + title = {Automatic generation and detection of highly reliable fiducial markers under occlusion}, + year = {2014}, + pages = {2280 - 2292}, + journal = {Pattern Recognition}, + volume = {47}, + number = {6}, + issn = {0031-3203}, + doi = {http://dx.doi.org/10.1016/j.patcog.2014.01.005}, + url = {http://www.sciencedirect.com/science/article/pii/S0031320314000235} +} + +@inproceedings{wang2016iros, + author = {John Wang and Edwin Olson}, + title = {{AprilTag} 2: Efficient and robust fiducial detection}, + booktitle = {Proceedings of the {IEEE/RSJ} International Conference on Intelligent Robots and Systems {(IROS)}}, + year = {2016}, + month = {October} +} diff --git a/modules/objdetect/include/opencv2/objdetect.hpp b/modules/objdetect/include/opencv2/objdetect.hpp index 4e104df3ca..58f1aee3b7 100644 --- a/modules/objdetect/include/opencv2/objdetect.hpp +++ b/modules/objdetect/include/opencv2/objdetect.hpp @@ -851,5 +851,6 @@ protected: #include "opencv2/objdetect/detection_based_tracker.hpp" #include "opencv2/objdetect/face.hpp" +#include "opencv2/objdetect/aruco_detector.hpp" #endif diff --git a/modules/objdetect/include/opencv2/objdetect/aruco_board.hpp b/modules/objdetect/include/opencv2/objdetect/aruco_board.hpp new file mode 100644 index 0000000000..fb90c7b75d --- /dev/null +++ b/modules/objdetect/include/opencv2/objdetect/aruco_board.hpp @@ -0,0 +1,234 @@ +// This file is part of OpenCV project. +// It is subject to the license terms in the LICENSE file found in the top-level directory +// of this distribution and at http://opencv.org/license.html +#ifndef OPENCV_OBJDETECT_ARUCO_BOARD_HPP +#define OPENCV_OBJDETECT_ARUCO_BOARD_HPP + +#include + +namespace cv { +namespace aruco { +//! @addtogroup aruco +//! @{ + +class Dictionary; + +/** @brief Board of ArUco markers + * + * A board is a set of markers in the 3D space with a common coordinate system. + * The common form of a board of marker is a planar (2D) board, however any 3D layout can be used. + * A Board object is composed by: + * - The object points of the marker corners, i.e. their coordinates respect to the board system. + * - The dictionary which indicates the type of markers of the board + * - The identifier of all the markers in the board. + */ +class CV_EXPORTS_W Board { +protected: + Board(); // use ::create() +public: + /** @brief Draw a planar board + * + * @param outSize size of the output image in pixels. + * @param img output image with the board. The size of this image will be outSize + * and the board will be on the center, keeping the board proportions. + * @param marginSize minimum margins (in pixels) of the board in the output image + * @param borderBits width of the marker borders. + * + * This function return the image of the GridBoard, ready to be printed. + */ + CV_WRAP virtual void generateImage(Size outSize, OutputArray img, int marginSize = 0, int borderBits = 1) const; + + /** @brief Provide way to create Board by passing necessary data. Specially needed in Python. + * + * @param objPoints array of object points of all the marker corners in the board + * @param dictionary the dictionary of markers employed for this board + * @param ids vector of the identifiers of the markers in the board + */ + CV_WRAP static Ptr create(InputArrayOfArrays objPoints, const Dictionary &dictionary, InputArray ids); + + /** @brief return the Dictionary of markers employed for this board + */ + CV_WRAP const Dictionary& getDictionary() const; + + /** @brief return array of object points of all the marker corners in the board. + * + * Each marker include its 4 corners in this order: + * - objPoints[i][0] - left-top point of i-th marker + * - objPoints[i][1] - right-top point of i-th marker + * - objPoints[i][2] - right-bottom point of i-th marker + * - objPoints[i][3] - left-bottom point of i-th marker + * + * Markers are placed in a certain order - row by row, left to right in every row. For M markers, the size is Mx4. + */ + CV_WRAP const std::vector >& getObjPoints() const; + + /** @brief vector of the identifiers of the markers in the board (should be the same size as objPoints) + * @return vector of the identifiers of the markers + */ + CV_WRAP const std::vector& getIds() const; + + /** @brief get coordinate of the bottom right corner of the board, is set when calling the function create() + */ + CV_WRAP const Point3f& getRightBottomCorner() const; + + /** @brief Given a board configuration and a set of detected markers, returns the corresponding + * image points and object points to call solvePnP + * + * @param detectedCorners List of detected marker corners of the board. + * @param detectedIds List of identifiers for each marker. + * @param objPoints Vector of vectors of board marker points in the board coordinate space. + * @param imgPoints Vector of vectors of the projections of board marker corner points. + */ + CV_WRAP void matchImagePoints(InputArrayOfArrays detectedCorners, InputArray detectedIds, + OutputArray objPoints, OutputArray imgPoints) const; + virtual ~Board(); +protected: + struct BoardImpl; + Ptr boardImpl; +}; + +/** @brief Planar board with grid arrangement of markers + * + * More common type of board. All markers are placed in the same plane in a grid arrangement. + * The board image can be drawn using generateImage() method. + */ +class CV_EXPORTS_W GridBoard : public Board { +protected: + GridBoard(); +public: + /** @brief Draw a GridBoard + * + * @param outSize size of the output image in pixels. + * @param img output image with the board. The size of this image will be outSize + * and the board will be on the center, keeping the board proportions. + * @param marginSize minimum margins (in pixels) of the board in the output image + * @param borderBits width of the marker borders. + * + * This function return the image of the GridBoard, ready to be printed. + */ + CV_WRAP void generateImage(Size outSize, OutputArray img, int marginSize = 0, int borderBits = 1) const CV_OVERRIDE; + + /** + * @brief Create a GridBoard object + * + * @param markersX number of markers in X direction + * @param markersY number of markers in Y direction + * @param markerLength marker side length (normally in meters) + * @param markerSeparation separation between two markers (same unit as markerLength) + * @param dictionary dictionary of markers indicating the type of markers + * @param ids set marker ids in dictionary to use on board. + * @return the output GridBoard object + * + * This functions creates a GridBoard object given the number of markers in each direction and + * the marker size and marker separation. + */ + CV_WRAP static Ptr create(int markersX, int markersY, float markerLength, float markerSeparation, + const Dictionary &dictionary, InputArray ids); + + /** + * @overload + * @brief Create a GridBoard object + * + * @param markersX number of markers in X direction + * @param markersY number of markers in Y direction + * @param markerLength marker side length (normally in meters) + * @param markerSeparation separation between two markers (same unit as markerLength) + * @param dictionary dictionary of markers indicating the type of markers + * @param firstMarker id of first marker in dictionary to use on board. + * @return the output GridBoard object + */ + CV_WRAP static Ptr create(int markersX, int markersY, float markerLength, float markerSeparation, + const Dictionary &dictionary, int firstMarker = 0); + + CV_WRAP Size getGridSize() const; + CV_WRAP float getMarkerLength() const; + CV_WRAP float getMarkerSeparation() const; + +protected: + struct GridImpl; + Ptr gridImpl; + friend class CharucoBoard; +}; + +/** + * @brief ChArUco board is a planar chessboard where the markers are placed inside the white squares of a chessboard. + * + * The benefits of ChArUco boards is that they provide both, ArUco markers versatility and chessboard corner precision, + * which is important for calibration and pose estimation. The board image can be drawn using generateImage() method. + */ +class CV_EXPORTS_W CharucoBoard : public Board { +protected: + CharucoBoard(); +public: + + /** @brief Draw a ChArUco board + * + * @param outSize size of the output image in pixels. + * @param img output image with the board. The size of this image will be outSize + * and the board will be on the center, keeping the board proportions. + * @param marginSize minimum margins (in pixels) of the board in the output image + * @param borderBits width of the marker borders. + * + * This function return the image of the ChArUco board, ready to be printed. + */ + CV_WRAP void generateImage(Size outSize, OutputArray img, int marginSize = 0, int borderBits = 1) const CV_OVERRIDE; + + + /** @brief Create a CharucoBoard object + * + * @param squaresX number of chessboard squares in X direction + * @param squaresY number of chessboard squares in Y direction + * @param squareLength chessboard square side length (normally in meters) + * @param markerLength marker side length (same unit than squareLength) + * @param dictionary dictionary of markers indicating the type of markers. + * @param ids array of id used markers + * The first markers in the dictionary are used to fill the white chessboard squares. + * @return the output CharucoBoard object + * + * This functions creates a CharucoBoard object given the number of squares in each direction + * and the size of the markers and chessboard squares. + */ + CV_WRAP static Ptr create(int squaresX, int squaresY, float squareLength, float markerLength, + const Dictionary &dictionary, InputArray ids = noArray()); + + CV_WRAP Size getChessboardSize() const; + CV_WRAP float getSquareLength() const; + CV_WRAP float getMarkerLength() const; + + /** @brief get CharucoBoard::chessboardCorners + */ + CV_WRAP std::vector getChessboardCorners() const; + + /** @brief get CharucoBoard::nearestMarkerIdx + */ + CV_PROP std::vector > getNearestMarkerIdx() const; + + /** @brief get CharucoBoard::nearestMarkerCorners + */ + CV_PROP std::vector > getNearestMarkerCorners() const; + + /** @brief check whether the ChArUco markers are collinear + * + * @param charucoIds list of identifiers for each corner in charucoCorners per frame. + * @return bool value, 1 (true) if detected corners form a line, 0 (false) if they do not. + * solvePnP, calibration functions will fail if the corners are collinear (true). + * + * The number of ids in charucoIDs should be <= the number of chessboard corners in the board. + * This functions checks whether the charuco corners are on a straight line (returns true, if so), or not (false). + * Axis parallel, as well as diagonal and other straight lines detected. Degenerate cases: + * for number of charucoIDs <= 2,the function returns true. + */ + CV_WRAP bool checkCharucoCornersCollinear(InputArray charucoIds) const; + +protected: + struct CharucoImpl; + friend struct CharucoImpl; + Ptr charucoImpl; +}; + +//! @} + +} +} + +#endif diff --git a/modules/objdetect/include/opencv2/objdetect/aruco_detector.hpp b/modules/objdetect/include/opencv2/objdetect/aruco_detector.hpp new file mode 100644 index 0000000000..69c7defd1c --- /dev/null +++ b/modules/objdetect/include/opencv2/objdetect/aruco_detector.hpp @@ -0,0 +1,396 @@ +// This file is part of OpenCV project. +// It is subject to the license terms in the LICENSE file found in the top-level directory +// of this distribution and at http://opencv.org/license.html +#ifndef OPENCV_OBJDETECT_ARUCO_DETECTOR_HPP +#define OPENCV_OBJDETECT_ARUCO_DETECTOR_HPP + +#include +#include + +namespace cv { +namespace aruco { + +/** @defgroup aruco ArUco Marker Detection + * Square fiducial markers (also known as Augmented Reality Markers) are useful for easy, + * fast and robust camera pose estimation. + * + * The main functionality of ArucoDetector class is detection of markers in an image. There are even more + * functionalities implemented in the aruco contrib module (files aruco.hpp, charuco.hpp, aruco_calib.hpp): + * - Pose estimation from a single marker or from a board/set of markers + * - Detection of ChArUco board for high subpixel accuracy + * - Camera calibration from both, ArUco boards and ChArUco boards. + * - Detection of ChArUco diamond markers + * The functionalities from the aruco contrib module is planned to be transferred to the main repository. + * + * The implementation is based on the ArUco Library by R. Muñoz-Salinas and S. Garrido-Jurado @cite Aruco2014. + * + * Markers can also be detected based on the AprilTag 2 @cite wang2016iros fiducial detection method. + * + * @sa @cite Aruco2014 + * This code has been originally developed by Sergio Garrido-Jurado as a project + * for Google Summer of Code 2015 (GSoC 15). + */ + +//! @addtogroup aruco +//! @{ + +enum CornerRefineMethod{ + CORNER_REFINE_NONE, ///< Tag and corners detection based on the ArUco approach + CORNER_REFINE_SUBPIX, ///< ArUco approach and refine the corners locations using corner subpixel accuracy + CORNER_REFINE_CONTOUR, ///< ArUco approach and refine the corners locations using the contour-points line fitting + CORNER_REFINE_APRILTAG, ///< Tag and corners detection based on the AprilTag 2 approach @cite wang2016iros +}; + +/** @brief struct DetectorParameters is used by ArucoDetector + */ +struct CV_EXPORTS_W_SIMPLE DetectorParameters { + CV_WRAP DetectorParameters() { + adaptiveThreshWinSizeMin = 3; + adaptiveThreshWinSizeMax = 23; + adaptiveThreshWinSizeStep = 10; + adaptiveThreshConstant = 7; + minMarkerPerimeterRate = 0.03; + maxMarkerPerimeterRate = 4.; + polygonalApproxAccuracyRate = 0.03; + minCornerDistanceRate = 0.05; + minDistanceToBorder = 3; + minMarkerDistanceRate = 0.05; + cornerRefinementMethod = CORNER_REFINE_NONE; + cornerRefinementWinSize = 5; + cornerRefinementMaxIterations = 30; + cornerRefinementMinAccuracy = 0.1; + markerBorderBits = 1; + perspectiveRemovePixelPerCell = 4; + perspectiveRemoveIgnoredMarginPerCell = 0.13; + maxErroneousBitsInBorderRate = 0.35; + minOtsuStdDev = 5.0; + errorCorrectionRate = 0.6; + aprilTagQuadDecimate = 0.0; + aprilTagQuadSigma = 0.0; + aprilTagMinClusterPixels = 5; + aprilTagMaxNmaxima = 10; + aprilTagCriticalRad = (float)(10* CV_PI /180); + aprilTagMaxLineFitMse = 10.0; + aprilTagMinWhiteBlackDiff = 5; + aprilTagDeglitch = 0; + detectInvertedMarker = false; + useAruco3Detection = false; + minSideLengthCanonicalImg = 32; + minMarkerLengthRatioOriginalImg = 0.0; + }; + + /** @brief Read a new set of DetectorParameters from FileNode (use FileStorage.root()). + */ + CV_WRAP bool readDetectorParameters(const FileNode& fn); + + /** @brief Write a set of DetectorParameters to FileStorage + */ + bool writeDetectorParameters(FileStorage& fs); + + /** @brief simplified API for language bindings + */ + CV_WRAP bool writeDetectorParameters(const Ptr& fs, const String& name = String()); + + /// minimum window size for adaptive thresholding before finding contours (default 3). + CV_PROP_RW int adaptiveThreshWinSizeMin; + + /// maximum window size for adaptive thresholding before finding contours (default 23). + CV_PROP_RW int adaptiveThreshWinSizeMax; + + /// increments from adaptiveThreshWinSizeMin to adaptiveThreshWinSizeMax during the thresholding (default 10). + CV_PROP_RW int adaptiveThreshWinSizeStep; + + /// constant for adaptive thresholding before finding contours (default 7) + CV_PROP_RW double adaptiveThreshConstant; + + /** @brief determine minimum perimeter for marker contour to be detected. + * + * This is defined as a rate respect to the maximum dimension of the input image (default 0.03). + */ + CV_PROP_RW double minMarkerPerimeterRate; + + /** @brief determine maximum perimeter for marker contour to be detected. + * + * This is defined as a rate respect to the maximum dimension of the input image (default 4.0). + */ + CV_PROP_RW double maxMarkerPerimeterRate; + + /// minimum accuracy during the polygonal approximation process to determine which contours are squares. (default 0.03) + CV_PROP_RW double polygonalApproxAccuracyRate; + + /// minimum distance between corners for detected markers relative to its perimeter (default 0.05) + CV_PROP_RW double minCornerDistanceRate; + + /// minimum distance of any corner to the image border for detected markers (in pixels) (default 3) + CV_PROP_RW int minDistanceToBorder; + + /** @brief minimum mean distance beetween two marker corners to be considered imilar, so that the smaller one is removed. + * + * The rate is relative to the smaller perimeter of the two markers (default 0.05). + */ + CV_PROP_RW double minMarkerDistanceRate; + + /** @brief default value CORNER_REFINE_NONE */ + CV_PROP_RW CornerRefineMethod cornerRefinementMethod; + + /// window size for the corner refinement process (in pixels) (default 5). + CV_PROP_RW int cornerRefinementWinSize; + + /// maximum number of iterations for stop criteria of the corner refinement process (default 30). + CV_PROP_RW int cornerRefinementMaxIterations; + + /// minimum error for the stop cristeria of the corner refinement process (default: 0.1) + CV_PROP_RW double cornerRefinementMinAccuracy; + + /// number of bits of the marker border, i.e. marker border width (default 1). + CV_PROP_RW int markerBorderBits; + + /// number of bits (per dimension) for each cell of the marker when removing the perspective (default 4). + CV_PROP_RW int perspectiveRemovePixelPerCell; + + /** @brief width of the margin of pixels on each cell not considered for the determination of the cell bit. + * + * Represents the rate respect to the total size of the cell, i.e. perspectiveRemovePixelPerCell (default 0.13) + */ + CV_PROP_RW double perspectiveRemoveIgnoredMarginPerCell; + + /** @brief maximum number of accepted erroneous bits in the border (i.e. number of allowed white bits in the border). + * + * Represented as a rate respect to the total number of bits per marker (default 0.35). + */ + CV_PROP_RW double maxErroneousBitsInBorderRate; + + /** @brief minimun standard deviation in pixels values during the decodification step to apply Otsu + * thresholding (otherwise, all the bits are set to 0 or 1 depending on mean higher than 128 or not) (default 5.0) + */ + CV_PROP_RW double minOtsuStdDev; + + /// error correction rate respect to the maximun error correction capability for each dictionary (default 0.6). + CV_PROP_RW double errorCorrectionRate; + + /** @brief April :: User-configurable parameters. + * + * Detection of quads can be done on a lower-resolution image, improving speed at a cost of + * pose accuracy and a slight decrease in detection rate. Decoding the binary payload is still + */ + CV_PROP_RW float aprilTagQuadDecimate; + + /// what Gaussian blur should be applied to the segmented image (used for quad detection?) + CV_PROP_RW float aprilTagQuadSigma; + + // April :: Internal variables + /// reject quads containing too few pixels (default 5). + CV_PROP_RW int aprilTagMinClusterPixels; + + /// how many corner candidates to consider when segmenting a group of pixels into a quad (default 10). + CV_PROP_RW int aprilTagMaxNmaxima; + + /** @brief reject quads where pairs of edges have angles that are close to straight or close to 180 degrees. + * + * Zero means that no quads are rejected. (In radians) (default 10*PI/180) + */ + CV_PROP_RW float aprilTagCriticalRad; + + /// when fitting lines to the contours, what is the maximum mean squared error + CV_PROP_RW float aprilTagMaxLineFitMse; + + /** @brief add an extra check that the white model must be (overall) brighter than the black model. + * + * When we build our model of black & white pixels, we add an extra check that the white model must be (overall) + * brighter than the black model. How much brighter? (in pixel values, [0,255]), (default 5) + */ + CV_PROP_RW int aprilTagMinWhiteBlackDiff; + + /// should the thresholded image be deglitched? Only useful for very noisy images (default 0). + CV_PROP_RW int aprilTagDeglitch; + + /** @brief to check if there is a white marker. + * + * In order to generate a "white" marker just invert a normal marker by using a tilde, ~markerImage. (default false) + */ + CV_PROP_RW bool detectInvertedMarker; + + /** @brief enable the new and faster Aruco detection strategy. + * + * Proposed in the paper: + * Romero-Ramirez et al: Speeded up detection of squared fiducial markers (2018) + * https://www.researchgate.net/publication/325787310_Speeded_Up_Detection_of_Squared_Fiducial_Markers + */ + CV_PROP_RW bool useAruco3Detection; + + /// minimum side length of a marker in the canonical image. Latter is the binarized image in which contours are searched. + CV_PROP_RW int minSideLengthCanonicalImg; + + /// range [0,1], eq (2) from paper. The parameter tau_i has a direct influence on the processing speed. + CV_PROP_RW float minMarkerLengthRatioOriginalImg; +}; + +/** @brief struct RefineParameters is used by ArucoDetector + */ +struct CV_EXPORTS_W_SIMPLE RefineParameters { + CV_WRAP RefineParameters(float minRepDistance = 10.f, float errorCorrectionRate = 3.f, bool checkAllOrders = true); + + + /** @brief Read a new set of RefineParameters from FileNode (use FileStorage.root()). + */ + CV_WRAP bool readRefineParameters(const FileNode& fn); + + /** @brief Write a set of RefineParameters to FileStorage + */ + bool writeRefineParameters(FileStorage& fs); + + /** @brief simplified API for language bindings + */ + CV_WRAP bool writeRefineParameters(const Ptr& fs, const String& name = String()); + + /** @brief minRepDistance minimum distance between the corners of the rejected candidate and the reprojected marker + in order to consider it as a correspondence. + */ + CV_PROP_RW float minRepDistance; + + /** @brief minRepDistance rate of allowed erroneous bits respect to the error correction capability of the used dictionary. + * + * -1 ignores the error correction step. + */ + CV_PROP_RW float errorCorrectionRate; + + /** @brief checkAllOrders consider the four posible corner orders in the rejectedCorners array. + * + * If it set to false, only the provided corner order is considered (default true). + */ + CV_PROP_RW bool checkAllOrders; +}; + +/** @brief The main functionality of ArucoDetector class is detection of markers in an image with detectMarkers() method. + * + * After detecting some markers in the image, you can try to find undetected markers from this dictionary with + * refineDetectedMarkers() method. + * + * @see DetectorParameters, RefineParameters + */ +class CV_EXPORTS_W ArucoDetector : public Algorithm +{ +public: + /** @brief Basic ArucoDetector constructor + * + * @param dictionary indicates the type of markers that will be searched + * @param detectorParams marker detection parameters + * @param refineParams marker refine detection parameters + */ + CV_WRAP ArucoDetector(const Dictionary &dictionary = getPredefinedDictionary(cv::aruco::DICT_4X4_50), + const DetectorParameters &detectorParams = DetectorParameters(), + const RefineParameters& refineParams = RefineParameters()); + + /** @brief Basic marker detection + * + * @param image input image + * @param corners vector of detected marker corners. For each marker, its four corners + * are provided, (e.g std::vector > ). For N detected markers, + * the dimensions of this array is Nx4. The order of the corners is clockwise. + * @param ids vector of identifiers of the detected markers. The identifier is of type int + * (e.g. std::vector). For N detected markers, the size of ids is also N. + * The identifiers have the same order than the markers in the imgPoints array. + * @param rejectedImgPoints contains the imgPoints of those squares whose inner code has not a + * correct codification. Useful for debugging purposes. + * + * Performs marker detection in the input image. Only markers included in the specific dictionary + * are searched. For each detected marker, it returns the 2D position of its corner in the image + * and its corresponding identifier. + * Note that this function does not perform pose estimation. + * @note The function does not correct lens distortion or takes it into account. It's recommended to undistort + * input image with corresponging camera model, if camera parameters are known + * @sa undistort, estimatePoseSingleMarkers, estimatePoseBoard + */ + CV_WRAP void detectMarkers(InputArray image, OutputArrayOfArrays corners, OutputArray ids, + OutputArrayOfArrays rejectedImgPoints = noArray()); + + /** @brief Refind not detected markers based on the already detected and the board layout + * + * @param image input image + * @param board layout of markers in the board. + * @param detectedCorners vector of already detected marker corners. + * @param detectedIds vector of already detected marker identifiers. + * @param rejectedCorners vector of rejected candidates during the marker detection process. + * @param cameraMatrix optional input 3x3 floating-point camera matrix + * \f$A = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\f$ + * @param distCoeffs optional vector of distortion coefficients + * \f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6],[s_1, s_2, s_3, s_4]])\f$ of 4, 5, 8 or 12 elements + * @param recoveredIdxs Optional array to returns the indexes of the recovered candidates in the + * original rejectedCorners array. + * + * This function tries to find markers that were not detected in the basic detecMarkers function. + * First, based on the current detected marker and the board layout, the function interpolates + * the position of the missing markers. Then it tries to find correspondence between the reprojected + * markers and the rejected candidates based on the minRepDistance and errorCorrectionRate parameters. + * If camera parameters and distortion coefficients are provided, missing markers are reprojected + * using projectPoint function. If not, missing marker projections are interpolated using global + * homography, and all the marker corners in the board must have the same Z coordinate. + */ + CV_WRAP void refineDetectedMarkers(InputArray image, const Ptr &board, + InputOutputArrayOfArrays detectedCorners, + InputOutputArray detectedIds, InputOutputArrayOfArrays rejectedCorners, + InputArray cameraMatrix = noArray(), InputArray distCoeffs = noArray(), + OutputArray recoveredIdxs = noArray()); + + CV_WRAP const Dictionary& getDictionary() const; + CV_WRAP void setDictionary(const Dictionary& dictionary); + + CV_WRAP const DetectorParameters& getDetectorParameters() const; + CV_WRAP void setDetectorParameters(const DetectorParameters& detectorParameters); + + CV_WRAP const RefineParameters& getRefineParameters() const; + CV_WRAP void setRefineParameters(const RefineParameters& refineParameters); + + /** @brief Stores algorithm parameters in a file storage + */ + virtual void write(FileStorage& fs) const override; + + /** @brief simplified API for language bindings + */ + CV_WRAP inline void write(const Ptr& fs, const String& name = String()) { Algorithm::write(fs, name); } + + /** @brief Reads algorithm parameters from a file storage + */ + CV_WRAP virtual void read(const FileNode& fn) override; +protected: + struct ArucoDetectorImpl; + Ptr arucoDetectorImpl; +}; + +/** @brief Draw detected markers in image + * + * @param image input/output image. It must have 1 or 3 channels. The number of channels is not altered. + * @param corners positions of marker corners on input image. + * (e.g std::vector > ). For N detected markers, the dimensions of + * this array should be Nx4. The order of the corners should be clockwise. + * @param ids vector of identifiers for markers in markersCorners . + * Optional, if not provided, ids are not painted. + * @param borderColor color of marker borders. Rest of colors (text color and first corner color) + * are calculated based on this one to improve visualization. + * + * Given an array of detected marker corners and its corresponding ids, this functions draws + * the markers in the image. The marker borders are painted and the markers identifiers if provided. + * Useful for debugging purposes. + */ +CV_EXPORTS_W void drawDetectedMarkers(InputOutputArray image, InputArrayOfArrays corners, + InputArray ids = noArray(), Scalar borderColor = Scalar(0, 255, 0)); + +/** @brief Generate a canonical marker image + * + * @param dictionary dictionary of markers indicating the type of markers + * @param id identifier of the marker that will be returned. It has to be a valid id in the specified dictionary. + * @param sidePixels size of the image in pixels + * @param img output image with the marker + * @param borderBits width of the marker border. + * + * This function returns a marker image in its canonical form (i.e. ready to be printed) + */ +CV_EXPORTS_W void generateImageMarker(const Dictionary &dictionary, int id, int sidePixels, OutputArray img, + int borderBits = 1); + +//! @} + +} +} + +#endif diff --git a/modules/objdetect/include/opencv2/objdetect/aruco_dictionary.hpp b/modules/objdetect/include/opencv2/objdetect/aruco_dictionary.hpp new file mode 100644 index 0000000000..e306c65fe8 --- /dev/null +++ b/modules/objdetect/include/opencv2/objdetect/aruco_dictionary.hpp @@ -0,0 +1,151 @@ +// This file is part of OpenCV project. +// It is subject to the license terms in the LICENSE file found in the top-level directory +// of this distribution and at http://opencv.org/license.html +#ifndef OPENCV_OBJDETECT_DICTIONARY_HPP +#define OPENCV_OBJDETECT_DICTIONARY_HPP + +#include + +namespace cv { +namespace aruco { + +//! @addtogroup aruco +//! @{ + + +/** @brief Dictionary/Set of markers, it contains the inner codification + * + * BytesList contains the marker codewords where: + * - bytesList.rows is the dictionary size + * - each marker is encoded using `nbytes = ceil(markerSize*markerSize/8.)` + * - each row contains all 4 rotations of the marker, so its length is `4*nbytes` + * + * `bytesList.ptr(i)[k*nbytes + j]` is then the j-th byte of i-th marker, in its k-th rotation. + */ +class CV_EXPORTS_W_SIMPLE Dictionary { + + public: + CV_PROP_RW Mat bytesList; // marker code information + CV_PROP_RW int markerSize; // number of bits per dimension + CV_PROP_RW int maxCorrectionBits; // maximum number of bits that can be corrected + + + CV_WRAP Dictionary(); + + CV_WRAP Dictionary(const Mat &bytesList, int _markerSize, int maxcorr = 0); + + + + /** @brief Read a new dictionary from FileNode. + * + * Dictionary format:\n + * nmarkers: 35\n + * markersize: 6\n + * maxCorrectionBits: 5\n + * marker_0: "101011111011111001001001101100000000"\n + * ...\n + * marker_34: "011111010000111011111110110101100101" + */ + CV_WRAP bool readDictionary(const cv::FileNode& fn); + + /** @brief Write a dictionary to FileStorage, format is the same as in readDictionary(). + */ + void writeDictionary(FileStorage& fs); + + /** @brief simplified API for language bindings + */ + CV_WRAP void writeDictionary(Ptr& fs, const String& name = String()); + + /** @brief Given a matrix of bits. Returns whether if marker is identified or not. + * + * It returns by reference the correct id (if any) and the correct rotation + */ + CV_WRAP bool identify(const Mat &onlyBits, CV_OUT int &idx, CV_OUT int &rotation, double maxCorrectionRate) const; + + /** @brief Returns the distance of the input bits to the specific id. + * + * If allRotations is true, the four posible bits rotation are considered + */ + CV_WRAP int getDistanceToId(InputArray bits, int id, bool allRotations = true) const; + + + /** @brief Generate a canonical marker image + */ + CV_WRAP void generateImageMarker(int id, int sidePixels, OutputArray _img, int borderBits = 1) const; + + + /** @brief Transform matrix of bits to list of bytes in the 4 rotations + */ + CV_WRAP static Mat getByteListFromBits(const Mat &bits); + + + /** @brief Transform list of bytes to matrix of bits + */ + CV_WRAP static Mat getBitsFromByteList(const Mat &byteList, int markerSize); +}; + + + + +/** @brief Predefined markers dictionaries/sets + * + * Each dictionary indicates the number of bits and the number of markers contained + * - DICT_ARUCO_ORIGINAL: standard ArUco Library Markers. 1024 markers, 5x5 bits, 0 minimum + distance + */ +enum PredefinedDictionaryType { + DICT_4X4_50 = 0, ///< 4x4 bits, minimum hamming distance between any two codes = 4, 50 codes + DICT_4X4_100, ///< 4x4 bits, minimum hamming distance between any two codes = 3, 100 codes + DICT_4X4_250, ///< 4x4 bits, minimum hamming distance between any two codes = 3, 250 codes + DICT_4X4_1000, ///< 4x4 bits, minimum hamming distance between any two codes = 2, 1000 codes + DICT_5X5_50, ///< 5x5 bits, minimum hamming distance between any two codes = 8, 50 codes + DICT_5X5_100, ///< 5x5 bits, minimum hamming distance between any two codes = 7, 100 codes + DICT_5X5_250, ///< 5x5 bits, minimum hamming distance between any two codes = 6, 250 codes + DICT_5X5_1000, ///< 5x5 bits, minimum hamming distance between any two codes = 5, 1000 codes + DICT_6X6_50, ///< 6x6 bits, minimum hamming distance between any two codes = 13, 50 codes + DICT_6X6_100, ///< 6x6 bits, minimum hamming distance between any two codes = 12, 100 codes + DICT_6X6_250, ///< 6x6 bits, minimum hamming distance between any two codes = 11, 250 codes + DICT_6X6_1000, ///< 6x6 bits, minimum hamming distance between any two codes = 9, 1000 codes + DICT_7X7_50, ///< 7x7 bits, minimum hamming distance between any two codes = 19, 50 codes + DICT_7X7_100, ///< 7x7 bits, minimum hamming distance between any two codes = 18, 100 codes + DICT_7X7_250, ///< 7x7 bits, minimum hamming distance between any two codes = 17, 250 codes + DICT_7X7_1000, ///< 7x7 bits, minimum hamming distance between any two codes = 14, 1000 codes + DICT_ARUCO_ORIGINAL, ///< 6x6 bits, minimum hamming distance between any two codes = 3, 1024 codes + DICT_APRILTAG_16h5, ///< 4x4 bits, minimum hamming distance between any two codes = 5, 30 codes + DICT_APRILTAG_25h9, ///< 5x5 bits, minimum hamming distance between any two codes = 9, 35 codes + DICT_APRILTAG_36h10, ///< 6x6 bits, minimum hamming distance between any two codes = 10, 2320 codes + DICT_APRILTAG_36h11 ///< 6x6 bits, minimum hamming distance between any two codes = 11, 587 codes +}; + + +/** @brief Returns one of the predefined dictionaries defined in PredefinedDictionaryType + */ +CV_EXPORTS Dictionary getPredefinedDictionary(PredefinedDictionaryType name); + + +/** @brief Returns one of the predefined dictionaries referenced by DICT_*. + */ +CV_EXPORTS_W Dictionary getPredefinedDictionary(int dict); + +/** @brief Extend base dictionary by new nMarkers + * + * @param nMarkers number of markers in the dictionary + * @param markerSize number of bits per dimension of each markers + * @param baseDictionary Include the markers in this dictionary at the beginning (optional) + * @param randomSeed a user supplied seed for theRNG() + * + * This function creates a new dictionary composed by nMarkers markers and each markers composed + * by markerSize x markerSize bits. If baseDictionary is provided, its markers are directly + * included and the rest are generated based on them. If the size of baseDictionary is higher + * than nMarkers, only the first nMarkers in baseDictionary are taken and no new marker is added. + */ +CV_EXPORTS_W Dictionary extendDictionary(int nMarkers, int markerSize, const Dictionary &baseDictionary = Dictionary(), + int randomSeed=0); + + + +//! @} +} +} + +#endif diff --git a/modules/objdetect/misc/java/test/ArucoTest.java b/modules/objdetect/misc/java/test/ArucoTest.java new file mode 100644 index 0000000000..685f78443d --- /dev/null +++ b/modules/objdetect/misc/java/test/ArucoTest.java @@ -0,0 +1,83 @@ +package org.opencv.test.aruco; + +import java.util.ArrayList; +import java.util.List; + +import org.opencv.test.OpenCVTestCase; +import org.opencv.core.Scalar; +import org.opencv.core.Mat; +import org.opencv.core.Size; +import org.opencv.core.CvType; +import org.opencv.objdetect.*; + + +public class ArucoTest extends OpenCVTestCase { + + public void testGenerateBoards() { + Dictionary dictionary = Objdetect.getPredefinedDictionary(Objdetect.DICT_4X4_50); + + Mat point1 = new Mat(4, 3, CvType.CV_32FC1); + int row = 0, col = 0; + double squareLength = 40.; + point1.put(row, col, 0, 0, 0, + 0, squareLength, 0, + squareLength, squareLength, 0, + 0, squareLength, 0); + ListobjPoints = new ArrayList(); + objPoints.add(point1); + + Mat ids = new Mat(1, 1, CvType.CV_32SC1); + ids.put(row, col, 0); + + Board board = Board.create(objPoints, dictionary, ids); + + Mat image = new Mat(); + board.generateImage(new Size(80, 80), image, 2); + + assertTrue(image.total() > 0); + } + + public void testArucoIssue3133() { + byte[][] marker = {{0,1,1},{1,1,1},{0,1,1}}; + Dictionary dictionary = Objdetect.extendDictionary(1, 3); + dictionary.set_maxCorrectionBits(0); + Mat markerBits = new Mat(3, 3, CvType.CV_8UC1); + for (int i = 0; i < 3; i++) { + for (int j = 0; j < 3; j++) { + markerBits.put(i, j, marker[i][j]); + } + } + + Mat markerCompressed = Dictionary.getByteListFromBits(markerBits); + assertMatNotEqual(markerCompressed, dictionary.get_bytesList()); + + dictionary.set_bytesList(markerCompressed); + assertMatEqual(markerCompressed, dictionary.get_bytesList()); + } + + public void testArucoDetector() { + Dictionary dictionary = Objdetect.getPredefinedDictionary(0); + DetectorParameters detectorParameters = new DetectorParameters(); + ArucoDetector detector = new ArucoDetector(dictionary, detectorParameters); + + Mat markerImage = new Mat(); + int id = 1, offset = 5, size = 40; + Objdetect.generateImageMarker(dictionary, id, size, markerImage, detectorParameters.get_markerBorderBits()); + + Mat image = new Mat(markerImage.rows() + 2*offset, markerImage.cols() + 2*offset, + CvType.CV_8UC1, new Scalar(255)); + Mat m = image.submat(offset, size+offset, offset, size+offset); + markerImage.copyTo(m); + + List corners = new ArrayList(); + Mat ids = new Mat(); + detector.detectMarkers(image, corners, ids); + + assertEquals(1, corners.size()); + Mat res = corners.get(0); + assertArrayEquals(new double[]{offset, offset}, res.get(0, 0), 0.0); + assertArrayEquals(new double[]{size + offset - 1, offset}, res.get(0, 1), 0.0); + assertArrayEquals(new double[]{size + offset - 1, size + offset - 1}, res.get(0, 2), 0.0); + assertArrayEquals(new double[]{offset, size + offset - 1}, res.get(0, 3), 0.0); + } +} diff --git a/modules/objdetect/misc/python/test/test_objdetect_aruco.py b/modules/objdetect/misc/python/test/test_objdetect_aruco.py new file mode 100644 index 0000000000..318159b5c7 --- /dev/null +++ b/modules/objdetect/misc/python/test/test_objdetect_aruco.py @@ -0,0 +1,94 @@ +#!/usr/bin/env python + +# Python 2/3 compatibility +from __future__ import print_function + +import os, numpy as np + +import cv2 as cv + +from tests_common import NewOpenCVTests + +class aruco_objdetect_test(NewOpenCVTests): + + def test_idsAccessibility(self): + + ids = np.arange(17) + rev_ids = ids[::-1] + + aruco_dict = cv.aruco.getPredefinedDictionary(cv.aruco.DICT_5X5_250) + board = cv.aruco.CharucoBoard_create(7, 5, 1, 0.5, aruco_dict) + + np.testing.assert_array_equal(board.getIds().squeeze(), ids) + + board = cv.aruco.CharucoBoard_create(7, 5, 1, 0.5, aruco_dict, rev_ids) + np.testing.assert_array_equal(board.getIds().squeeze(), rev_ids) + + board = cv.aruco.CharucoBoard_create(7, 5, 1, 0.5, aruco_dict, ids) + np.testing.assert_array_equal(board.getIds().squeeze(), ids) + + def test_identify(self): + aruco_dict = cv.aruco.getPredefinedDictionary(cv.aruco.DICT_4X4_50) + expected_idx = 9 + expected_rotation = 2 + bit_marker = np.array([[0, 1, 1, 0], [1, 0, 1, 0], [1, 1, 1, 1], [0, 0, 1, 1]], dtype=np.uint8) + + check, idx, rotation = aruco_dict.identify(bit_marker, 0) + + self.assertTrue(check, True) + self.assertEqual(idx, expected_idx) + self.assertEqual(rotation, expected_rotation) + + def test_getDistanceToId(self): + aruco_dict = cv.aruco.getPredefinedDictionary(cv.aruco.DICT_4X4_50) + idx = 7 + rotation = 3 + bit_marker = np.array([[0, 1, 0, 1], [0, 1, 1, 1], [1, 1, 0, 0], [0, 1, 0, 0]], dtype=np.uint8) + dist = aruco_dict.getDistanceToId(bit_marker, idx) + + self.assertEqual(dist, 0) + + def test_aruco_detector(self): + aruco_params = cv.aruco.DetectorParameters() + aruco_dict = cv.aruco.getPredefinedDictionary(cv.aruco.DICT_4X4_250) + aruco_detector = cv.aruco.ArucoDetector(aruco_dict, aruco_params) + id = 2 + marker_size = 100 + offset = 10 + img_marker = cv.aruco.generateImageMarker(aruco_dict, id, marker_size, aruco_params.markerBorderBits) + img_marker = np.pad(img_marker, pad_width=offset, mode='constant', constant_values=255) + gold_corners = np.array([[offset, offset],[marker_size+offset-1.0,offset], + [marker_size+offset-1.0,marker_size+offset-1.0], + [offset, marker_size+offset-1.0]], dtype=np.float32) + corners, ids, rejected = aruco_detector.detectMarkers(img_marker) + + self.assertEqual(1, len(ids)) + self.assertEqual(id, ids[0]) + for i in range(0, len(corners)): + np.testing.assert_array_equal(gold_corners, corners[i].reshape(4, 2)) + + def test_aruco_detector_refine(self): + aruco_params = cv.aruco.DetectorParameters() + aruco_dict = cv.aruco.getPredefinedDictionary(cv.aruco.DICT_4X4_250) + aruco_detector = cv.aruco.ArucoDetector(aruco_dict, aruco_params) + board_size = (3, 4) + board = cv.aruco.GridBoard_create(board_size[0], board_size[1], 5.0, 1.0, aruco_dict) + board_image = board.generateImage((board_size[0]*50, board_size[1]*50), marginSize=10) + + corners, ids, rejected = aruco_detector.detectMarkers(board_image) + self.assertEqual(board_size[0]*board_size[1], len(ids)) + + part_corners, part_ids, part_rejected = corners[:-1], ids[:-1], list(rejected) + part_rejected.append(corners[-1]) + + refine_corners, refine_ids, refine_rejected, recovered_ids = aruco_detector.refineDetectedMarkers(board_image, board, part_corners, part_ids, part_rejected) + + self.assertEqual(board_size[0] * board_size[1], len(refine_ids)) + self.assertEqual(1, len(recovered_ids)) + + self.assertEqual(ids[-1], refine_ids[-1]) + self.assertEqual((1, 4, 2), refine_corners[0].shape) + np.testing.assert_array_equal(corners, refine_corners) + +if __name__ == '__main__': + NewOpenCVTests.bootstrap() diff --git a/modules/objdetect/src/aruco/apriltag/apriltag_quad_thresh.cpp b/modules/objdetect/src/aruco/apriltag/apriltag_quad_thresh.cpp new file mode 100644 index 0000000000..38d1b2ffb8 --- /dev/null +++ b/modules/objdetect/src/aruco/apriltag/apriltag_quad_thresh.cpp @@ -0,0 +1,1666 @@ +// This file is part of OpenCV project. +// It is subject to the license terms in the LICENSE file found in the top-level directory +// of this distribution and at http://opencv.org/license.html. +// +// Copyright (C) 2013-2016, The Regents of The University of Michigan. +// +// This software was developed in the APRIL Robotics Lab under the +// direction of Edwin Olson, ebolson@umich.edu. This software may be +// available under alternative licensing terms; contact the address above. +// +// The views and conclusions contained in the software and documentation are those +// of the authors and should not be interpreted as representing official policies, +// either expressed or implied, of the Regents of The University of Michigan. + +// limitation: image size must be <32768 in width and height. This is +// because we use a fixed-point 16 bit integer representation with one +// fractional bit. + +#include "../../precomp.hpp" +#include "apriltag_quad_thresh.hpp" + +//#define APRIL_DEBUG +#ifdef APRIL_DEBUG + #include "opencv2/imgcodecs.hpp" + #include +#endif + +namespace cv { +namespace aruco { + +static void ptsort_(struct pt *pts, int sz); // forward delaration + +static inline +void ptsort(struct pt *pts, int sz) +{ +#define MAYBE_SWAP(arr,apos,bpos) \ + if (arr[apos].theta > arr[bpos].theta) { \ + tmp = arr[apos]; arr[apos] = arr[bpos]; arr[bpos] = tmp; \ + }; + + if (sz <= 1) + return; + + if (sz == 2) { + struct pt tmp; + MAYBE_SWAP(pts, 0, 1); + return; + } + + // NB: Using less-branch-intensive sorting networks here on the + // hunch that it's better for performance. + if (sz == 3) { // 3 element bubble sort is optimal + struct pt tmp; + MAYBE_SWAP(pts, 0, 1); + MAYBE_SWAP(pts, 1, 2); + MAYBE_SWAP(pts, 0, 1); + return; + } + + if (sz == 4) { // 4 element optimal sorting network. + struct pt tmp; + MAYBE_SWAP(pts, 0, 1); // sort each half, like a merge sort + MAYBE_SWAP(pts, 2, 3); + MAYBE_SWAP(pts, 0, 2); // minimum value is now at 0. + MAYBE_SWAP(pts, 1, 3); // maximum value is now at end. + MAYBE_SWAP(pts, 1, 2); // that only leaves the middle two. + return; + } + + if (sz == 5) { + // this 9-step swap is optimal for a sorting network, but two + // steps slower than a generic sort. + struct pt tmp; + MAYBE_SWAP(pts, 0, 1); // sort each half (3+2), like a merge sort + MAYBE_SWAP(pts, 3, 4); + MAYBE_SWAP(pts, 1, 2); + MAYBE_SWAP(pts, 0, 1); + MAYBE_SWAP(pts, 0, 3); // minimum element now at 0 + MAYBE_SWAP(pts, 2, 4); // maximum element now at end + MAYBE_SWAP(pts, 1, 2); // now resort the three elements 1-3. + MAYBE_SWAP(pts, 2, 3); + MAYBE_SWAP(pts, 1, 2); + return; + } + +#undef MAYBE_SWAP + + ptsort_(pts, sz); +} + +void ptsort_(struct pt *pts, int sz) +{ + // a merge sort with temp storage. + + // Use stack storage if it's not too big. + cv::AutoBuffer _tmp_stack(sz); + memcpy(_tmp_stack.data(), pts, sizeof(struct pt) * sz); + + int asz = sz/2; + int bsz = sz - asz; + + struct pt *as = &_tmp_stack[0]; + struct pt *bs = &_tmp_stack[asz]; + + ptsort(as, asz); + ptsort(bs, bsz); + +#define MERGE(apos,bpos) \ + if (as[apos].theta < bs[bpos].theta) \ + pts[outpos++] = as[apos++]; \ + else \ + pts[outpos++] = bs[bpos++]; + + int apos = 0, bpos = 0, outpos = 0; + while (apos + 8 < asz && bpos + 8 < bsz) { + MERGE(apos,bpos); MERGE(apos,bpos); MERGE(apos,bpos); MERGE(apos,bpos); + MERGE(apos,bpos); MERGE(apos,bpos); MERGE(apos,bpos); MERGE(apos,bpos); + } + + while (apos < asz && bpos < bsz) { + MERGE(apos,bpos); + } + + if (apos < asz) + memcpy(&pts[outpos], &as[apos], (asz-apos)*sizeof(struct pt)); + if (bpos < bsz) + memcpy(&pts[outpos], &bs[bpos], (bsz-bpos)*sizeof(struct pt)); + +#undef MERGE +} + +/** + * lfps contains *cumulative* moments for N points, with + * index j reflecting points [0,j] (inclusive). + * fit a line to the points [i0, i1] (inclusive). i0, i1 are both (0, sz) + * if i1 < i0, we treat this as a wrap around. + */ +void fit_line(struct line_fit_pt *lfps, int sz, int i0, int i1, double *lineparm, double *err, double *mse){ + CV_Assert(i0 != i1); + CV_Assert(i0 >= 0 && i1 >= 0 && i0 < sz && i1 < sz); + + double Mx, My, Mxx, Myy, Mxy, W; + int N; // how many points are included in the set? + + if (i0 < i1) { + N = i1 - i0 + 1; + + Mx = lfps[i1].Mx; + My = lfps[i1].My; + Mxx = lfps[i1].Mxx; + Mxy = lfps[i1].Mxy; + Myy = lfps[i1].Myy; + W = lfps[i1].W; + + if (i0 > 0) { + Mx -= lfps[i0-1].Mx; + My -= lfps[i0-1].My; + Mxx -= lfps[i0-1].Mxx; + Mxy -= lfps[i0-1].Mxy; + Myy -= lfps[i0-1].Myy; + W -= lfps[i0-1].W; + } + + } else { + // i0 > i1, e.g. [15, 2]. Wrap around. + CV_Assert(i0 > 0); + + Mx = lfps[sz-1].Mx - lfps[i0-1].Mx; + My = lfps[sz-1].My - lfps[i0-1].My; + Mxx = lfps[sz-1].Mxx - lfps[i0-1].Mxx; + Mxy = lfps[sz-1].Mxy - lfps[i0-1].Mxy; + Myy = lfps[sz-1].Myy - lfps[i0-1].Myy; + W = lfps[sz-1].W - lfps[i0-1].W; + + Mx += lfps[i1].Mx; + My += lfps[i1].My; + Mxx += lfps[i1].Mxx; + Mxy += lfps[i1].Mxy; + Myy += lfps[i1].Myy; + W += lfps[i1].W; + + N = sz - i0 + i1 + 1; + } + + CV_Assert(N >= 2); + + double Ex = Mx / W; + double Ey = My / W; + double Cxx = Mxx / W - Ex*Ex; + double Cxy = Mxy / W - Ex*Ey; + double Cyy = Myy / W - Ey*Ey; + + double nx, ny; + + if (1) { + // on iOS about 5% of total CPU spent in these trig functions. + // 85 ms per frame on 5S, example.pnm + // + // XXX this was using the double-precision atan2. Was there a case where + // we needed that precision? Seems doubtful. + float normal_theta = float(.5f * (CV_PI / 180)) * cv::fastAtan2((float)(-2*Cxy), (float)(Cyy - Cxx)); + nx = cosf(normal_theta); + ny = sinf(normal_theta); + } else { + // 73.5 ms per frame on 5S, example.pnm + double ty = -2*Cxy; + double tx = (Cyy - Cxx); + double mag = ty*ty + tx*tx; + + if (mag == 0) { + nx = 1; + ny = 0; + } else { + float norm = sqrtf((float)(ty*ty + tx*tx)); + tx /= norm; + + // ty is now sin(2theta) + // tx is now cos(2theta). We want sin(theta) and cos(theta) + + // due to precision err, tx could still have slightly too large magnitude. + if (tx > 1) { + ny = 0; + nx = 1; + } else if (tx < -1) { + ny = 1; + nx = 0; + } else { + // half angle formula + ny = sqrtf((1.0f - (float)tx)*0.5f); + nx = sqrtf((1.0f + (float)tx)*0.5f); + + // pick a consistent branch cut + if (ty < 0) + ny = - ny; + } + } + } + + if (lineparm) { + lineparm[0] = Ex; + lineparm[1] = Ey; + lineparm[2] = nx; + lineparm[3] = ny; + } + + // sum of squared errors = + // + // SUM_i ((p_x - ux)*nx + (p_y - uy)*ny)^2 + // SUM_i nx*nx*(p_x - ux)^2 + 2nx*ny(p_x -ux)(p_y-uy) + ny*ny*(p_y-uy)*(p_y-uy) + // nx*nx*SUM_i((p_x -ux)^2) + 2nx*ny*SUM_i((p_x-ux)(p_y-uy)) + ny*ny*SUM_i((p_y-uy)^2) + // + // nx*nx*N*Cxx + 2nx*ny*N*Cxy + ny*ny*N*Cyy + + // sum of squared errors + if (err) + *err = nx*nx*N*Cxx + 2*nx*ny*N*Cxy + ny*ny*N*Cyy; + + // mean squared error + if (mse) + *mse = nx*nx*Cxx + 2*nx*ny*Cxy + ny*ny*Cyy; +} + +int err_compare_descending(const void *_a, const void *_b){ + const double *a = (const double*)_a; + const double *b = (const double*)_b; + + return ((*a) < (*b)) ? 1 : -1; +} + +/** + 1. Identify A) white points near a black point and B) black points near a white point. + + 2. Find the connected components within each of the classes above, + yielding clusters of "white-near-black" and + "black-near-white". (These two classes are kept separate). Each + segment has a unique id. + + 3. For every pair of "white-near-black" and "black-near-white" + clusters, find the set of points that are in one and adjacent to the + other. In other words, a "boundary" layer between the two + clusters. (This is actually performed by iterating over the pixels, + rather than pairs of clusters.) Critically, this helps keep nearby + edges from becoming connected. + **/ +int quad_segment_maxima(const DetectorParameters &td, int sz, struct line_fit_pt *lfps, int indices[4]){ + + // ksz: when fitting points, how many points on either side do we consider? + // (actual "kernel" width is 2ksz). + // + // This value should be about: 0.5 * (points along shortest edge). + // + // If all edges were equally-sized, that would give a value of + // sz/8. We make it somewhat smaller to account for tags at high + // aspects. + + // XXX Tunable. Maybe make a multiple of JPEG block size to increase robustness + // to JPEG compression artifacts? + //int ksz = imin(20, sz / 12); + int ksz = 20 < (sz/12)? 20: (sz/12); + + // can't fit a quad if there are too few points. + if (ksz < 2) + return 0; + + // printf("sz %5d, ksz %3d\n", sz, ksz); + + std::vector errs(sz); + + for (int i = 0; i < sz; i++) { + fit_line(lfps, sz, (i + sz - ksz) % sz, (i + ksz) % sz, NULL, &errs[i], NULL); + } + + // apply a low-pass filter to errs + if (1) { + std::vector y(sz); + + // how much filter to apply? + + // XXX Tunable + double sigma = 1; // was 3 + + // cutoff = exp(-j*j/(2*sigma*sigma)); + // log(cutoff) = -j*j / (2*sigma*sigma) + // log(cutoff)*2*sigma*sigma = -j*j; + + // how big a filter should we use? We make our kernel big + // enough such that we represent any values larger than + // 'cutoff'. + + // XXX Tunable (though not super useful to change) + double cutoff = 0.05; + int fsz = cvFloor(sqrt(-log(cutoff)*2*sigma*sigma)) + 1; + fsz = 2*fsz + 1; + + // For default values of cutoff = 0.05, sigma = 3, + // we have fsz = 17. + std::vector f(fsz); + + for (int i = 0; i < fsz; i++) { + int j = i - fsz / 2; + f[i] = (float)exp(-j*j/(2*sigma*sigma)); + } + + for (int iy = 0; iy < sz; iy++) { + double acc = 0; + + for (int i = 0; i < fsz; i++) { + acc += errs[(iy + i - fsz / 2 + sz) % sz] * f[i]; + } + y[iy] = acc; + } + copy(y.begin(), y.end(), errs.begin()); + } + + std::vector maxima(sz); + std::vector maxima_errs(sz); + int nmaxima = 0; + + for (int i = 0; i < sz; i++) { + if (errs[i] > errs[(i+1)%sz] && errs[i] > errs[(i+sz-1)%sz]) { + maxima[nmaxima] = i; + maxima_errs[nmaxima] = errs[i]; + nmaxima++; + } + } + // if we didn't get at least 4 maxima, we can't fit a quad. + if (nmaxima < 4) + return 0; + + // select only the best maxima if we have too many + int max_nmaxima = td.aprilTagMaxNmaxima; + + if (nmaxima > max_nmaxima) { + std::vector maxima_errs_copy(maxima_errs.begin(), maxima_errs.begin()+nmaxima); + + // throw out all but the best handful of maxima. Sorts descending. + qsort(maxima_errs_copy.data(), nmaxima, sizeof(double), err_compare_descending); + + double maxima_thresh = maxima_errs_copy[max_nmaxima]; + int out = 0; + for (int in = 0; in < nmaxima; in++) { + if (maxima_errs[in] <= maxima_thresh) + continue; + maxima[out++] = maxima[in]; + } + nmaxima = out; + } + + int best_indices[4]; + double best_error = HUGE_VALF; + + double err01, err12, err23, err30; + double mse01, mse12, mse23, mse30; + double params01[4], params12[4], params23[4], params30[4]; + + // disallow quads where the angle is less than a critical value. + double max_dot = cos(td.aprilTagCriticalRad); //25*M_PI/180); + + for (int m0 = 0; m0 < nmaxima - 3; m0++) { + int i0 = maxima[m0]; + + for (int m1 = m0+1; m1 < nmaxima - 2; m1++) { + int i1 = maxima[m1]; + + fit_line(lfps, sz, i0, i1, params01, &err01, &mse01); + + if (mse01 > td.aprilTagMaxLineFitMse) + continue; + + for (int m2 = m1+1; m2 < nmaxima - 1; m2++) { + int i2 = maxima[m2]; + + fit_line(lfps, sz, i1, i2, params12, &err12, &mse12); + if (mse12 > td.aprilTagMaxLineFitMse) + continue; + + double dot = params01[2]*params12[2] + params01[3]*params12[3]; + if (fabs(dot) > max_dot) + continue; + + for (int m3 = m2+1; m3 < nmaxima; m3++) { + int i3 = maxima[m3]; + + fit_line(lfps, sz, i2, i3, params23, &err23, &mse23); + if (mse23 > td.aprilTagMaxLineFitMse) + continue; + + fit_line(lfps, sz, i3, i0, params30, &err30, &mse30); + if (mse30 > td.aprilTagMaxLineFitMse) + continue; + + double err = err01 + err12 + err23 + err30; + if (err < best_error) { + best_error = err; + best_indices[0] = i0; + best_indices[1] = i1; + best_indices[2] = i2; + best_indices[3] = i3; + } + } + } + } + } + + if (best_error == HUGE_VALF) + return 0; + + for (int i = 0; i < 4; i++) + indices[i] = best_indices[i]; + + if (best_error / sz < td.aprilTagMaxLineFitMse) + return 1; + return 0; +} + +/** + * returns 0 if the cluster looks bad. + */ +int quad_segment_agg(int sz, struct line_fit_pt *lfps, int indices[4]){ + //int sz = zarray_size(cluster); + + zmaxheap_t *heap = zmaxheap_create(sizeof(struct remove_vertex*)); + + // We will initially allocate sz rvs. We then have two types of + // iterations: some iterations that are no-ops in terms of + // allocations, and those that remove a vertex and allocate two + // more children. This will happen at most (sz-4) times. Thus we + // need: sz + 2*(sz-4) entries. + + int rvalloc_pos = 0; + int rvalloc_size = 3*sz; + cv::AutoBuffer rvalloc_(std::max(1, rvalloc_size)); + memset(rvalloc_.data(), 0, sizeof(rvalloc_[0]) * rvalloc_.size()); // TODO Add AutoBuffer zero fill + struct remove_vertex *rvalloc = rvalloc_.data(); + cv::AutoBuffer segs_(std::max(1, sz)); // TODO Add AutoBuffer zero fill + memset(segs_.data(), 0, sizeof(segs_[0]) * segs_.size()); + struct segment *segs = segs_.data(); + + // populate with initial entries + for (int i = 0; i < sz; i++) { + struct remove_vertex *rv = &rvalloc[rvalloc_pos++]; + rv->i = i; + if (i == 0) { + rv->left = sz-1; + rv->right = 1; + } else { + rv->left = i-1; + rv->right = (i+1) % sz; + } + + fit_line(lfps, sz, rv->left, rv->right, NULL, NULL, &rv->err); + + //TODO is finite CV_Assert(): + CV_DbgAssert (!cvIsNaN(-rv->err) && "zmaxheap_add: Trying to add non-finite number to heap. NaN's prohibited, could allow INF with testing"); + zmaxheap_add(heap, &rv, (float)-rv->err); + + segs[i].left = rv->left; + segs[i].right = rv->right; + segs[i].is_vertex = 1; + } + + int nvertices = sz; + + while (nvertices > 4) { + CV_Assert(rvalloc_pos < rvalloc_size); + + struct remove_vertex *rv; + float err; + + int res = zmaxheap_remove_max(heap, &rv, &err); + if (!res) + return 0; + CV_Assert(res); + + // is this remove_vertex valid? (Or has one of the left/right + // vertices changes since we last looked?) + if (!segs[rv->i].is_vertex || + !segs[rv->left].is_vertex || + !segs[rv->right].is_vertex) { + continue; + } + + // we now merge. + CV_Assert(segs[rv->i].is_vertex); + + segs[rv->i].is_vertex = 0; + segs[rv->left].right = rv->right; + segs[rv->right].left = rv->left; + + // create the join to the left + if (1) { + struct remove_vertex *child = &rvalloc[rvalloc_pos++]; + child->i = rv->left; + child->left = segs[rv->left].left; + child->right = rv->right; + + fit_line(lfps, sz, child->left, child->right, NULL, NULL, &child->err); + + //TODO is finite CV_Assert(): + CV_DbgAssert (!cvIsNaN(-child->err) && "zmaxheap_add: Trying to add non-finite number to heap. NaN's prohibited, could allow INF with testing"); + zmaxheap_add(heap, &child, (float)-child->err); + } + + // create the join to the right + if (1) { + struct remove_vertex *child = &rvalloc[rvalloc_pos++]; + child->i = rv->right; + child->left = rv->left; + child->right = segs[rv->right].right; + + fit_line(lfps, sz, child->left, child->right, NULL, NULL, &child->err); + + //TODO is finite CV_Assert(): + CV_DbgAssert (!cvIsNaN(-child->err) && "zmaxheap_add: Trying to add non-finite number to heap. NaN's prohibited, could allow INF with testing"); + zmaxheap_add(heap, &child, (float)-child->err); + } + + // we now have one less vertex + nvertices--; + } + + zmaxheap_destroy(heap); + + int idx = 0; + for (int i = 0; i < sz; i++) { + if (segs[i].is_vertex) { + indices[idx++] = i; + } + } + + return 1; +} + +#define DO_UNIONFIND(dx, dy) if (im.data[y*s + dy*s + x + dx] == v) unionfind_connect(uf, y*w + x, y*w + dy*w + x + dx); +static void do_unionfind_line(unionfind_t *uf, Mat &im, int w, int s, int y){ + CV_Assert(y+1 < im.rows); + CV_Assert(!im.empty()); + + for (int x = 1; x < w - 1; x++) { + uint8_t v = im.data[y*s + x]; + + if (v == 127) + continue; + + // (dx,dy) pairs for 8 connectivity: + // (REFERENCE) (1, 0) + // (-1, 1) (0, 1) (1, 1) + // + DO_UNIONFIND(1, 0); + DO_UNIONFIND(0, 1); + if (v == 255) { + DO_UNIONFIND(-1, 1); + DO_UNIONFIND(1, 1); + } + } +} +#undef DO_UNIONFIND + +/** + * return 1 if the quad looks okay, 0 if it should be discarded + * quad + **/ +int fit_quad(const DetectorParameters &_params, const Mat im, zarray_t *cluster, struct sQuad *quad){ + CV_Assert(cluster != NULL); + + int res = 0; + + int sz = _zarray_size(cluster); + if (sz < 4) // can't fit a quad to less than 4 points + return 0; + + ///////////////////////////////////////////////////////////// + // Step 1. Sort points so they wrap around the center of the + // quad. We will constrain our quad fit to simply partition this + // ordered set into 4 groups. + + // compute a bounding box so that we can order the points + // according to their angle WRT the center. + int32_t xmax = 0, xmin = INT32_MAX, ymax = 0, ymin = INT32_MAX; + + for (int pidx = 0; pidx < sz; pidx++) { + struct pt *p; + _zarray_get_volatile(cluster, pidx, &p); + + //(a > b) ? a : b; + //xmax = imax(xmax, p->x); + //xmin = imin(xmin, p->x); + //ymax = imax(ymax, p->y); + //ymin = imin(ymin, p->y); + + xmax = xmax > p->x? xmax : p->x; + xmin = xmin < p->x? xmin : p->x; + + ymax = ymax > p->y? ymax : p->y; + ymin = ymin < p->y? ymin : p->y; + } + + // add some noise to (cx,cy) so that pixels get a more diverse set + // of theta estimates. This will help us remove more points. + // (Only helps a small amount. The actual noise values here don't + // matter much at all, but we want them [-1, 1]. (XXX with + // fixed-point, should range be bigger?) + double cx = (xmin + xmax) * 0.5 + 0.05118; + double cy = (ymin + ymax) * 0.5 + -0.028581; + + double dot = 0; + + for (int pidx = 0; pidx < sz; pidx++) { + struct pt *p; + _zarray_get_volatile(cluster, pidx, &p); + + double dx = p->x - cx; + double dy = p->y - cy; + + p->theta = cv::fastAtan2((float)dy, (float)dx) * (float)(CV_PI/180); + + dot += dx*p->gx + dy*p->gy; + } + + // Ensure that the black border is inside the white border. + if (dot < 0) + return 0; + + // we now sort the points according to theta. This is a preparatory + // step for segmenting them into four lines. + if (1) { + // zarray_sort(cluster, pt_compare_theta); + ptsort((struct pt*) cluster->data, sz); + + // remove duplicate points. (A byproduct of our segmentation system.) + if (1) { + int outpos = 1; + + struct pt *last; + _zarray_get_volatile(cluster, 0, &last); + + for (int i = 1; i < sz; i++) { + + struct pt *p; + _zarray_get_volatile(cluster, i, &p); + + if (p->x != last->x || p->y != last->y) { + + if (i != outpos) { + struct pt *out; + _zarray_get_volatile(cluster, outpos, &out); + memcpy(out, p, sizeof(struct pt)); + } + + outpos++; + } + + last = p; + } + + cluster->size = outpos; + sz = outpos; + } + + } else { + // This is a counting sort in which we retain at most one + // point for every bucket; the bucket index is computed from + // theta. Since a good quad completes a complete revolution, + // there's reason to think that we should get a good + // distribution of thetas. We might "lose" a few points due + // to collisions, but this shouldn't affect quality very much. + + // XXX tunable. Increase to reduce the likelihood of "losing" + // points due to collisions. + int nbuckets = 4*sz; + +#define ASSOC 2 + std::vector > v(nbuckets, std::vector(ASSOC)); + + // put each point into a bucket. + for (int i = 0; i < sz; i++) { + struct pt *p; + _zarray_get_volatile(cluster, i, &p); + + CV_Assert(p->theta >= -CV_PI && p->theta <= CV_PI); + + int bucket = cvFloor((nbuckets - 1) * (p->theta + CV_PI) / (2*CV_PI)); + CV_Assert(bucket >= 0 && bucket < nbuckets); + + for (int j = 0; j < ASSOC; j++) { + if (v[bucket][j].theta == 0) { + v[bucket][j] = *p; + break; + } + } + } + + // collect the points from the buckets and put them back into the array. + int outsz = 0; + for (int i = 0; i < nbuckets; i++) { + for (int j = 0; j < ASSOC; j++) { + if (v[i][j].theta != 0) { + _zarray_set(cluster, outsz, &v[i][j], NULL); + outsz++; + } + } + } + + _zarray_truncate(cluster, outsz); + sz = outsz; + } + + if (sz < 4) + return 0; + + ///////////////////////////////////////////////////////////// + // Step 2. Precompute statistics that allow line fit queries to be + // efficiently computed for any contiguous range of indices. + + cv::AutoBuffer lfps_(sz); + memset(lfps_.data(), 0, sizeof(lfps_[0]) * lfps_.size()); // TODO Add AutoBuffer zero fill + struct line_fit_pt *lfps = lfps_.data(); + + for (int i = 0; i < sz; i++) { + struct pt *p; + _zarray_get_volatile(cluster, i, &p); + + if (i > 0) { + memcpy(&lfps[i], &lfps[i-1], sizeof(struct line_fit_pt)); + } + + if (0) { + // we now undo our fixed-point arithmetic. + double delta = 0.5; + double x = p->x * .5 + delta; + double y = p->y * .5 + delta; + double W; + + for (int dy = -1; dy <= 1; dy++) { + int iy = cvFloor(y + dy); + + if (iy < 0 || iy + 1 >= im.rows) + continue; + + for (int dx = -1; dx <= 1; dx++) { + int ix = cvFloor(x + dx); + + if (ix < 0 || ix + 1 >= im.cols) + continue; + + int grad_x = im.data[iy * im.cols + ix + 1] - + im.data[iy * im.cols + ix - 1]; + + int grad_y = im.data[(iy+1) * im.cols + ix] - + im.data[(iy-1) * im.cols + ix]; + + W = sqrtf(float(grad_x*grad_x + grad_y*grad_y)) + 1; + + // double fx = x + dx, fy = y + dy; + double fx = ix + .5, fy = iy + .5; + lfps[i].Mx += W * fx; + lfps[i].My += W * fy; + lfps[i].Mxx += W * fx * fx; + lfps[i].Mxy += W * fx * fy; + lfps[i].Myy += W * fy * fy; + lfps[i].W += W; + } + } + } else { + // we now undo our fixed-point arithmetic. + double delta = 0.5; // adjust for pixel center bias + double x = p->x * .5 + delta; + double y = p->y * .5 + delta; + int ix = cvFloor(x), iy = cvFloor(y); + double W = 1; + + if (ix > 0 && ix+1 < im.cols && iy > 0 && iy+1 < im.rows) { + int grad_x = im.data[iy * im.cols + ix + 1] - + im.data[iy * im.cols + ix - 1]; + + int grad_y = im.data[(iy+1) * im.cols + ix] - + im.data[(iy-1) * im.cols + ix]; + + // XXX Tunable. How to shape the gradient magnitude? + W = sqrt(grad_x*grad_x + grad_y*grad_y) + 1; + } + + double fx = x, fy = y; + lfps[i].Mx += W * fx; + lfps[i].My += W * fy; + lfps[i].Mxx += W * fx * fx; + lfps[i].Mxy += W * fx * fy; + lfps[i].Myy += W * fy * fy; + lfps[i].W += W; + } + } + + int indices[4]; + if (1) { + if (!quad_segment_maxima(_params, _zarray_size(cluster), lfps, indices)) + goto finish; + } else { + if (!quad_segment_agg(sz, lfps, indices)) + goto finish; + } + + // printf("%d %d %d %d\n", indices[0], indices[1], indices[2], indices[3]); + + if (0) { + // no refitting here; just use those points as the vertices. + // Note, this is useful for debugging, but pretty bad in + // practice since this code path also omits several + // plausibility checks that save us tons of time in quad + // decoding. + for (int i = 0; i < 4; i++) { + struct pt *p; + _zarray_get_volatile(cluster, indices[i], &p); + + quad->p[i][0] = (float)(.5*p->x); // undo fixed-point arith. + quad->p[i][1] = (float)(.5*p->y); + } + + res = 1; + + } else { + double lines[4][4]; + + for (int i = 0; i < 4; i++) { + int i0 = indices[i]; + int i1 = indices[(i+1)&3]; + + if (0) { + // if there are enough points, skip the points near the corners + // (because those tend not to be very good.) + if (i1-i0 > 8) { + int t = (i1-i0)/6; + if (t < 0) + t = -t; + + i0 = (i0 + t) % sz; + i1 = (i1 + sz - t) % sz; + } + } + + double err; + fit_line(lfps, sz, i0, i1, lines[i], NULL, &err); + + if (err > _params.aprilTagMaxLineFitMse) { + res = 0; + goto finish; + } + } + + for (int i = 0; i < 4; i++) { + // solve for the intersection of lines (i) and (i+1)&3. + // p0 + lambda0*u0 = p1 + lambda1*u1, where u0 and u1 + // are the line directions. + // + // lambda0*u0 - lambda1*u1 = (p1 - p0) + // + // rearrange (solve for lambdas) + // + // [u0_x -u1_x ] [lambda0] = [ p1_x - p0_x ] + // [u0_y -u1_y ] [lambda1] [ p1_y - p0_y ] + // + // remember that lines[i][0,1] = p, lines[i][2,3] = NORMAL vector. + // We want the unit vector, so we need the perpendiculars. Thus, below + // we have swapped the x and y components and flipped the y components. + + const int i1 = (i + 1) & 3; + double A00 = lines[i][3], A01 = -lines[i1][3]; + double A10 = -lines[i][2], A11 = lines[i1][2]; + double B0 = -lines[i][0] + lines[i1][0]; + double B1 = -lines[i][1] + lines[i1][1]; + + double det = A00 * A11 - A10 * A01; + if (fabs(det) < 0.001) { + res = 0; + goto finish; + } + + // inverse. + double det_inv = 1.0 / det; + double W00 = A11 * det_inv, W01 = -A01 * det_inv; + + // solve + double L0 = W00*B0 + W01*B1; + + // compute intersection + quad->p[i][0] = (float)(lines[i][0] + L0*A00); + quad->p[i][1] = (float)(lines[i][1] + L0*A10); + +#if !defined(NDEBUG) + { + // we should get the same intersection starting + // from point p1 and moving L1*u1. + double W10 = -A10 * det_inv, W11 = A00 * det_inv; + double L1 = W10*B0 + W11*B1; + + double x = lines[i1][0] - L1*A01; + double y = lines[i1][1] - L1*A11; + + CV_Assert(fabs(x - quad->p[i][0]) < 0.001); + CV_Assert(fabs(y - quad->p[i][1]) < 0.001); + } +#endif // NDEBUG + + res = 1; + } + } + + // reject quads that are too small + if (1) { + double area = 0; + + // get area of triangle formed by points 0, 1, 2, 0 + double length[3], p; + for (int i = 0; i < 3; i++) { + int idxa = i; // 0, 1, 2, + int idxb = (i+1) % 3; // 1, 2, 0 + //length[i] = sqrt( + // sq(quad->p[idxb][0] - quad->p[idxa][0]) + // + sq(quad->p[idxb][1] - quad->p[idxa][1])); + double sq1 = quad->p[idxb][0] - quad->p[idxa][0]; + sq1 = sq1 * sq1; + double sq2 = quad->p[idxb][1] - quad->p[idxa][1]; + sq2 = sq2 * sq2; + length[i] = sqrt(sq1 + sq2); + } + p = (length[0] + length[1] + length[2]) / 2; + + area += sqrt(p*(p-length[0])*(p-length[1])*(p-length[2])); + + // get area of triangle formed by points 2, 3, 0, 2 + for (int i = 0; i < 3; i++) { + int idxs[] = { 2, 3, 0, 2 }; + int idxa = idxs[i]; + int idxb = idxs[i+1]; + //length[i] = sqrt( + // sq(quad->p[idxb][0] - quad->p[idxa][0]) + // + sq(quad->p[idxb][1] - quad->p[idxa][1])); + double sq1 = quad->p[idxb][0] - quad->p[idxa][0]; + sq1 = sq1 * sq1; + double sq2 = quad->p[idxb][1] - quad->p[idxa][1]; + sq2 = sq2 * sq2; + length[i] = sqrt(sq1 + sq2); + } + p = (length[0] + length[1] + length[2]) / 2; + + area += sqrt(p*(p-length[0])*(p-length[1])*(p-length[2])); + + // we don't actually know the family yet (quad detection is generic.) + // This threshold is based on a 6x6 tag (which is actually 8x8) + // int d = fam->d + fam->black_border*2; + int d = 8; + if (area < d*d) { + res = 0; + goto finish; + } + } + + // reject quads whose cumulative angle change isn't equal to 2PI + if(1){ + double total = 0; + + for (int i = 0; i < 4; i++) { + int i0 = i, i1 = (i+1)&3, i2 = (i+2)&3; + + double theta0 = atan2f(quad->p[i0][1] - quad->p[i1][1], + quad->p[i0][0] - quad->p[i1][0]); + double theta1 = atan2f(quad->p[i2][1] - quad->p[i1][1], + quad->p[i2][0] - quad->p[i1][0]); + + double dtheta = theta0 - theta1; + if (dtheta < 0) + dtheta += 2*CV_PI; + + if (dtheta < _params.aprilTagCriticalRad || dtheta > (CV_PI - _params.aprilTagCriticalRad)) + res = 0; + + total += dtheta; + } + + // looking for 2PI + if (total < 6.2 || total > 6.4) { + res = 0; + goto finish; + } + } + + finish: + + return res; +} + + +static void do_quad(int nCidx0, int nCidx1, zarray_t &nClusters, int nW, int nH, zarray_t *nquads, const DetectorParameters &td, const Mat im){ + + CV_Assert(nquads != NULL); + + //struct quad_task *task = (struct quad_task*) p; + + //zarray_t *clusters = nClusters; + zarray_t *quads = nquads; + int w = nW, h = nH; + + for (int cidx = nCidx0; cidx < nCidx1; cidx++) { + + zarray_t *cluster; + _zarray_get(&nClusters, cidx, &cluster); + + if (_zarray_size(cluster) < td.aprilTagMinClusterPixels) + continue; + + // a cluster should contain only boundary points around the + // tag. it cannot be bigger than the whole screen. (Reject + // large connected blobs that will be prohibitively slow to + // fit quads to.) A typical point along an edge is added three + // times (because it has 3 neighbors). The maximum perimeter + // is 2w+2h. + if (_zarray_size(cluster) > 3*(2*w+2*h)) { + continue; + } + + struct sQuad quad; + memset(&quad, 0, sizeof(struct sQuad)); + + if (fit_quad(td, im, cluster, &quad)) { + //pthread_mutex_lock(&td.mutex); + _zarray_add(quads, &quad); + //pthread_mutex_unlock(&td.mutex); + } + } +} + +void threshold(const Mat mIm, const DetectorParameters ¶meters, Mat& mThresh){ + int w = mIm.cols, h = mIm.rows; + int s = (unsigned) mIm.step; + CV_Assert(w < 32768); + CV_Assert(h < 32768); + + CV_Assert(mThresh.step == (unsigned)s); + + // The idea is to find the maximum and minimum values in a + // window around each pixel. If it's a contrast-free region + // (max-min is small), don't try to binarize. Otherwise, + // threshold according to (max+min)/2. + // + // Mark low-contrast regions with value 127 so that we can skip + // future work on these areas too. + + // however, computing max/min around every pixel is needlessly + // expensive. We compute max/min for tiles. To avoid artifacts + // that arise when high-contrast features appear near a tile + // edge (and thus moving from one tile to another results in a + // large change in max/min value), the max/min values used for + // any pixel are computed from all 3x3 surrounding tiles. Thus, + // the max/min sampling area for nearby pixels overlap by at least + // one tile. + // + // The important thing is that the windows be large enough to + // capture edge transitions; the tag does not need to fit into + // a tile. + + // XXX Tunable. Generally, small tile sizes--- so long as they're + // large enough to span a single tag edge--- seem to be a winner. + const int tilesz = 4; + + // the last (possibly partial) tiles along each row and column will + // just use the min/max value from the last full tile. + int tw = w / tilesz; + int th = h / tilesz; + + uint8_t *im_max = (uint8_t*)calloc(tw*th, sizeof(uint8_t)); + uint8_t *im_min = (uint8_t*)calloc(tw*th, sizeof(uint8_t)); + + + // first, collect min/max statistics for each tile + for (int ty = 0; ty < th; ty++) { + for (int tx = 0; tx < tw; tx++) { + uint8_t max = 0, min = 255; + + for (int dy = 0; dy < tilesz; dy++) { + + for (int dx = 0; dx < tilesz; dx++) { + + uint8_t v = mIm.data[(ty*tilesz+dy)*s + tx*tilesz + dx]; + if (v < min) + min = v; + if (v > max) + max = v; + } + } + im_max[ty*tw+tx] = max; + im_min[ty*tw+tx] = min; + } + } + + // second, apply 3x3 max/min convolution to "blur" these values + // over larger areas. This reduces artifacts due to abrupt changes + // in the threshold value. + uint8_t *im_max_tmp = (uint8_t*)calloc(tw*th, sizeof(uint8_t)); + uint8_t *im_min_tmp = (uint8_t*)calloc(tw*th, sizeof(uint8_t)); + + for (int ty = 0; ty < th; ty++) { + for (int tx = 0; tx < tw; tx++) { + uint8_t max = 0, min = 255; + + for (int dy = -1; dy <= 1; dy++) { + if (ty+dy < 0 || ty+dy >= th) + continue; + for (int dx = -1; dx <= 1; dx++) { + if (tx+dx < 0 || tx+dx >= tw) + continue; + + uint8_t m = im_max[(ty+dy)*tw+tx+dx]; + if (m > max) + max = m; + m = im_min[(ty+dy)*tw+tx+dx]; + if (m < min) + min = m; + } + } + + im_max_tmp[ty*tw + tx] = max; + im_min_tmp[ty*tw + tx] = min; + } + } + free(im_max); + free(im_min); + im_max = im_max_tmp; + im_min = im_min_tmp; + + for (int ty = 0; ty < th; ty++) { + for (int tx = 0; tx < tw; tx++) { + + int min_ = im_min[ty*tw + tx]; + int max_ = im_max[ty*tw + tx]; + + // low contrast region? (no edges) + if (max_ - min_ < parameters.aprilTagMinWhiteBlackDiff) { + for (int dy = 0; dy < tilesz; dy++) { + int y = ty*tilesz + dy; + + for (int dx = 0; dx < tilesz; dx++) { + int x = tx*tilesz + dx; + + //threshim->buf[y*s+x] = 127; + mThresh.data[y*s+x] = 127; + } + } + continue; + } + + // otherwise, actually threshold this tile. + + // argument for biasing towards dark; specular highlights + // can be substantially brighter than white tag parts + uint8_t thresh = saturate_cast((max_ + min_) / 2); + + for (int dy = 0; dy < tilesz; dy++) { + int y = ty*tilesz + dy; + + for (int dx = 0; dx < tilesz; dx++) { + int x = tx*tilesz + dx; + + uint8_t v = mIm.data[y*s+x]; + mThresh.data[y*s+x] = (v > thresh) ? 255 : 0; + } + } + } + } + + // we skipped over the non-full-sized tiles above. Fix those now. + for (int y = 0; y < h; y++) { + + // what is the first x coordinate we need to process in this row? + + int x0; + + if (y >= th*tilesz) { + x0 = 0; // we're at the bottom; do the whole row. + } else { + x0 = tw*tilesz; // we only need to do the right most part. + } + + // compute tile coordinates and clamp. + int ty = y / tilesz; + if (ty >= th) + ty = th - 1; + + for (int x = x0; x < w; x++) { + int tx = x / tilesz; + if (tx >= tw) + tx = tw - 1; + + int max = im_max[ty*tw + tx]; + int min = im_min[ty*tw + tx]; + int thresh = min + (max - min) / 2; + + uint8_t v = mIm.data[y*s+x]; + if (v > thresh){ + mThresh.data[y*s+x] = 255; + } + else{ + mThresh.data[y*s+x] = 0; + } + } + } + free(im_min); + free(im_max); + + // this is a dilate/erode deglitching scheme that does not improve + // anything as far as I can tell. + if (parameters.aprilTagDeglitch) { + Mat tmp(h,w, mIm.type()); + for (int y = 1; y + 1 < h; y++) { + for (int x = 1; x + 1 < w; x++) { + uint8_t max = 0; + for (int dy = -1; dy <= 1; dy++) { + for (int dx = -1; dx <= 1; dx++) { + uint8_t v = mThresh.data[(y+dy)*s + x + dx]; + if (v > max) + max = v; + } + } + tmp.data[y*s+x] = max; + } + } + + for (int y = 1; y + 1 < h; y++) { + for (int x = 1; x + 1 < w; x++) { + uint8_t min = 255; + for (int dy = -1; dy <= 1; dy++) { + for (int dx = -1; dx <= 1; dx++) { + uint8_t v = tmp.data[(y+dy)*s + x + dx]; + if (v < min) + min = v; + } + } + mThresh.data[y*s+x] = min; + } + } + } + +} + +#ifdef APRIL_DEBUG +static void _darken(const Mat &im){ + for (int y = 0; y < im.rows; y++) { + for (int x = 0; x < im.cols; x++) { + im.data[im.cols*y+x] /= 2; + } + } +} +#endif + +zarray_t *apriltag_quad_thresh(const DetectorParameters ¶meters, const Mat & mImg, std::vector > &contours){ + + //////////////////////////////////////////////////////// + // step 1. threshold the image, creating the edge image. + + int w = mImg.cols, h = mImg.rows; + + Mat thold(h, w, mImg.type()); + threshold(mImg, parameters, thold); + + int ts = thold.cols; + +#ifdef APRIL_DEBUG + imwrite("2.2 debug_threshold.pnm", thold); +#endif + + //////////////////////////////////////////////////////// + // step 2. find connected components. + + unionfind_t *uf = unionfind_create(w * h); + + // TODO PARALLELIZE + for (int y = 0; y < h - 1; y++) { + do_unionfind_line(uf, thold, w, ts, y); + } + + // XXX sizing?? + int nclustermap = 2*w*h - 1; + + struct uint64_zarray_entry **clustermap = (struct uint64_zarray_entry**)calloc(nclustermap, sizeof(struct uint64_zarray_entry*)); + + for (int y = 1; y < h-1; y++) { + for (int x = 1; x < w-1; x++) { + + uint8_t v0 = thold.data[y*ts + x]; + if (v0 == 127) + continue; + + // XXX don't query this until we know we need it? + uint64_t rep0 = unionfind_get_representative(uf, y*w + x); + + // whenever we find two adjacent pixels such that one is + // white and the other black, we add the point half-way + // between them to a cluster associated with the unique + // ids of the white and black regions. + // + // We additionally compute the gradient direction (i.e., which + // direction was the white pixel?) Note: if (v1-v0) == 255, then + // (dx,dy) points towards the white pixel. if (v1-v0) == -255, then + // (dx,dy) points towards the black pixel. p.gx and p.gy will thus + // be -255, 0, or 255. + // + // Note that any given pixel might be added to multiple + // different clusters. But in the common case, a given + // pixel will be added multiple times to the same cluster, + // which increases the size of the cluster and thus the + // computational costs. + // + // A possible optimization would be to combine entries + // within the same cluster. + +#define DO_CONN(dx, dy) \ + if (1) { \ + uint8_t v1 = thold.data[y*ts + dy*ts + x + dx]; \ + \ + if (v0 + v1 == 255) { \ + uint64_t rep1 = unionfind_get_representative(uf, y*w + dy*w + x + dx); \ + uint64_t clusterid; \ + if (rep0 < rep1) \ + clusterid = (rep1 << 32) + rep0; \ + else \ + clusterid = (rep0 << 32) + rep1; \ + \ + /* XXX lousy hash function */ \ + uint32_t clustermap_bucket = u64hash_2(clusterid) % nclustermap; \ + struct uint64_zarray_entry *entry = clustermap[clustermap_bucket]; \ + while (entry && entry->id != clusterid) { \ + entry = entry->next; \ + } \ + \ + if (!entry) { \ + entry = (struct uint64_zarray_entry*)calloc(1, sizeof(struct uint64_zarray_entry)); \ + entry->id = clusterid; \ + entry->cluster = _zarray_create(sizeof(struct pt)); \ + entry->next = clustermap[clustermap_bucket]; \ + clustermap[clustermap_bucket] = entry; \ + } \ + \ + struct pt p; \ + p.x = saturate_cast(2*x + dx); \ + p.y = saturate_cast(2*y + dy); \ + p.gx = saturate_cast(dx*((int) v1-v0)); \ + p.gy = saturate_cast(dy*((int) v1-v0)); \ + _zarray_add(entry->cluster, &p); \ + } \ + } + + // do 4 connectivity. NB: Arguments must be [-1, 1] or we'll overflow .gx, .gy + DO_CONN(1, 0); + DO_CONN(0, 1); + + // do 8 connectivity + DO_CONN(-1, 1); + DO_CONN(1, 1); +} +} +#undef DO_CONN + +#ifdef APRIL_DEBUG +Mat out = Mat::zeros(h, w, CV_8UC3); + +uint32_t *colors = (uint32_t*) calloc(w*h, sizeof(*colors)); + +for (int y = 0; y < h; y++) { + for (int x = 0; x < w; x++) { + uint32_t v = unionfind_get_representative(uf, y*w+x); + + if (unionfind_get_set_size(uf, v) < parameters->aprilTagMinClusterPixels) + continue; + + uint32_t color = colors[v]; + uint8_t r = color >> 16, + g = color >> 8, + b = color; + + if (color == 0) { + const int bias = 50; + r = bias + (random() % (200-bias)); + g = bias + (random() % (200-bias)); + b = bias + (random() % (200-bias)); + colors[v] = (r << 16) | (g << 8) | b; + } + out.at(y, x)[0]=b; + out.at(y, x)[1]=g; + out.at(y, x)[2]=r; + } +} +free(colors); +imwrite("2.3 debug_segmentation.pnm", out); +out = Mat::zeros(h, w, CV_8UC3); +#endif + + //////////////////////////////////////////////////////// + // step 3. process each connected component. + zarray_t *clusters = _zarray_create(sizeof(zarray_t*)); //, uint64_zarray_hash_size(clustermap)); + CV_Assert(clusters != NULL); + + for (int i = 0; i < nclustermap; i++) { + for (struct uint64_zarray_entry *entry = clustermap[i]; entry; entry = entry->next) { + // XXX reject clusters here? + _zarray_add(clusters, &entry->cluster); + } + } + +#ifdef APRIL_DEBUG +for (int i = 0; i < _zarray_size(clusters); i++) { + zarray_t *cluster; + _zarray_get(clusters, i, &cluster); + + uint32_t r, g, b; + + const int bias = 50; + r = bias + (random() % (200-bias)); + g = bias + (random() % (200-bias)); + b = bias + (random() % (200-bias)); + + for (int j = 0; j < _zarray_size(cluster); j++) { + struct pt *p; + _zarray_get_volatile(cluster, j, &p); + + int x = p->x / 2; + int y = p->y / 2; + out.at(y, x)[0]=b; + out.at(y, x)[1]=g; + out.at(y, x)[2]=r; + } +} + +imwrite("2.4 debug_clusters.pnm", out); +out = Mat::zeros(h, w, CV_8UC3); +#endif + + for (int i = 0; i < _zarray_size(clusters); i++) { + zarray_t *cluster; + _zarray_get(clusters, i, &cluster); + + std::vector cnt; + for (int j = 0; j < _zarray_size(cluster); j++) { + struct pt *p; + _zarray_get_volatile(cluster, j, &p); + + Point pnt(p->x, p->y); + cnt.push_back(pnt); + } + contours.push_back(cnt); + } + + for (int i = 0; i < nclustermap; i++) { + struct uint64_zarray_entry *entry = clustermap[i]; + while (entry) { + struct uint64_zarray_entry *tmp = entry->next; + free(entry); + entry = tmp; + } + } + free(clustermap); + + zarray_t *quads = _zarray_create(sizeof(struct sQuad)); + + //int chunksize = 1 + sz / (APRILTAG_TASKS_PER_THREAD_TARGET * numberOfThreads); + int chunksize = std::max(1, h / (10 * getNumThreads())); + int sz = _zarray_size(clusters); + + // TODO PARALLELIZE + for (int i = 0; i < sz; i += chunksize) { + int min = sz < (i+chunksize)? sz: (i+chunksize); + do_quad(i, min, *clusters, w, h, quads, parameters, mImg); + } + +#ifdef APRIL_DEBUG +mImg.copyTo(out); +_darken(out); +_darken(out); +srandom(0); + +for (int i = 0; i < _zarray_size(quads); i++) { + struct sQuad *quad; + _zarray_get_volatile(quads, i, &quad); + + float rgb[3]; + int bias = 100; + + for (int i = 0; i < 3; i++) + rgb[i] = bias + (random() % (255-bias)); + + line(out, Point(quad->p[0][0], quad->p[0][1]), Point(quad->p[1][0], quad->p[1][1]), rgb[i]); + line(out, Point(quad->p[1][0], quad->p[1][1]), Point(quad->p[2][0], quad->p[2][1]), rgb[i]); + line(out, Point(quad->p[2][0], quad->p[2][1]), Point(quad->p[3][0], quad->p[3][1]), rgb[i]); + line(out, Point(quad->p[3][0], quad->p[3][1]), Point(quad->p[0][0], quad->p[0][1]), rgb[i]); +} +imwrite("2.5 debug_lines.pnm", out); +#endif + + unionfind_destroy(uf); + + for (int i = 0; i < _zarray_size(clusters); i++) { + zarray_t *cluster; + _zarray_get(clusters, i, &cluster); + _zarray_destroy(cluster); + } + _zarray_destroy(clusters); + return quads; +} + +void _apriltag(Mat im_orig, const DetectorParameters & _params, std::vector > &candidates, + std::vector > &contours){ + + /////////////////////////////////////////////////////////// + /// Step 1. Detect quads according to requested image decimation + /// and blurring parameters. + Mat quad_im; + + if (_params.aprilTagQuadDecimate > 1){ + resize(im_orig, quad_im, Size(), 1/_params.aprilTagQuadDecimate, 1/_params.aprilTagQuadDecimate, INTER_AREA); + } + else { + im_orig.copyTo(quad_im); + } + + // Apply a Blur + if (_params.aprilTagQuadSigma != 0) { + // compute a reasonable kernel width by figuring that the + // kernel should go out 2 std devs. + // + // max sigma ksz + // 0.499 1 (disabled) + // 0.999 3 + // 1.499 5 + // 1.999 7 + + float sigma = fabsf((float) _params.aprilTagQuadSigma); + + int ksz = cvFloor(4 * sigma); // 2 std devs in each direction + ksz |= 1; // make odd number + + if (ksz > 1) { + if (_params.aprilTagQuadSigma > 0) + GaussianBlur(quad_im, quad_im, Size(ksz, ksz), sigma, sigma, BORDER_REPLICATE); + else { + Mat orig; + quad_im.copyTo(orig); + GaussianBlur(quad_im, quad_im, Size(ksz, ksz), sigma, sigma, BORDER_REPLICATE); + + // SHARPEN the image by subtracting the low frequency components. + for (int y = 0; y < orig.rows; y++) { + for (int x = 0; x < orig.cols; x++) { + int vorig = orig.data[y*orig.step + x]; + int vblur = quad_im.data[y*quad_im.step + x]; + + int v = 2*vorig - vblur; + if (v < 0) + v = 0; + if (v > 255) + v = 255; + + quad_im.data[y*quad_im.step + x] = (uint8_t) v; + } + } + } + } + } + +#ifdef APRIL_DEBUG + imwrite("1.1 debug_preprocess.pnm", quad_im); +#endif + + /////////////////////////////////////////////////////////// + /// Step 2. do the Threshold :: get the set of candidate quads + zarray_t *quads = apriltag_quad_thresh(_params, quad_im, contours); + + CV_Assert(quads != NULL); + + // adjust centers of pixels so that they correspond to the + // original full-resolution image. + if (_params.aprilTagQuadDecimate > 1) { + for (int i = 0; i < _zarray_size(quads); i++) { + struct sQuad *q; + _zarray_get_volatile(quads, i, &q); + for (int j = 0; j < 4; j++) { + q->p[j][0] *= _params.aprilTagQuadDecimate; + q->p[j][1] *= _params.aprilTagQuadDecimate; + } + } + } + +#ifdef APRIL_DEBUG + Mat im_quads = im_orig.clone(); + im_quads = im_quads*0.5; + srandom(0); + + for (int i = 0; i < _zarray_size(quads); i++) { + struct sQuad *quad; + _zarray_get_volatile(quads, i, &quad); + + const int bias = 100; + int color = bias + (random() % (255-bias)); + + line(im_quads, Point(quad->p[0][0], quad->p[0][1]), Point(quad->p[1][0], quad->p[1][1]), color, 1); + line(im_quads, Point(quad->p[1][0], quad->p[1][1]), Point(quad->p[2][0], quad->p[2][1]), color, 1); + line(im_quads, Point(quad->p[2][0], quad->p[2][1]), Point(quad->p[3][0], quad->p[3][1]), color, 1); + line(im_quads, Point(quad->p[3][0], quad->p[3][1]), Point(quad->p[0][0], quad->p[0][1]), color, 1); + } + imwrite("1.2 debug_quads_raw.pnm", im_quads); +#endif + + //////////////////////////////////////////////////////////////// + /// Step 3. Save the output :: candidate corners + for (int i = 0; i < _zarray_size(quads); i++) { + struct sQuad *quad; + _zarray_get_volatile(quads, i, &quad); + + std::vector corners; + corners.push_back(Point2f(quad->p[3][0], quad->p[3][1])); //pA + corners.push_back(Point2f(quad->p[0][0], quad->p[0][1])); //pB + corners.push_back(Point2f(quad->p[1][0], quad->p[1][1])); //pC + corners.push_back(Point2f(quad->p[2][0], quad->p[2][1])); //pD + + candidates.push_back(corners); + } + + _zarray_destroy(quads); +} + +}} diff --git a/modules/objdetect/src/aruco/apriltag/apriltag_quad_thresh.hpp b/modules/objdetect/src/aruco/apriltag/apriltag_quad_thresh.hpp new file mode 100644 index 0000000000..bc1334a12d --- /dev/null +++ b/modules/objdetect/src/aruco/apriltag/apriltag_quad_thresh.hpp @@ -0,0 +1,117 @@ +// This file is part of OpenCV project. +// It is subject to the license terms in the LICENSE file found in the top-level directory +// of this distribution and at http://opencv.org/license.html. +// +// Copyright (C) 2013-2016, The Regents of The University of Michigan. +// +// This software was developed in the APRIL Robotics Lab under the +// direction of Edwin Olson, ebolson@umich.edu. This software may be +// available under alternative licensing terms; contact the address above. +// +// The views and conclusions contained in the software and documentation are those +// of the authors and should not be interpreted as representing official policies, +// either expressed or implied, of the Regents of The University of Michigan. + +// limitation: image size must be <32768 in width and height. This is +// because we use a fixed-point 16 bit integer representation with one +// fractional bit. + +#ifndef _OPENCV_APRIL_QUAD_THRESH_HPP_ +#define _OPENCV_APRIL_QUAD_THRESH_HPP_ + +#include "unionfind.hpp" +#include "zmaxheap.hpp" +#include "zarray.hpp" + +namespace cv { +namespace aruco { + +static inline uint32_t u64hash_2(uint64_t x) { + return uint32_t((2654435761UL * x) >> 32); +} + +struct uint64_zarray_entry{ + uint64_t id; + zarray_t *cluster; + + struct uint64_zarray_entry *next; +}; + +struct pt{ + // Note: these represent 2*actual value. + uint16_t x, y; + float theta; + int16_t gx, gy; +}; + +struct remove_vertex{ + int i; // which vertex to remove? + int left, right; // left vertex, right vertex + + double err; +}; + +struct segment{ + int is_vertex; + + // always greater than zero, but right can be > size, which denotes + // a wrap around back to the beginning of the points. and left < right. + int left, right; +}; + +struct line_fit_pt{ + double Mx, My; + double Mxx, Myy, Mxy; + double W; // total weight +}; + +/** + * lfps contains *cumulative* moments for N points, with + * index j reflecting points [0,j] (inclusive). + * fit a line to the points [i0, i1] (inclusive). i0, i1 are both (0, sz) + * if i1 < i0, we treat this as a wrap around. + */ +void fit_line(struct line_fit_pt *lfps, int sz, int i0, int i1, double *lineparm, double *err, double *mse); + +int err_compare_descending(const void *_a, const void *_b); + +/** + 1. Identify A) white points near a black point and B) black points near a white point. + + 2. Find the connected components within each of the classes above, + yielding clusters of "white-near-black" and + "black-near-white". (These two classes are kept separate). Each + segment has a unique id. + + 3. For every pair of "white-near-black" and "black-near-white" + clusters, find the set of points that are in one and adjacent to the + other. In other words, a "boundary" layer between the two + clusters. (This is actually performed by iterating over the pixels, + rather than pairs of clusters.) Critically, this helps keep nearby + edges from becoming connected. + **/ +int quad_segment_maxima(const DetectorParameters &td, int sz, struct line_fit_pt *lfps, int indices[4]); + +/** + * returns 0 if the cluster looks bad. + */ +int quad_segment_agg(int sz, struct line_fit_pt *lfps, int indices[4]); + +/** + * return 1 if the quad looks okay, 0 if it should be discarded + * quad + **/ +int fit_quad(const DetectorParameters &_params, const Mat im, zarray_t *cluster, struct sQuad *quad); + + +void threshold(const Mat mIm, const DetectorParameters ¶meters, Mat& mThresh); + + +zarray_t *apriltag_quad_thresh(const DetectorParameters ¶meters, const Mat & mImg, + std::vector > &contours); + +void _apriltag(Mat im_orig, const DetectorParameters &_params, std::vector > &candidates, + std::vector > &contours); + +}} +#endif diff --git a/modules/objdetect/src/aruco/apriltag/predefined_dictionaries_apriltag.hpp b/modules/objdetect/src/aruco/apriltag/predefined_dictionaries_apriltag.hpp new file mode 100644 index 0000000000..cad9802f53 --- /dev/null +++ b/modules/objdetect/src/aruco/apriltag/predefined_dictionaries_apriltag.hpp @@ -0,0 +1,14900 @@ +// This file is part of OpenCV project. +// It is subject to the license terms in the LICENSE file found in the top-level directory +// of this distribution and at http://opencv.org/license.html. + +namespace { + +/** + * Dictionaries are stored as a list of bytes in its four rotations. + * On each rotation, the marker is divided in bytes assuming a row-major order. + * This format allows a faster marker identification. + * For a dictionary composed by M markers of NxN bits, the structure dimensions should be: + * const char name[nMarkers][4rotations][nBytes], or more specifically: + * const char name[M][4][ceil(NxN/8)] + * The element [i][j][k] represents the k-th byte of the i-th marker in the dictionary + * in its j-th rotation. + * Each rotation implies a 90 degree rotation of the marker in anticlockwise direction. + */ +static unsigned char DICT_APRILTAG_16h5_BYTES[][4][2] = +{ + { {216, 196}, + {128, 190}, + {35, 27}, + {125, 1} + }, + { {165, 116}, + {106, 120}, + {46, 165}, + {30, 86} + }, + { {86, 44}, + {134, 209}, + {52, 106}, + {139, 97} + }, + { {157, 162}, + {195, 78}, + {69, 185}, + {114, 195} + }, + { {101, 158}, + {105, 211}, + {121, 166}, + {203, 150} + }, + { {214, 254}, + {167, 251}, + {127, 107}, + {223, 229} + }, + { {26, 205}, + {148, 55}, + {179, 88}, + {236, 41} + }, + { {162, 231}, + {31, 58}, + {231, 69}, + {92, 248} + }, + { {154, 127}, + {183, 61}, + {254, 89}, + {188, 237} + }, + { {182, 168}, + {142, 75}, + {21, 109}, + {210, 113} + }, + { {208, 28}, + {160, 153}, + {56, 11}, + {153, 5} + }, + { {213, 15}, + {209, 217}, + {240, 171}, + {155, 139} + }, + { {33, 176}, + {106, 2}, + {13, 132}, + {64, 86} + }, + { {108, 226}, + {11, 230}, + {71, 54}, + {103, 208} + }, + { {78, 49}, + {54, 196}, + {140, 114}, + {35, 108} + }, + { {8, 245}, + {50, 54}, + {175, 16}, + {108, 76} + }, + { {60, 144}, + {168, 70}, + {9, 60}, + {98, 21} + }, + { {45, 201}, + {88, 103}, + {147, 180}, + {230, 26} + }, + { {192, 165}, + {18, 154}, + {165, 3}, + {89, 72} + }, + { {241, 98}, + {203, 168}, + {70, 143}, + {21, 211} + }, + { {236, 135}, + {25, 222}, + {225, 55}, + {123, 152} + }, + { {169, 234}, + {75, 47}, + {87, 149}, + {244, 210} + }, + { {66, 251}, + {55, 163}, + {223, 66}, + {197, 236} + }, + { {184, 56}, + {170, 13}, + {28, 29}, + {176, 85} + }, + { {59, 151}, + {253, 22}, + {233, 220}, + {104, 191} + }, + { {181, 206}, + {201, 123}, + {115, 173}, + {222, 147} + }, + { {250, 181}, + {190, 158}, + {173, 95}, + {121, 125} + }, + { {12, 171}, + {19, 71}, + {213, 48}, + {226, 200} + }, + { {83, 224}, + {198, 162}, + {7, 202}, + {69, 99} + }, + { {116, 245}, + {186, 242}, + {175, 46}, + {79, 93} + } +}; + + + +static unsigned char DICT_APRILTAG_25h9_BYTES[][4][4] = +{ + { {143, 211, 170, 1}, + {234, 146, 237, 1}, + {170, 229, 248, 1}, + {219, 164, 171, 1} + }, + { {109, 139, 39, 1}, + {170, 251, 21, 0}, + {242, 104, 219, 0}, + {84, 111, 170, 1} + }, + { {22, 208, 222, 1}, + {94, 6, 244, 1}, + {189, 133, 180, 0}, + {151, 176, 61, 0} + }, + { {179, 147, 87, 1}, + {62, 118, 217, 0}, + {245, 100, 230, 1}, + {77, 183, 62, 0} + }, + { {115, 40, 116, 1}, + {28, 189, 146, 0}, + {151, 10, 103, 0}, + {36, 222, 156, 0} + }, + { {221, 18, 172, 0}, + {164, 145, 124, 1}, + {26, 164, 93, 1}, + {159, 68, 146, 1} + }, + { {103, 234, 238, 0}, + {98, 191, 182, 1}, + {59, 171, 243, 0}, + {182, 254, 163, 0} + }, + { {213, 186, 96, 1}, + {46, 157, 78, 0}, + {131, 46, 213, 1}, + {57, 92, 186, 0} + }, + { {231, 69, 93, 1}, + {89, 117, 157, 1}, + {221, 81, 115, 1}, + {220, 215, 77, 0} + }, + { {17, 101, 123, 0}, + {85, 214, 3, 1}, + {111, 83, 68, 0}, + {224, 53, 213, 0} + }, + { {228, 155, 129, 0}, + {34, 105, 109, 0}, + {64, 236, 147, 1}, + {91, 75, 34, 0} + }, + { {130, 77, 138, 0}, + {65, 10, 169, 1}, + {40, 217, 32, 1}, + {202, 168, 65, 0} + }, + { {117, 19, 219, 0}, + {52, 119, 101, 1}, + {109, 228, 87, 0}, + {211, 119, 22, 0} + }, + { {152, 112, 167, 1}, + {204, 194, 122, 0}, + {242, 135, 12, 1}, + {47, 33, 153, 1} + }, + { {75, 152, 26, 1}, + {154, 27, 192, 1}, + {172, 12, 233, 0}, + {129, 236, 44, 1} + }, + { {65, 65, 182, 1}, + {88, 147, 49, 0}, + {182, 193, 65, 0}, + {70, 100, 141, 0} + }, + { {172, 7, 198, 1}, + {169, 38, 61, 0}, + {177, 240, 26, 1}, + {94, 50, 74, 1} + }, + { {129, 217, 185, 0}, + {82, 216, 105, 1}, + {78, 205, 192, 1}, + {203, 13, 165, 0} + }, + { {35, 119, 206, 1}, + {105, 54, 243, 1}, + {185, 247, 98, 0}, + {231, 182, 75, 0} + }, + { {144, 92, 117, 0}, + {85, 204, 88, 0}, + {87, 29, 4, 1}, + {13, 25, 213, 0} + }, + { {138, 62, 250, 0}, + {177, 142, 234, 1}, + {47, 190, 40, 1}, + {171, 184, 198, 1} + }, + { {63, 236, 133, 1}, + {207, 120, 182, 0}, + {208, 155, 254, 0}, + {54, 143, 121, 1} + }, + { {70, 169, 59, 0}, + {18, 203, 135, 1}, + {110, 74, 177, 0}, + {240, 233, 164, 0} + }, + { {162, 116, 1, 1}, + {73, 96, 202, 0}, + {192, 23, 34, 1}, + {41, 131, 73, 0} + }, + { {52, 42, 195, 1}, + {44, 110, 38, 0}, + {225, 170, 22, 0}, + {50, 59, 26, 0} + }, + { {37, 240, 225, 0}, + {66, 244, 102, 0}, + {67, 135, 210, 0}, + {51, 23, 161, 0} + }, + { {144, 226, 137, 0}, + {102, 64, 42, 1}, + {72, 163, 132, 1}, + {170, 1, 51, 0} + }, + { {15, 33, 102, 1}, + {136, 150, 151, 0}, + {179, 66, 120, 0}, + {116, 180, 136, 1} + }, + { {165, 79, 19, 0}, + {113, 122, 13, 0}, + {100, 121, 82, 1}, + {88, 47, 71, 0} + }, + { {221, 124, 193, 0}, + {197, 93, 110, 0}, + {65, 159, 93, 1}, + {59, 93, 81, 1} + }, + { {254, 142, 154, 0}, + {183, 43, 172, 1}, + {44, 184, 191, 1}, + {154, 234, 118, 1} + }, + { {10, 11, 60, 1}, + {184, 136, 145, 1}, + {158, 104, 40, 0}, + {196, 136, 142, 1} + }, + { {139, 80, 95, 0}, + {208, 86, 216, 1}, + {125, 5, 104, 1}, + {141, 181, 5, 1} + }, + { {13, 198, 237, 1}, + {235, 212, 52, 1}, + {219, 177, 216, 0}, + {150, 21, 235, 1} + }, + { {115, 137, 157, 0}, + {22, 121, 177, 1}, + {92, 200, 231, 0}, + {198, 207, 52, 0} + } +}; + + + +static unsigned char DICT_APRILTAG_36h10_BYTES[][4][5] = +{ + { {225, 101, 73, 83, 8}, + {49, 6, 165, 238, 1}, + {28, 169, 42, 104, 7}, + {135, 122, 86, 8, 12} + }, + { {50, 53, 132, 160, 4}, + {65, 139, 98, 33, 2}, + {32, 82, 26, 196, 12}, + {72, 68, 109, 24, 2} + }, + { {107, 237, 252, 94, 4}, + {43, 167, 244, 249, 13}, + {39, 163, 251, 125, 6}, + {185, 242, 254, 93, 4} + }, + { {217, 189, 115, 45, 4}, + {123, 106, 82, 246, 12}, + {43, 76, 235, 217, 11}, + {54, 244, 165, 109, 14} + }, + { {87, 115, 222, 38, 12}, + {233, 207, 79, 209, 1}, + {54, 71, 188, 238, 10}, + {136, 191, 47, 57, 7} + }, + { {245, 43, 80, 249, 12}, + {161, 42, 235, 222, 10}, + {57, 240, 173, 74, 15}, + {87, 189, 117, 72, 5} + }, + { {46, 91, 153, 155, 12}, + {210, 166, 237, 21, 11}, + {61, 153, 157, 167, 4}, + {218, 139, 118, 84, 11} + }, + { {127, 167, 237, 114, 2}, + {179, 155, 190, 233, 5}, + {68, 235, 126, 95, 14}, + {169, 119, 221, 156, 13} + }, + { {72, 191, 207, 28, 10}, + {123, 243, 157, 160, 8}, + {83, 143, 63, 209, 2}, + {16, 91, 156, 253, 14} + }, + { {235, 64, 193, 206, 10}, + {58, 180, 33, 203, 3}, + {87, 56, 48, 45, 7}, + {205, 56, 66, 213, 12} + }, + { {215, 152, 253, 186, 6}, + {240, 185, 214, 211, 15}, + {101, 219, 241, 158, 11}, + {252, 182, 185, 208, 15} + }, + { {92, 212, 54, 176, 14}, + {194, 93, 211, 176, 6}, + {112, 214, 194, 179, 10}, + {96, 220, 187, 164, 3} + }, + { {114, 66, 21, 239, 14}, + {24, 61, 107, 157, 3}, + {127, 122, 132, 36, 14}, + {203, 157, 107, 193, 8} + }, + { {200, 18, 236, 76, 1}, + {110, 161, 12, 138, 4}, + {131, 35, 116, 129, 3}, + {37, 19, 8, 87, 6} + }, + { {27, 178, 99, 54, 1}, + {127, 72, 154, 65, 5}, + {134, 204, 100, 221, 8}, + {168, 37, 145, 47, 14} + }, + { {185, 202, 170, 229, 1}, + {14, 204, 62, 78, 14}, + {138, 117, 85, 57, 13}, + {119, 39, 195, 55, 0} + }, + { {55, 38, 64, 234, 9}, + {165, 40, 43, 105, 3}, + {149, 112, 38, 78, 12}, + {201, 109, 65, 74, 5} + }, + { {141, 86, 137, 137, 9}, + {214, 164, 13, 102, 2}, + {153, 25, 22, 171, 1}, + {70, 107, 2, 86, 11} + }, + { {220, 110, 245, 96, 5}, + {183, 141, 74, 186, 12}, + {160, 106, 247, 99, 11}, + {53, 213, 43, 30, 13} + }, + { {81, 225, 58, 109, 5}, + {13, 110, 86, 220, 4}, + {171, 101, 200, 120, 10}, + {35, 182, 167, 107, 0} + }, + { {40, 201, 94, 212, 13}, + {46, 71, 245, 24, 10}, + {178, 183, 169, 49, 4}, + {81, 138, 254, 39, 4} + }, + { {155, 25, 144, 102, 13}, + {78, 138, 67, 91, 9}, + {182, 96, 153, 141, 9}, + {157, 172, 37, 23, 2} + }, + { {198, 37, 228, 219, 13}, + {165, 163, 193, 175, 7}, + {189, 178, 122, 70, 3}, + {239, 88, 60, 90, 5} + }, + { {238, 221, 198, 163, 3}, + {230, 215, 50, 167, 11}, + {204, 86, 59, 183, 7}, + {222, 84, 206, 182, 7} + }, + { {168, 123, 189, 36, 7}, + {95, 151, 110, 18, 12}, + {226, 75, 221, 225, 5}, + {52, 135, 110, 159, 10} + }, + { {38, 247, 86, 43, 7}, + {229, 119, 122, 53, 1}, + {237, 70, 174, 246, 4}, + {138, 197, 238, 234, 7} + }, + { {119, 95, 17, 146, 15}, + {212, 30, 233, 241, 11}, + {244, 152, 143, 174, 14}, + {216, 249, 119, 130, 11} + }, + { {227, 232, 42, 118, 0}, + {9, 68, 182, 203, 13}, + {6, 229, 65, 124, 7}, + {189, 54, 210, 41, 0} + }, + { {219, 116, 9, 26, 8}, + {83, 44, 133, 227, 1}, + {21, 137, 2, 237, 11}, + {140, 122, 19, 76, 10} + }, + { {166, 92, 117, 179, 8}, + {240, 5, 163, 55, 15}, + {28, 218, 227, 166, 5}, + {254, 204, 90, 0, 15} + }, + { {247, 162, 51, 66, 4}, + {145, 72, 120, 219, 5}, + {36, 44, 196, 94, 15}, + {173, 177, 225, 40, 9} + }, + { {45, 210, 218, 190, 4}, + {234, 228, 254, 80, 3}, + {39, 213, 180, 187, 4}, + {192, 167, 242, 117, 7} + }, + { {158, 138, 87, 237, 4}, + {186, 105, 90, 31, 10}, + {43, 126, 165, 23, 9}, + {95, 133, 169, 101, 13} + }, + { {192, 186, 16, 180, 12}, + {73, 0, 219, 146, 10}, + {50, 208, 133, 208, 3}, + {84, 157, 176, 9, 2} + }, + { {19, 70, 233, 230, 12}, + {56, 140, 79, 105, 7}, + {54, 121, 118, 44, 8}, + {233, 111, 35, 17, 12} + }, + { {177, 22, 100, 69, 12}, + {104, 9, 105, 110, 4}, + {58, 34, 102, 136, 13}, + {39, 105, 105, 1, 6} + }, + { {74, 118, 173, 59, 12}, + {83, 165, 207, 165, 5}, + {61, 203, 86, 229, 2}, + {170, 95, 58, 92, 10} + }, + { {133, 254, 70, 49, 2}, + {225, 85, 154, 102, 8}, + {72, 198, 39, 250, 1}, + {22, 101, 154, 168, 7} + }, + { {173, 105, 121, 110, 10}, + {187, 54, 39, 90, 13}, + {87, 105, 233, 107, 5}, + {181, 174, 70, 205, 13} + }, + { {32, 21, 210, 100, 6}, + {104, 210, 98, 56, 0}, + {98, 100, 186, 128, 4}, + {1, 196, 100, 177, 6} + }, + { {147, 181, 91, 6, 6}, + {121, 90, 84, 115, 1}, + {102, 13, 170, 220, 9}, + {140, 226, 165, 169, 14} + }, + { {202, 157, 31, 171, 6}, + {82, 115, 86, 183, 11}, + {109, 95, 139, 149, 3}, + {222, 214, 172, 228, 10} + }, + { {187, 35, 104, 210, 14}, + {35, 26, 237, 75, 7}, + {116, 177, 108, 77, 13}, + {237, 43, 117, 140, 4} + }, + { {52, 107, 195, 95, 14}, + {185, 254, 233, 12, 9}, + {127, 172, 61, 98, 12}, + {147, 9, 119, 249, 13} + }, + { {160, 207, 113, 248, 9}, + {52, 38, 187, 58, 14}, + {145, 248, 239, 48, 5}, + {117, 205, 214, 66, 12} + }, + { {83, 31, 184, 90, 9}, + {68, 170, 141, 249, 13}, + {149, 161, 223, 140, 10}, + {185, 251, 21, 82, 2} + }, + { {241, 127, 53, 41, 9}, + {85, 47, 43, 246, 12}, + {153, 74, 207, 232, 15}, + {54, 253, 79, 74, 10} + }, + { {152, 80, 211, 144, 5}, + {118, 204, 192, 18, 2}, + {160, 156, 176, 161, 9}, + {68, 128, 51, 54, 14} + }, + { {123, 240, 90, 34, 5}, + {103, 76, 118, 209, 1}, + {164, 69, 160, 253, 14}, + {136, 182, 227, 46, 6} + }, + { {197, 168, 151, 126, 5}, + {157, 225, 210, 218, 9}, + {167, 238, 145, 90, 3}, + {149, 180, 184, 123, 9} + }, + { {22, 216, 30, 157, 5}, + {204, 109, 212, 21, 10}, + {171, 151, 129, 182, 8}, + {90, 130, 187, 99, 3} + }, + { {180, 132, 224, 47, 5}, + {172, 168, 114, 38, 5}, + {175, 64, 114, 18, 13}, + {166, 68, 225, 83, 5} + }, + { {237, 52, 164, 150, 13}, + {207, 129, 225, 226, 7}, + {182, 146, 82, 203, 7}, + {228, 120, 120, 31, 3} + }, + { {9, 146, 15, 177, 3}, + {86, 81, 158, 68, 2}, + {200, 223, 4, 153, 0}, + {66, 39, 152, 166, 10} + }, + { {251, 90, 185, 188, 11}, + {94, 188, 175, 211, 14}, + {211, 217, 213, 173, 15}, + {124, 191, 83, 215, 10} + }, + { {37, 6, 52, 30, 11}, + {140, 49, 169, 112, 5}, + {215, 130, 198, 10, 4}, + {160, 233, 88, 195, 1} + }, + { {224, 145, 168, 72, 15}, + {68, 178, 117, 138, 4}, + {241, 33, 88, 144, 7}, + {37, 26, 228, 210, 2} + }, + { {194, 115, 147, 11, 8}, + {81, 230, 9, 151, 1}, + {29, 12, 156, 228, 3}, + {142, 153, 6, 120, 10} + }, + { {16, 43, 26, 208, 4}, + {1, 74, 204, 24, 10}, + {32, 181, 141, 64, 8}, + {81, 131, 53, 40, 0} + }, + { {56, 215, 41, 175, 4}, + {90, 46, 126, 36, 7}, + {47, 89, 78, 177, 12}, + {226, 71, 231, 69, 10} + }, + { {214, 63, 130, 165, 12}, + {201, 202, 75, 167, 10}, + {58, 84, 31, 198, 11}, + {94, 93, 37, 57, 3} + }, + { {93, 176, 247, 42, 2}, + {243, 249, 18, 208, 5}, + {69, 78, 240, 219, 10}, + {160, 180, 137, 252, 15} + }, + { {115, 36, 212, 252, 10}, + {41, 185, 163, 249, 2}, + {83, 242, 178, 76, 14}, + {73, 252, 89, 217, 4} + }, + { {71, 220, 230, 148, 6}, + {232, 213, 208, 225, 14}, + {98, 150, 115, 190, 2}, + {120, 112, 186, 177, 7} + }, + { {221, 26, 76, 114, 14}, + {226, 25, 207, 202, 9}, + {116, 227, 37, 139, 11}, + {149, 63, 57, 132, 7} + }, + { {154, 222, 49, 181, 1}, + {94, 12, 154, 55, 14}, + {138, 216, 199, 181, 9}, + {126, 197, 147, 7, 10} + }, + { {76, 25, 234, 75, 9}, + {230, 226, 5, 140, 13}, + {157, 37, 121, 131, 2}, + {179, 26, 4, 118, 7} + }, + { {129, 149, 32, 65, 5}, + {68, 2, 80, 110, 4}, + {168, 32, 74, 152, 1}, + {39, 96, 164, 2, 2} + }, + { {208, 173, 68, 239, 5}, + {45, 43, 82, 174, 11}, + {175, 114, 43, 80, 11}, + {215, 84, 173, 75, 4} + }, + { {169, 3, 2, 54, 13}, + {14, 66, 235, 66, 1}, + {182, 196, 12, 9, 5}, + {132, 45, 116, 39, 0} + }, + { {90, 99, 243, 101, 13}, + {63, 206, 75, 157, 4}, + {186, 108, 252, 101, 10}, + {43, 157, 39, 63, 12} + }, + { {167, 56, 140, 168, 15}, + {197, 177, 103, 67, 10}, + {241, 83, 17, 206, 5}, + {92, 46, 104, 218, 3} + }, + { {193, 252, 209, 46, 0}, + {121, 164, 18, 242, 9}, + {7, 72, 179, 248, 3}, + {148, 244, 130, 89, 14} + }, + { {18, 162, 88, 245, 0}, + {41, 8, 158, 29, 2}, + {10, 241, 164, 84, 8}, + {75, 135, 145, 9, 4} + }, + { {176, 210, 149, 151, 0}, + {88, 141, 184, 22, 3}, + {14, 154, 148, 176, 13}, + {198, 129, 219, 17, 10} + }, + { {172, 158, 132, 125, 4}, + {202, 161, 250, 46, 8}, + {43, 226, 23, 147, 5}, + {23, 69, 248, 85, 3} + }, + { {112, 105, 55, 71, 12}, + {25, 79, 97, 156, 13}, + {62, 46, 201, 96, 14}, + {179, 152, 111, 41, 8} + }, + { {68, 181, 20, 179, 2}, + {193, 19, 146, 180, 3}, + {76, 210, 138, 210, 2}, + {194, 212, 156, 136, 3} + }, + { {231, 77, 237, 224, 10}, + {176, 151, 39, 235, 14}, + {80, 123, 123, 46, 7}, + {125, 126, 78, 144, 13} + }, + { {53, 29, 98, 66, 10}, + {224, 90, 33, 104, 13}, + {84, 36, 107, 138, 12}, + {177, 104, 69, 160, 7} + }, + { {142, 125, 171, 62, 10}, + {219, 246, 135, 35, 13}, + {87, 205, 91, 231, 1}, + {188, 78, 22, 253, 11} + }, + { {82, 219, 5, 133, 6}, + {88, 31, 88, 133, 10}, + {106, 26, 13, 180, 10}, + {90, 17, 175, 129, 10} + }, + { {240, 135, 244, 59, 6}, + {32, 187, 250, 182, 5}, + {109, 194, 254, 16, 15}, + {166, 213, 253, 208, 4} + }, + { {78, 144, 152, 110, 1}, + {206, 160, 22, 153, 1}, + {135, 97, 144, 151, 2}, + {137, 150, 128, 87, 3} + }, + { {210, 100, 39, 89, 9}, + {21, 109, 129, 175, 4}, + {153, 174, 66, 100, 11}, + {47, 88, 27, 106, 8} + }, + { {36, 194, 245, 253, 5}, + {188, 165, 250, 28, 6}, + {171, 250, 244, 50, 4}, + {99, 133, 250, 83, 13} + }, + { {50, 142, 228, 41, 3}, + {36, 185, 58, 37, 12}, + {201, 66, 119, 20, 12}, + {58, 69, 201, 210, 4} + }, + { {107, 62, 162, 144, 11}, + {71, 208, 169, 225, 14}, + {208, 148, 87, 205, 6}, + {120, 121, 80, 190, 2} + }, + { {217, 65, 43, 194, 11}, + {22, 94, 5, 202, 7}, + {212, 61, 72, 41, 11}, + {229, 58, 7, 166, 8} + }, + { {156, 165, 116, 197, 7}, + {175, 27, 80, 62, 6}, + {234, 50, 234, 83, 9}, + {103, 192, 173, 143, 5} + }, + { {17, 109, 219, 74, 15}, + {53, 254, 69, 120, 9}, + {245, 45, 187, 104, 8}, + {145, 234, 39, 250, 12} + }, + { {174, 87, 71, 134, 8}, + {250, 71, 41, 35, 3}, + {22, 30, 46, 167, 5}, + {204, 73, 78, 37, 15} + }, + { {114, 224, 117, 97, 4}, + {49, 13, 114, 157, 4}, + {40, 106, 224, 116, 14}, + {43, 148, 235, 8, 12} + }, + { {198, 150, 180, 86, 6}, + {200, 145, 216, 187, 5}, + {102, 162, 214, 150, 3}, + {173, 209, 184, 145, 3} + }, + { {168, 197, 195, 205, 1}, + {62, 230, 48, 46, 2}, + {139, 60, 58, 49, 5}, + {71, 64, 198, 119, 12} + }, + { {91, 21, 74, 119, 1}, + {110, 74, 134, 237, 1}, + {142, 229, 42, 141, 10}, + {139, 118, 21, 39, 6} + }, + { {205, 163, 184, 200, 5}, + {135, 162, 92, 218, 6}, + {161, 49, 220, 91, 3}, + {101, 179, 164, 94, 1} + }, + { {74, 204, 221, 214, 7}, + {62, 149, 212, 185, 11}, + {230, 187, 179, 53, 2}, + {217, 210, 186, 151, 12} + }, + { {102, 82, 239, 170, 15}, + {244, 245, 111, 129, 7}, + {245, 95, 116, 166, 6}, + {232, 31, 106, 242, 15} + }, + { {173, 218, 37, 160, 0}, + {210, 5, 58, 66, 14}, + {0, 90, 69, 187, 5}, + {116, 37, 202, 4, 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{167, 103, 245, 103, 1}, + {189, 135, 42, 127, 5}, + {142, 106, 254, 110, 5}, + {175, 229, 78, 27, 13} + }, + { {91, 165, 158, 70, 11}, + {15, 219, 21, 249, 1}, + {214, 39, 154, 93, 10}, + {137, 250, 141, 191, 0} + }, + { {88, 61, 62, 106, 2}, + {67, 123, 6, 184, 13}, + {69, 103, 203, 193, 10}, + {177, 214, 13, 236, 2} + }, + { {191, 77, 67, 125, 10}, + {186, 126, 163, 111, 8}, + {91, 236, 43, 47, 13}, + {31, 108, 87, 229, 13} + }, + { {160, 164, 162, 247, 2}, + {9, 208, 178, 46, 7}, + {78, 244, 82, 80, 5}, + {231, 68, 208, 185, 0} + }, + { {93, 52, 153, 184, 6}, + {211, 184, 198, 240, 2}, + {97, 217, 146, 203, 10}, + {64, 246, 49, 220, 11} + }, + { {211, 7, 214, 157, 5}, + {44, 235, 200, 247, 2}, + {171, 150, 190, 12, 11}, + {78, 241, 61, 115, 4} + }, + { {155, 172, 247, 16, 14}, + {51, 217, 209, 115, 12}, + {112, 142, 243, 93, 9}, + {60, 232, 185, 188, 12} + }, + { {196, 108, 246, 252, 13}, + {173, 229, 195, 186, 14}, + {179, 246, 243, 98, 3}, + {117, 220, 58, 123, 5} + }, + { {184, 1, 141, 118, 12}, + {26, 139, 231, 10, 1}, + {54, 235, 24, 1, 13}, + {133, 14, 125, 21, 8} + }, + { {232, 151, 127, 181, 13}, + {126, 67, 255, 182, 6}, + {186, 223, 238, 145, 7}, + {102, 223, 252, 39, 14} + }, + { {11, 60, 141, 188, 5}, + {95, 161, 198, 97, 10}, + {163, 219, 19, 205, 0}, + {88, 102, 56, 95, 10} + }, + { {20, 20, 133, 139, 8}, + {208, 169, 1, 36, 3}, + {29, 26, 18, 130, 8}, + {194, 72, 9, 80, 11} + }, + { {115, 104, 16, 10, 4}, + {1, 44, 96, 209, 9}, + {37, 0, 129, 108, 14}, + {152, 176, 99, 72, 0} + }, + { {18, 132, 134, 239, 3}, + {12, 249, 18, 45, 3}, + {207, 118, 18, 20, 8}, + {203, 68, 137, 243, 0} + }, + { {210, 252, 86, 125, 0}, + {105, 109, 146, 191, 8}, + {11, 230, 163, 244, 11}, + {31, 212, 155, 105, 6} + }, + { {91, 207, 66, 130, 14}, + {34, 94, 89, 225, 11}, + {116, 20, 47, 61, 10}, + {216, 121, 167, 164, 4} + }, + { {73, 183, 123, 167, 3}, + {127, 82, 30, 244, 7}, + {206, 93, 238, 217, 2}, + {226, 247, 132, 175, 14} + }, + { {97, 229, 12, 169, 15}, + {5, 55, 119, 228, 2}, + {249, 83, 10, 120, 6}, + {66, 126, 238, 202, 0} + }, + { {28, 221, 19, 226, 0}, + {210, 78, 18, 56, 11}, + {4, 124, 139, 179, 8}, + {209, 196, 135, 36, 11} + }, + { {241, 23, 253, 83, 15}, + {116, 155, 237, 254, 5}, + {252, 171, 254, 136, 15}, + {167, 251, 125, 146, 14} + }, + { {141, 51, 92, 19, 13}, + {231, 3, 205, 86, 1}, + {188, 131, 172, 203, 1}, + {134, 171, 60, 14, 7} + }, + { {248, 223, 155, 48, 4}, + {82, 206, 254, 178, 8}, + {32, 205, 159, 177, 15}, + {20, 215, 247, 52, 10} + }, + { {205, 115, 59, 196, 0}, + {219, 70, 12, 218, 6}, + {2, 61, 204, 235, 3}, + {101, 179, 6, 45, 11} + }, + { {35, 29, 150, 151, 9}, + {76, 195, 161, 117, 11}, + {158, 150, 155, 140, 4}, + {218, 232, 92, 51, 2} + }, + { {44, 151, 177, 71, 6}, + {218, 146, 120, 60, 5}, + {110, 40, 222, 147, 4}, + {163, 193, 228, 149, 11} + }, + { {230, 105, 156, 80, 1}, + {133, 135, 164, 155, 8}, + {128, 163, 153, 102, 7}, + {29, 146, 94, 26, 1} + }, + { {181, 161, 208, 86, 14}, + {169, 154, 241, 90, 1}, + {118, 160, 184, 90, 13}, + {133, 168, 245, 153, 5} + }, + { {60, 125, 33, 88, 4}, + {211, 46, 224, 40, 12}, + {33, 168, 75, 227, 12}, + {49, 64, 119, 76, 11} + }, + { {173, 20, 11, 20, 5}, + {222, 64, 228, 98, 0}, + {162, 141, 2, 139, 5}, + {4, 98, 112, 39, 11} + }, + { {251, 9, 110, 114, 3}, + {38, 91, 166, 203, 13}, + {196, 231, 105, 13, 15}, + {189, 54, 93, 166, 4} + }, + { {23, 132, 105, 191, 13}, + {188, 40, 215, 101, 7}, + {191, 217, 98, 30, 8}, + {234, 110, 177, 67, 13} + }, + { {36, 48, 61, 47, 6}, + {217, 49, 102, 20, 5}, + {111, 75, 192, 194, 4}, + {162, 134, 104, 201, 11} + }, + { {235, 214, 231, 21, 5}, + {126, 197, 248, 231, 4}, + {170, 142, 118, 189, 7}, + {46, 113, 250, 55, 14} + }, + { {147, 91, 170, 215, 11}, + {76, 222, 141, 79, 15}, + {222, 181, 93, 172, 9}, + {255, 43, 23, 179, 2} + }, + { {209, 95, 34, 205, 13}, + {76, 110, 73, 238, 14}, + {187, 52, 79, 168, 11}, + {119, 121, 39, 99, 2} + }, + { {55, 178, 213, 83, 15}, + {245, 153, 249, 93, 1}, + {252, 170, 180, 222, 12}, + {139, 169, 249, 154, 15} + }, + { {211, 101, 213, 98, 8}, + {49, 143, 3, 251, 1}, + {20, 106, 186, 108, 11}, + {141, 252, 15, 24, 12} + }, + { {29, 118, 183, 146, 15}, + {215, 221, 201, 112, 7}, + {244, 158, 214, 235, 8}, + {224, 233, 59, 190, 11} + }, + { {87, 185, 126, 171, 11}, + {229, 123, 23, 213, 15}, + {221, 87, 233, 222, 10}, + {250, 190, 141, 234, 7} + }, + { {9, 11, 171, 164, 4}, + {26, 194, 78, 64, 14}, + {34, 93, 93, 9, 0}, + {112, 39, 36, 53, 8} + }, + { {163, 131, 97, 118, 11}, + {60, 18, 187, 75, 5}, + {214, 232, 108, 28, 5}, + {173, 45, 212, 131, 12} + }, + { {156, 250, 125, 156, 6}, + {251, 61, 220, 18, 14}, + {99, 155, 229, 243, 9}, + {116, 131, 187, 205, 15} + }, + { {76, 134, 94, 122, 15}, + {166, 113, 223, 184, 1}, + {245, 231, 166, 19, 2}, + {129, 223, 184, 230, 5} + }, + { {249, 13, 22, 148, 11}, + {14, 91, 161, 242, 10}, + {210, 150, 139, 9, 15}, + {84, 248, 93, 167, 0} + }, + { {120, 93, 12, 212, 1}, + {78, 15, 164, 168, 10}, + {130, 179, 11, 161, 14}, + {81, 82, 95, 7, 2} + }, + { {51, 98, 95, 192, 1}, + {53, 77, 44, 89, 2}, + {128, 63, 164, 108, 12}, + {73, 163, 75, 42, 12} + }, + { {0, 213, 240, 148, 3}, + {108, 150, 144, 48, 6}, + {194, 144, 250, 176, 0}, + {96, 192, 150, 147, 6} + }, + { {167, 185, 175, 176, 8}, + {209, 195, 183, 67, 14}, + {16, 223, 89, 222, 5}, + {124, 46, 220, 56, 11} + }, + { {223, 59, 151, 88, 10}, + {211, 251, 137, 219, 8}, + {81, 174, 157, 207, 11}, + {29, 185, 29, 252, 11} + }, + { {182, 138, 31, 89, 2}, + {144, 121, 188, 31, 8}, + {73, 175, 133, 22, 13}, + {31, 131, 217, 224, 9} + }, + { {103, 50, 106, 212, 0}, + {233, 64, 172, 201, 6}, + {2, 181, 100, 206, 6}, + {105, 51, 80, 41, 7} + }, + { {7, 184, 90, 134, 3}, + {237, 80, 20, 81, 11}, + {198, 21, 161, 222, 0}, + {216, 162, 128, 171, 7} + }, + { {37, 38, 25, 247, 15}, + {157, 16, 239, 124, 3}, + {254, 249, 134, 74, 4}, + {195, 239, 112, 139, 9} + }, + { {130, 206, 71, 104, 3}, + {52, 117, 26, 43, 8}, + {193, 110, 39, 52, 1}, + {29, 69, 138, 226, 12} + }, + { {108, 230, 33, 121, 12}, + {147, 36, 251, 172, 4}, + {57, 232, 70, 115, 6}, + {35, 93, 242, 76, 9} + }, + { {98, 230, 221, 55, 8}, + {57, 133, 191, 181, 1}, + {30, 203, 182, 116, 6}, + {138, 223, 218, 25, 12} + }, + { {62, 92, 11, 17, 10}, + {210, 92, 165, 37, 8}, + {88, 141, 3, 167, 12}, + {26, 74, 83, 164, 11} + }, + { {57, 245, 112, 80, 8}, + {99, 14, 177, 120, 4}, + {16, 160, 234, 249, 12}, + {33, 232, 215, 12, 6} + }, + { {214, 87, 51, 142, 6}, + {216, 126, 72, 179, 7}, + {103, 28, 206, 166, 11}, + {236, 209, 39, 225, 11} + }, + { {192, 98, 168, 92, 12}, + {9, 164, 205, 138, 4}, + {51, 161, 84, 96, 3}, + {37, 27, 50, 89, 0} + }, + { {131, 220, 0, 222, 5}, + {76, 36, 208, 107, 11}, + {167, 176, 3, 188, 1}, + {221, 96, 178, 67, 2} + }, + { {177, 33, 195, 250, 3}, + {53, 250, 162, 74, 3}, + {197, 252, 56, 72, 13}, + {197, 36, 85, 250, 12} + }, + { {227, 149, 10, 113, 14}, + {64, 82, 247, 239, 0}, + {120, 229, 10, 156, 7}, + {15, 126, 244, 160, 2} + }, + { {113, 29, 253, 190, 8}, + {120, 171, 167, 240, 15}, + {23, 219, 251, 136, 14}, + {240, 254, 93, 81, 14} + }, + { {130, 171, 112, 191, 2}, + {41, 50, 154, 23, 15}, + {79, 208, 237, 84, 1}, + {254, 133, 148, 201, 4} + }, + { {93, 123, 132, 66, 1}, + {199, 143, 8, 200, 9}, + {132, 34, 29, 235, 10}, + {145, 49, 15, 30, 3} + }, + { {103, 239, 52, 200, 12}, + {129, 39, 121, 249, 14}, + {49, 50, 207, 126, 6}, + {121, 249, 238, 72, 1} + }, + { {202, 53, 231, 230, 13}, + {127, 195, 67, 171, 7}, + {182, 126, 122, 197, 3}, + {237, 92, 44, 63, 14} + }, + { {36, 1, 77, 111, 11}, + {188, 51, 39, 12, 1}, + {223, 107, 40, 2, 4}, + {131, 14, 76, 195, 13} + }, + { {183, 239, 157, 161, 14}, + {145, 159, 127, 119, 10}, + {120, 91, 159, 126, 13}, + {94, 239, 239, 152, 9} + }, + { {176, 76, 172, 188, 7}, + {12, 189, 230, 34, 14}, + {227, 211, 83, 32, 13}, + {116, 70, 123, 211, 0} + }, + { {193, 166, 3, 154, 8}, + {17, 96, 153, 226, 3}, + {21, 156, 6, 88, 3}, + {196, 121, 144, 104, 8} + }, + { {197, 1, 82, 163, 10}, + {160, 82, 3, 214, 3}, + {92, 84, 168, 10, 3}, + {198, 188, 4, 160, 5} + }, + { {220, 202, 43, 43, 7}, + {150, 124, 94, 134, 13}, + {237, 77, 69, 51, 11}, + {182, 23, 163, 230, 9} + }, + { {88, 6, 54, 143, 3}, + {14, 121, 8, 180, 7}, + {207, 22, 198, 1, 10}, + {226, 209, 9, 231, 0} + }, + { {139, 223, 114, 151, 10}, + {106, 86, 153, 119, 15}, + {94, 148, 239, 189, 1}, + {254, 233, 150, 165, 6} + }, + { {118, 72, 225, 171, 10}, + {176, 188, 35, 133, 15}, + {93, 88, 113, 38, 14}, + {250, 28, 67, 208, 13} + }, + { {224, 20, 244, 247, 7}, + {108, 145, 226, 190, 7}, + {238, 242, 242, 128, 7}, + {231, 212, 120, 147, 6} + }, + { {113, 170, 60, 249, 0}, + {1, 41, 190, 220, 14}, + {9, 243, 197, 88, 14}, + {115, 183, 217, 72, 0} + }, + { {156, 171, 243, 108, 14}, + {187, 250, 91, 26, 12}, + {115, 108, 253, 83, 9}, + {53, 141, 165, 253, 13} + }, + { {135, 84, 73, 90, 15}, + {244, 52, 197, 107, 1}, + {245, 169, 34, 174, 1}, + {141, 106, 50, 194, 15} + }, + { {154, 153, 213, 71, 2}, + {122, 155, 16, 31, 9}, + {78, 42, 185, 149, 9}, + {159, 128, 141, 149, 14} + }, + { {231, 44, 187, 69, 6}, + {153, 208, 100, 255, 12}, + {106, 45, 211, 78, 7}, + {63, 242, 96, 185, 9} + }, + { {196, 176, 203, 147, 1}, + {245, 192, 148, 134, 3}, + {140, 157, 48, 210, 3}, + {198, 18, 144, 58, 15} + }, + { {137, 237, 4, 93, 7}, + {15, 55, 208, 110, 8}, + {235, 162, 11, 121, 1}, + {23, 96, 190, 207, 0} + }, + { {199, 169, 10, 58, 11}, + {133, 114, 151, 195, 9}, + {213, 197, 9, 94, 3}, + {156, 62, 148, 234, 1} + }, + { {65, 90, 235, 196, 2}, + {120, 212, 12, 200, 14}, + {66, 61, 117, 168, 2}, + {113, 51, 2, 177, 14} + }, + { {127, 85, 215, 48, 2}, + {242, 223, 162, 241, 0}, + {64, 206, 186, 175, 14}, + {8, 244, 95, 180, 15} + }, + { {17, 75, 16, 122, 6}, + {0, 62, 202, 88, 9}, + {101, 224, 141, 40, 8}, + {145, 165, 55, 192, 0} + }, + { {230, 235, 111, 39, 4}, + {185, 71, 126, 135, 13}, + {46, 79, 109, 118, 7}, + {190, 23, 238, 41, 13} + }, + { {132, 244, 176, 135, 15}, + {205, 148, 81, 54, 7}, + {254, 16, 210, 242, 1}, + {230, 200, 162, 155, 3} + }, + { {91, 222, 44, 8, 8}, + {66, 45, 29, 225, 12}, + {17, 3, 71, 189, 10}, + {56, 123, 139, 68, 2} + }, + { {205, 253, 149, 194, 7}, + {215, 151, 80, 250, 11}, + {228, 58, 155, 251, 3}, + {213, 240, 174, 158, 11} + }, + { {51, 193, 37, 123, 3}, + {20, 63, 178, 77, 5}, + {205, 234, 72, 60, 12}, + {171, 36, 223, 194, 8} + }, + { {99, 27, 71, 141, 15}, + {124, 115, 105, 197, 10}, + {251, 30, 45, 140, 6}, + {90, 57, 108, 227, 14} + }, + { {229, 239, 80, 81, 11}, + {165, 22, 185, 254, 8}, + {216, 160, 175, 122, 7}, + {23, 249, 214, 138, 5} + }, + { {65, 141, 160, 190, 12}, + {8, 162, 211, 224, 15}, + {55, 208, 91, 24, 2}, + {240, 124, 180, 81, 0} + }, + { {193, 184, 36, 139, 1}, + {69, 33, 16, 198, 15}, + {141, 18, 65, 216, 3}, + {246, 48, 136, 74, 2} + }, + { {118, 222, 87, 133, 11}, + {252, 93, 57, 181, 10}, + {218, 30, 167, 182, 14}, + {90, 217, 203, 163, 15} + }, + { {219, 201, 87, 218, 6}, + {50, 127, 208, 219, 11}, + {101, 190, 169, 61, 11}, + {221, 176, 191, 228, 12} + }, + { {202, 225, 244, 5, 4}, + {43, 135, 80, 151, 4}, + {42, 2, 248, 117, 3}, + {46, 144, 174, 29, 4} + }, + { {145, 76, 36, 42, 2}, + {0, 61, 2, 98, 13}, + {69, 66, 67, 40, 9}, + {180, 100, 11, 192, 0} + }, + { {69, 163, 208, 168, 2}, + {161, 178, 26, 208, 2}, + {65, 80, 188, 90, 2}, + {64, 181, 132, 216, 5} + }, + { {136, 154, 125, 93, 13}, + {126, 33, 221, 30, 12}, + {187, 171, 229, 145, 1}, + {55, 139, 184, 71, 14} + }, + { {154, 61, 179, 211, 2}, + {83, 218, 128, 63, 15}, + {76, 188, 219, 197, 9}, + {255, 192, 21, 188, 10} + }, + { {208, 44, 134, 112, 15}, + {5, 217, 195, 170, 8}, + {240, 230, 19, 64, 11}, + {21, 92, 57, 186, 0} + }, + { {21, 123, 52, 80, 12}, + {193, 15, 201, 88, 12}, + {48, 162, 205, 234, 8}, + {49, 169, 63, 8, 3} + }, + { {137, 13, 55, 91, 10}, + {18, 115, 129, 126, 13}, + {93, 174, 203, 9, 1}, + {183, 232, 28, 228, 8} + }, + { {137, 27, 201, 59, 10}, + {114, 178, 143, 70, 9}, + {93, 201, 61, 137, 1}, + {150, 47, 20, 212, 14} + }, + { {138, 2, 216, 10, 3}, + {38, 176, 12, 19, 1}, + {197, 1, 180, 5, 1}, + {140, 131, 0, 214, 4} + }, + { {30, 93, 243, 65, 14}, + {242, 222, 65, 61, 12}, + {120, 44, 251, 167, 8}, + {59, 200, 39, 180, 15} + }, + { {120, 109, 137, 131, 2}, + {19, 158, 36, 164, 11}, + {76, 25, 27, 97, 14}, + {210, 82, 71, 156, 8} + }, + { {172, 247, 228, 126, 13}, + {239, 167, 251, 42, 5}, + {183, 226, 126, 243, 5}, + {165, 77, 254, 95, 7} + }, + { {28, 22, 226, 90, 0}, + {226, 232, 136, 40, 5}, + {5, 164, 118, 131, 8}, + {161, 65, 17, 116, 7} + }, + { {46, 169, 4, 13, 9}, + {143, 35, 49, 5, 8}, + {155, 2, 9, 87, 4}, + {26, 8, 204, 79, 1} + }, + { {243, 38, 138, 238, 5}, + {13, 232, 110, 235, 3}, + {167, 117, 22, 76, 15}, + {205, 119, 97, 123, 0} + }, + { {128, 232, 75, 204, 11}, + {61, 116, 21, 10, 10}, + {211, 61, 33, 112, 1}, + {85, 10, 130, 235, 12} + }, + { {162, 190, 211, 245, 12}, + {121, 192, 251, 63, 10}, + {58, 252, 183, 212, 5}, + {95, 205, 240, 57, 14} + }, + { {179, 172, 4, 251, 2}, + {1, 57, 178, 111, 11}, + {77, 242, 3, 92, 13}, + {223, 100, 217, 200, 0} + }, + { {132, 89, 129, 25, 2}, + {208, 182, 128, 6, 8}, + {73, 136, 25, 162, 1}, + {22, 0, 22, 208, 11} + }, + { {96, 167, 159, 201, 4}, + {17, 227, 124, 188, 2}, + {41, 63, 158, 80, 6}, + {67, 211, 236, 120, 8} + }, + { {19, 143, 250, 197, 9}, + {44, 202, 29, 125, 14}, + {154, 53, 255, 28, 8}, + {123, 235, 133, 51, 4} + }, + { {214, 125, 112, 144, 3}, + {229, 30, 128, 179, 14}, + {192, 144, 235, 230, 11}, + {124, 208, 23, 138, 7} + }, + { {43, 138, 160, 242, 5}, + {6, 128, 250, 73, 15}, + {164, 240, 85, 29, 4}, + {249, 37, 240, 22, 0} + }, + { {41, 131, 176, 59, 10}, + {2, 178, 187, 84, 5}, + {93, 192, 220, 25, 4}, + {162, 173, 212, 212, 0} + }, + { {140, 215, 81, 28, 8}, + {250, 38, 153, 50, 0}, + {19, 136, 174, 179, 1}, + {4, 201, 150, 69, 15} + }, + { {47, 222, 77, 2, 12}, + {242, 5, 125, 97, 9}, + {52, 11, 39, 191, 4}, + {152, 107, 234, 4, 15} + }, + { {213, 4, 207, 5, 12}, + {184, 201, 69, 230, 0}, + {58, 15, 50, 10, 11}, + {6, 122, 41, 49, 13} + }, + { {186, 231, 214, 153, 0}, + {35, 239, 184, 55, 2}, + {9, 150, 190, 117, 13}, + {78, 193, 223, 124, 4} + }, + { {156, 243, 126, 164, 13}, + {239, 79, 95, 18, 6}, + {178, 87, 236, 243, 9}, + {100, 143, 175, 47, 7} + }, + { {143, 79, 97, 177, 14}, + {178, 22, 203, 103, 14}, + {120, 216, 111, 47, 1}, + {126, 109, 54, 132, 13} + }, + { {137, 255, 175, 206, 6}, + {91, 247, 92, 106, 15}, + {103, 63, 95, 249, 1}, + {245, 99, 174, 253, 10} + }, + { {124, 126, 177, 202, 2}, + {211, 188, 40, 184, 15}, + {69, 56, 215, 227, 14}, + {241, 209, 67, 220, 11} + }, + { {150, 194, 61, 167, 11}, + {156, 29, 31, 23, 7}, + {222, 91, 196, 54, 9}, + {238, 143, 139, 131, 9} + } +}; + + + +static unsigned char DICT_APRILTAG_36h11_BYTES[][4][5] = +{ + { {33, 161, 70, 186, 11}, + {37, 115, 179, 64, 3}, + {213, 214, 40, 88, 4}, + {192, 44, 220, 234, 4} + }, + { {146, 209, 143, 233, 11}, + {84, 255, 23, 15, 2}, + {217, 127, 24, 180, 9}, + {79, 14, 143, 242, 10} + }, + { {112, 137, 1, 75, 11}, + {20, 58, 49, 140, 9}, + {221, 40, 9, 16, 14}, + {147, 24, 197, 194, 8} + }, + { {25, 57, 121, 226, 7}, + {119, 26, 70, 88, 15}, + {228, 121, 233, 201, 8}, + {241, 166, 37, 142, 14} + }, + { {68, 21, 61, 61, 7}, + {220, 51, 198, 180, 4}, + {235, 203, 202, 130, 2}, + {34, 214, 60, 195, 11} + }, + { {53, 205, 91, 140, 15}, + {188, 126, 117, 112, 10}, + {243, 29, 171, 58, 12}, + {80, 234, 231, 227, 13} + }, + { {161, 11, 165, 106, 0}, + {16, 163, 42, 74, 13}, + {5, 106, 93, 8, 5}, + {181, 37, 76, 80, 8} + }, + { {43, 135, 74, 96, 8}, + {34, 66, 63, 105, 0}, + {16, 101, 46, 29, 4}, + {9, 111, 196, 36, 4} + }, + { {181, 127, 184, 212, 4}, + {201, 142, 236, 122, 14}, + {34, 177, 223, 234, 13}, + {117, 227, 119, 25, 3} + }, + { {78, 32, 181, 166, 4}, + {155, 129, 66, 145, 7}, + {38, 90, 208, 71, 2}, + {232, 148, 40, 29, 9} + }, + { {97, 216, 151, 242, 12}, + {80, 197, 243, 216, 11}, + {52, 254, 145, 184, 6}, + {209, 188, 250, 48, 10} + }, + { {171, 52, 105, 255, 12}, + {123, 32, 231, 111, 7}, + {63, 249, 98, 205, 5}, + {239, 110, 112, 77, 14} + }, + { {89, 76, 164, 92, 2}, + {10, 189, 128, 232, 12}, + {67, 162, 83, 41, 10}, + {49, 112, 27, 213, 0} + }, + { {250, 28, 45, 46, 2}, + {90, 57, 38, 163, 13}, + {71, 75, 67, 133, 15}, + {188, 86, 73, 197, 10} + }, + { {151, 194, 75, 151, 2}, + {184, 92, 156, 71, 3}, + {78, 157, 36, 62, 9}, + {206, 35, 147, 161, 13} + }, + { {117, 146, 134, 36, 10}, + {200, 217, 59, 192, 0}, + {82, 70, 20, 154, 14}, + {0, 61, 201, 177, 3} + }, + { {28, 170, 254, 153, 10}, + {163, 249, 157, 20, 14}, + {89, 151, 245, 83, 8}, + {114, 139, 153, 252, 5} + }, + { {50, 54, 221, 193, 6}, + {113, 153, 108, 61, 2}, + {104, 59, 182, 196, 12}, + {75, 195, 105, 152, 14} + }, + { {136, 78, 82, 125, 6}, + {42, 116, 202, 62, 8}, + {107, 228, 167, 33, 1}, + {23, 197, 50, 229, 4} + }, + { {87, 113, 168, 199, 14}, + {201, 158, 69, 205, 7}, + {126, 49, 88, 238, 10}, + {235, 58, 39, 153, 3} + }, + { {245, 41, 37, 184, 1}, + {149, 43, 162, 194, 14}, + {129, 218, 73, 74, 15}, + {116, 52, 93, 74, 9} + }, + { {46, 89, 204, 26, 1}, + {230, 167, 164, 1, 9}, + {133, 131, 57, 167, 4}, + {152, 2, 94, 86, 7} + }, + { {127, 165, 138, 179, 1}, + {135, 202, 182, 229, 3}, + {140, 213, 26, 95, 14}, + {202, 118, 213, 62, 1} + }, + { {235, 67, 56, 79, 9}, + {14, 38, 45, 223, 5}, + {159, 33, 204, 45, 7}, + {175, 187, 70, 71, 0} + }, + { {57, 19, 213, 52, 5}, + {126, 139, 234, 80, 0}, + {162, 202, 188, 137, 12}, + {0, 165, 125, 23, 14} + }, + { {215, 155, 26, 59, 5}, + {196, 106, 222, 215, 9}, + {173, 197, 141, 158, 11}, + {158, 183, 181, 98, 3} + }, + { {13, 251, 231, 104, 13}, + {247, 231, 91, 72, 12}, + {177, 110, 125, 251, 0}, + {49, 45, 174, 126, 15} + }, + { {92, 215, 160, 49, 13}, + {198, 142, 219, 164, 4}, + {184, 192, 94, 179, 10}, + {34, 93, 183, 22, 3} + }, + { {185, 200, 247, 164, 11}, + {62, 221, 51, 82, 14}, + {210, 94, 241, 57, 13}, + {116, 172, 203, 183, 12} + }, + { {70, 152, 126, 6, 11}, + {236, 81, 21, 145, 13}, + {214, 7, 225, 150, 2}, + {184, 154, 136, 163, 7} + }, + { {110, 12, 93, 82, 7}, + {182, 17, 228, 185, 9}, + {228, 171, 163, 7, 6}, + {153, 210, 120, 134, 13} + }, + { {91, 197, 103, 187, 4}, + {50, 111, 210, 229, 7}, + {45, 222, 106, 61, 10}, + {234, 116, 191, 100, 12} + }, + { {30, 99, 2, 188, 2}, + {139, 126, 138, 1, 2}, + {67, 212, 12, 103, 8}, + {72, 5, 23, 237, 1} + }, + { {138, 199, 208, 70, 10}, + {42, 150, 25, 59, 1}, + {86, 32, 190, 53, 1}, + {141, 201, 134, 149, 4} + }, + { {166, 95, 226, 50, 6}, + {224, 214, 234, 35, 13}, + {100, 196, 127, 166, 5}, + {188, 69, 118, 176, 7} + }, + { {84, 0, 235, 97, 6}, + {176, 216, 70, 140, 4}, + {104, 109, 112, 2, 10}, + {35, 22, 33, 176, 13} + }, + { {247, 160, 102, 131, 6}, + {161, 89, 112, 199, 7}, + {108, 22, 96, 94, 15}, + {238, 48, 233, 168, 5} + }, + { {45, 208, 175, 223, 6}, + {218, 245, 244, 76, 7}, + {111, 191, 80, 187, 4}, + {227, 34, 250, 245, 11} + }, + { {59, 156, 182, 11, 1}, + {70, 233, 48, 117, 13}, + {141, 6, 211, 157, 12}, + {186, 224, 201, 118, 2} + }, + { {173, 106, 28, 175, 9}, + {143, 37, 47, 86, 11}, + {159, 83, 133, 107, 5}, + {214, 175, 74, 79, 1} + }, + { {147, 182, 46, 251, 5}, + {69, 105, 222, 111, 7}, + {173, 247, 70, 220, 9}, + {239, 103, 185, 106, 2} + }, + { {187, 33, 13, 147, 13}, + {23, 11, 229, 71, 3}, + {188, 155, 8, 77, 13}, + {206, 42, 125, 14, 8} + }, + { {222, 229, 80, 148, 11}, + {175, 30, 145, 179, 2}, + {210, 144, 170, 119, 11}, + {76, 216, 151, 143, 5} + }, + { {160, 205, 20, 121, 11}, + {4, 55, 179, 62, 8}, + {217, 226, 139, 48, 5}, + {23, 204, 222, 194, 0} + }, + { {42, 35, 171, 178, 7}, + {23, 210, 238, 1, 7}, + {228, 221, 92, 69, 4}, + {232, 7, 116, 190, 8} + }, + { {79, 103, 244, 181, 15}, + {175, 151, 203, 245, 6}, + {250, 210, 254, 111, 2}, + {106, 253, 62, 159, 5} + }, + { {88, 168, 21, 129, 8}, + {19, 9, 17, 148, 10}, + {24, 26, 129, 81, 10}, + {82, 152, 137, 12, 8} + }, + { {116, 52, 39, 214, 4}, + {217, 73, 224, 168, 7}, + {38, 190, 66, 194, 14}, + {225, 80, 121, 41, 11} + }, + { {29, 236, 64, 135, 4}, + {171, 12, 80, 100, 11}, + {46, 16, 35, 123, 8}, + {210, 96, 163, 13, 5} + }, + { {137, 42, 179, 160, 2}, + {19, 208, 10, 82, 14}, + {64, 92, 213, 73, 1}, + {116, 165, 0, 188, 8} + }, + { {56, 213, 116, 46, 14}, + {106, 63, 115, 48, 5}, + {119, 66, 234, 177, 12}, + {160, 204, 239, 197, 6} + }, + { {12, 67, 86, 122, 1}, + {166, 103, 138, 24, 1}, + {133, 230, 172, 35, 0}, + {129, 133, 30, 102, 5} + }, + { {93, 179, 17, 203, 1}, + {215, 42, 24, 220, 3}, + {141, 56, 140, 219, 10}, + {195, 177, 133, 78, 11} + }, + { {201, 87, 202, 31, 9}, + {110, 230, 141, 230, 1}, + {159, 133, 62, 169, 3}, + {134, 123, 22, 119, 6} + }, + { {162, 36, 87, 130, 3}, + {53, 81, 32, 51, 3}, + {196, 30, 162, 68, 5}, + {204, 192, 72, 170, 12} + }, + { {41, 172, 233, 143, 3}, + {63, 176, 52, 100, 15}, + {207, 25, 115, 89, 4}, + {242, 98, 192, 223, 12} + }, + { {204, 197, 44, 82, 8}, + {130, 7, 149, 170, 5}, + {20, 163, 74, 51, 3}, + {165, 90, 158, 4, 1} + }, + { {218, 139, 53, 120, 12}, + {18, 43, 219, 155, 12}, + {49, 234, 205, 21, 11}, + {61, 157, 189, 68, 8} + }, + { {213, 180, 185, 227, 6}, + {209, 152, 86, 254, 7}, + {108, 121, 210, 218, 11}, + {231, 246, 161, 152, 11} + }, + { {172, 156, 221, 60, 14}, + {250, 177, 247, 50, 8}, + {115, 203, 179, 147, 5}, + {20, 206, 248, 213, 15} + }, + { {203, 218, 168, 57, 1}, + {70, 164, 158, 199, 12}, + {137, 193, 85, 189, 3}, + {62, 55, 146, 86, 2} + }, + { {25, 134, 37, 107, 1}, + {22, 41, 26, 108, 5}, + {141, 106, 70, 25, 8}, + {163, 101, 137, 70, 8} + }, + { {186, 230, 204, 136, 9}, + {39, 173, 61, 35, 2}, + {145, 19, 54, 117, 13}, + {76, 75, 203, 94, 4} + }, + { {223, 145, 177, 14, 5}, + {222, 170, 80, 211, 5}, + {167, 8, 216, 159, 11}, + {172, 176, 165, 87, 11} + }, + { {161, 169, 213, 167, 5}, + {61, 131, 114, 86, 11}, + {174, 90, 185, 88, 5}, + {214, 164, 236, 27, 12} + }, + { {43, 101, 26, 169, 13}, + {7, 102, 103, 117, 2}, + {185, 85, 138, 109, 4}, + {74, 238, 102, 110, 0} + }, + { {77, 92, 46, 25, 13}, + {198, 101, 197, 228, 12}, + {185, 135, 67, 171, 2}, + {50, 122, 58, 102, 3} + }, + { {91, 22, 55, 54, 11}, + {94, 89, 139, 241, 5}, + {214, 206, 198, 141, 10}, + {168, 253, 25, 167, 10} + }, + { {247, 83, 214, 10, 8}, + {224, 239, 41, 211, 1}, + {21, 6, 188, 174, 15}, + {140, 185, 79, 112, 7} + }, + { {94, 132, 179, 125, 2}, + {154, 248, 146, 189, 4}, + {75, 236, 210, 23, 10}, + {43, 212, 145, 245, 9} + }, + { {252, 228, 58, 159, 2}, + {139, 124, 180, 182, 7}, + {79, 149, 194, 115, 15}, + {230, 210, 211, 237, 1} + }, + { {187, 146, 109, 26, 6}, + {114, 57, 252, 67, 5}, + {101, 139, 100, 157, 13}, + {172, 35, 249, 196, 14} + }, + { {237, 141, 35, 110, 5}, + {158, 98, 114, 234, 13}, + {167, 108, 75, 27, 7}, + {181, 116, 228, 103, 9} + }, + { {106, 248, 70, 243, 7}, + {103, 85, 242, 141, 11}, + {236, 246, 33, 245, 6}, + {219, 20, 250, 174, 6} + }, + { {234, 86, 165, 19, 8}, + {82, 133, 169, 167, 5}, + {28, 138, 86, 165, 7}, + {174, 89, 90, 20, 10} + }, + { {93, 73, 113, 70, 12}, + {186, 14, 65, 216, 13}, + {54, 40, 233, 43, 10}, + {177, 184, 39, 5, 13} + }, + { {71, 3, 96, 236, 10}, + {168, 50, 11, 201, 6}, + {83, 112, 108, 14, 2}, + {105, 61, 4, 193, 5} + }, + { {140, 75, 205, 103, 10}, + {186, 151, 15, 14, 9}, + {94, 107, 61, 35, 1}, + {151, 15, 14, 149, 13} + }, + { {41, 95, 57, 1, 14}, + {82, 22, 109, 116, 12}, + {120, 9, 207, 169, 4}, + {50, 235, 102, 132, 10} + }, + { {246, 181, 119, 233, 7}, + {245, 123, 114, 191, 6}, + {233, 126, 234, 214, 15}, + {111, 212, 237, 234, 15} + }, + { {82, 6, 2, 245, 10}, + {8, 88, 139, 173, 2}, + {90, 244, 6, 4, 10}, + {75, 93, 17, 161, 0} + }, + { {181, 17, 148, 146, 14}, + {192, 155, 225, 82, 3}, + {116, 146, 152, 138, 13}, + {196, 168, 125, 144, 3} + }, + { {72, 226, 153, 171, 7}, + {23, 180, 94, 148, 3}, + {237, 89, 148, 113, 2}, + {194, 151, 162, 222, 8} + }, + { {183, 159, 87, 55, 10}, + {248, 91, 187, 119, 9}, + {94, 206, 175, 158, 13}, + {158, 237, 221, 161, 15} + }, + { {168, 20, 198, 131, 14}, + {98, 209, 97, 38, 3}, + {124, 22, 50, 129, 5}, + {198, 72, 104, 180, 6} + }, + { {45, 169, 0, 88, 3}, + {135, 50, 176, 72, 8}, + {193, 160, 9, 91, 4}, + {17, 32, 212, 206, 1} + }, + { {212, 171, 164, 121, 7}, + {133, 187, 218, 142, 12}, + {233, 226, 93, 82, 11}, + {55, 21, 189, 218, 1} + }, + { {152, 42, 14, 101, 12}, + {11, 73, 79, 14, 8}, + {58, 103, 5, 65, 9}, + {23, 15, 41, 45, 0} + }, + { {244, 128, 204, 193, 5}, + {164, 137, 116, 142, 2}, + {168, 51, 48, 18, 15}, + {71, 18, 233, 18, 5} + }, + { {11, 32, 234, 115, 2}, + {35, 208, 134, 77, 5}, + {76, 229, 112, 77, 0}, + {171, 38, 16, 188, 4} + }, + { {169, 80, 103, 16, 10}, + {114, 85, 161, 66, 4}, + {80, 142, 96, 169, 5}, + {36, 40, 90, 164, 14} + }, + { {4, 134, 226, 238, 1}, + {172, 224, 26, 40, 7}, + {135, 116, 118, 18, 0}, + {225, 69, 128, 115, 5} + }, + { {176, 169, 114, 97, 5}, + {37, 74, 114, 30, 12}, + {168, 100, 233, 80, 13}, + {55, 132, 229, 42, 4} + }, + { {231, 63, 58, 37, 7}, + {205, 82, 110, 247, 12}, + {234, 69, 207, 206, 7}, + {62, 247, 100, 171, 3} + }, + { {23, 226, 5, 185, 8}, + {145, 45, 155, 69, 2}, + {25, 218, 4, 126, 8}, + {74, 45, 155, 72, 9} + }, + { {236, 154, 178, 178, 4}, + {194, 192, 250, 146, 15}, + {36, 212, 213, 147, 7}, + {244, 149, 240, 52, 3} + }, + { {217, 51, 158, 7, 6}, + {75, 219, 76, 214, 1}, + {110, 7, 156, 201, 11}, + {134, 179, 45, 189, 2} + }, + { {235, 136, 116, 249, 9}, + {38, 33, 179, 223, 14}, + {153, 242, 225, 29, 7}, + {127, 188, 216, 70, 4} + }, + { {148, 32, 165, 92, 12}, + {153, 169, 193, 10, 4}, + {51, 170, 80, 66, 9}, + {37, 8, 57, 89, 9} + }, + { {227, 100, 255, 153, 2}, + {49, 245, 164, 247, 6}, + {73, 159, 242, 108, 7}, + {110, 242, 90, 248, 12} + }, + { {138, 76, 184, 240, 10}, + {2, 148, 135, 59, 14}, + {80, 241, 211, 37, 1}, + {125, 206, 18, 148, 0} + }, + { {247, 42, 238, 118, 6}, + {169, 217, 238, 203, 13}, + {102, 231, 117, 78, 15}, + {189, 55, 121, 185, 5} + }, + { {115, 204, 107, 86, 9}, + {60, 76, 181, 233, 13}, + {150, 173, 99, 60, 14}, + {185, 122, 211, 35, 12} + }, + { {201, 156, 166, 165, 9}, + {78, 193, 19, 230, 14}, + {154, 86, 83, 153, 3}, + {118, 124, 136, 55, 2} + }, + { {54, 106, 12, 83, 5}, + {133, 13, 236, 13, 9}, + {172, 163, 5, 102, 12}, + {155, 3, 123, 10, 1} + }, + { {80, 158, 81, 148, 3}, + {124, 24, 152, 176, 10}, + {194, 152, 167, 144, 10}, + {80, 209, 145, 131, 14} + }, + { {186, 109, 34, 125, 1}, + {15, 110, 162, 47, 12}, + {139, 228, 75, 101, 13}, + {63, 68, 87, 111, 0} + }, + { {210, 172, 241, 99, 11}, + {53, 152, 19, 191, 13}, + {220, 104, 243, 84, 11}, + {191, 220, 129, 154, 12} + }, + { {217, 137, 254, 246, 8}, + {42, 203, 151, 218, 15}, + {22, 247, 249, 25, 11}, + {245, 190, 157, 53, 4} + }, + { {100, 23, 7, 187, 2}, + {208, 115, 170, 164, 3}, + {77, 222, 14, 130, 6}, + {194, 85, 92, 224, 11} + }, + { {249, 189, 49, 42, 11}, + {87, 58, 51, 242, 13}, + {213, 72, 203, 217, 15}, + {180, 252, 197, 206, 10} + }, + { {119, 115, 156, 32, 7}, + {197, 159, 110, 209, 0}, + {224, 67, 156, 238, 14}, + {8, 183, 111, 154, 3} + }, + { {104, 191, 141, 27, 15}, + {87, 179, 253, 164, 9}, + {253, 139, 31, 209, 6}, + {146, 91, 252, 222, 10} + }, + { {222, 221, 132, 166, 14}, + {202, 159, 83, 163, 11}, + {118, 82, 27, 183, 11}, + {220, 92, 175, 149, 3} + }, + { {66, 234, 236, 73, 11}, + {37, 181, 29, 141, 12}, + {217, 35, 117, 116, 2}, + {59, 27, 138, 218, 4} + }, + { {48, 43, 104, 213, 3}, + {45, 26, 172, 12, 14}, + {202, 177, 109, 64, 12}, + {115, 3, 85, 139, 4} + }, + { {78, 187, 147, 12, 14}, + {219, 242, 89, 145, 8}, + {115, 12, 157, 215, 2}, + {24, 153, 164, 253, 11} + }, + { {67, 156, 93, 155, 5}, + {116, 33, 212, 245, 11}, + {173, 155, 163, 156, 2}, + {218, 242, 184, 66, 14} + }, + { {225, 252, 146, 40, 13}, + {69, 228, 115, 242, 8}, + {177, 68, 147, 248, 7}, + {20, 252, 226, 122, 2} + }, + { {248, 166, 168, 212, 10}, + {11, 152, 189, 170, 6}, + {82, 177, 86, 81, 15}, + {101, 91, 209, 157, 0} + }, + { {181, 57, 2, 161, 8}, + {193, 74, 35, 70, 10}, + {24, 84, 9, 202, 13}, + {86, 44, 69, 40, 3} + }, + { 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{154, 160, 48, 46, 2}, + {11, 56, 18, 19, 5}, + {71, 64, 192, 85, 9}, + {172, 132, 129, 205, 0} + }, + { {236, 24, 40, 209, 7}, + {198, 16, 228, 142, 14}, + {232, 177, 65, 131, 7}, + {119, 18, 112, 134, 3} + }, + { {188, 80, 121, 99, 5}, + {246, 12, 102, 30, 5}, + {172, 105, 224, 163, 13}, + {167, 134, 99, 6, 15} + }, + { {135, 133, 193, 183, 9}, + {188, 130, 147, 103, 3}, + {158, 216, 58, 30, 1}, + {206, 108, 148, 19, 13} + }, + { {211, 122, 173, 183, 10}, + {89, 157, 143, 199, 15}, + {94, 219, 85, 236, 11}, + {254, 63, 27, 153, 10} + }, + { {129, 127, 2, 206, 0}, + {73, 102, 8, 106, 11}, + {7, 52, 15, 232, 1}, + {213, 97, 6, 105, 2} + }, + { {253, 99, 223, 176, 10}, + {179, 223, 175, 210, 2}, + {80, 223, 188, 107, 15}, + {68, 191, 95, 188, 13} + }, + { {81, 10, 193, 175, 2}, + {56, 184, 10, 196, 11}, + {79, 88, 53, 8, 10}, + {210, 53, 1, 209, 12} + }, + { {61, 30, 223, 141, 3}, + {254, 249, 44, 116, 10}, + {203, 31, 183, 139, 12}, + {82, 227, 73, 247, 15} + }, + { {244, 183, 58, 64, 2}, + {193, 90, 60, 186, 4}, + {64, 37, 206, 210, 15}, + {37, 211, 197, 168, 3} + }, + { {55, 215, 137, 233, 12}, + {208, 174, 127, 109, 2}, + {57, 121, 30, 190, 12}, + {75, 111, 231, 80, 11} + }, + { {143, 17, 199, 124, 10}, + {250, 243, 131, 75, 0}, + {83, 238, 56, 143, 1}, + {13, 44, 28, 245, 15} + }, + { {196, 189, 3, 107, 14}, + {209, 114, 83, 174, 9}, + {125, 108, 11, 210, 3}, + {151, 92, 164, 232, 11} + }, + { {125, 250, 153, 92, 9}, + {223, 172, 189, 216, 8}, + {147, 169, 149, 251, 14}, + {17, 187, 211, 95, 11} + }, + { {123, 20, 232, 37, 1}, + {110, 136, 38, 229, 4}, + {138, 65, 114, 141, 14}, + {42, 118, 65, 23, 6} + }, + { {202, 7, 14, 127, 4}, + {10, 99, 206, 175, 1}, + {47, 231, 14, 5, 3}, + {143, 87, 60, 101, 0} + }, + { {92, 34, 219, 205, 5}, + {191, 232, 76, 156, 2}, + {171, 61, 180, 67, 10}, + {67, 147, 33, 127, 13} + }, + { {160, 219, 114, 108, 8}, + {104, 102, 59, 26, 12}, + {19, 100, 237, 176, 5}, + {53, 141, 198, 97, 6} + }, + { {107, 119, 118, 222, 2}, + {107, 119, 168, 249, 7}, + {71, 182, 238, 237, 6}, + {233, 241, 94, 237, 6} + }, + { {128, 245, 142, 116, 8}, + {73, 199, 151, 42, 0}, + {18, 231, 26, 240, 1}, + {5, 78, 158, 57, 2} + }, + { {225, 172, 31, 244, 10}, + {25, 81, 183, 250, 10}, + {82, 255, 131, 88, 7}, + {85, 254, 216, 169, 8} + }, + { {27, 186, 234, 133, 12}, + {107, 200, 93, 69, 14}, + {58, 21, 117, 221, 8}, + {122, 43, 161, 61, 6} + }, + { {38, 172, 85, 127, 12}, + {185, 33, 243, 61, 9}, + {63, 234, 163, 86, 4}, + {155, 204, 248, 73, 13} + }, + { {229, 209, 239, 53, 7}, + {252, 215, 246, 198, 4}, + {234, 207, 120, 186, 7}, + {38, 54, 254, 179, 15} + }, + { {31, 41, 212, 225, 0}, + {163, 139, 2, 93, 10}, + {8, 114, 185, 79, 8}, + {91, 164, 13, 28, 5} + }, + { {69, 159, 187, 21, 11}, + {220, 210, 157, 244, 12}, + {218, 141, 223, 154, 2}, + {50, 251, 148, 179, 11} + }, + { {212, 176, 73, 85, 9}, + {253, 8, 149, 142, 0}, + {154, 169, 32, 210, 11}, + {7, 26, 145, 11, 15} + }, + { {108, 183, 10, 207, 8}, + {203, 98, 61, 172, 3}, + {31, 53, 14, 211, 6}, + {195, 91, 196, 109, 3} + }, + { {248, 97, 122, 81, 8}, + {35, 78, 165, 158, 4}, + {24, 165, 232, 97, 15}, + {39, 154, 87, 44, 4} + }, + { {195, 145, 218, 195, 4}, + {96, 194, 84, 223, 3}, + {44, 53, 184, 156, 3}, + {207, 178, 164, 48, 6} + }, + { {81, 35, 94, 44, 12}, + {41, 107, 79, 208, 0}, + {51, 71, 172, 72, 10}, + {0, 191, 45, 105, 4} + }, + { {116, 64, 124, 79, 14}, + {168, 61, 101, 156, 5}, + {127, 35, 224, 34, 14}, + {163, 154, 107, 193, 5} + }, + { {223, 22, 9, 162, 4}, + {210, 8, 78, 227, 3}, + {36, 89, 6, 143, 11}, + {204, 119, 33, 4, 11} + }, + { {206, 210, 125, 193, 7}, + {246, 21, 92, 159, 6}, + {232, 59, 228, 183, 3}, + {111, 147, 170, 134, 15} + } +}; + +}//namespace diff --git a/modules/objdetect/src/aruco/apriltag/unionfind.hpp b/modules/objdetect/src/aruco/apriltag/unionfind.hpp new file mode 100644 index 0000000000..6ecc58a407 --- /dev/null +++ b/modules/objdetect/src/aruco/apriltag/unionfind.hpp @@ -0,0 +1,131 @@ +// This file is part of OpenCV project. +// It is subject to the license terms in the LICENSE file found in the top-level directory +// of this distribution and at http://opencv.org/license.html. +// +// Copyright (C) 2013-2016, The Regents of The University of Michigan. +// +// This software was developed in the APRIL Robotics Lab under the +// direction of Edwin Olson, ebolson@umich.edu. This software may be +// available under alternative licensing terms; contact the address above. +// +// The views and conclusions contained in the software and documentation are those +// of the authors and should not be interpreted as representing official policies, +// either expressed or implied, of the Regents of The University of Michigan. +#ifndef _OPENCV_UNIONFIND_HPP_ +#define _OPENCV_UNIONFIND_HPP_ + +namespace cv { +namespace aruco { + +typedef struct unionfind unionfind_t; +struct unionfind{ + uint32_t maxid; + struct ufrec *data; +}; + +struct ufrec{ + // the parent of this node. If a node's parent is its own index, + // then it is a root. + uint32_t parent; + + // for the root of a connected component, the number of components + // connected to it. For intermediate values, it's not meaningful. + uint32_t size; +}; + +static inline unionfind_t *unionfind_create(uint32_t maxid){ + unionfind_t *uf = (unionfind_t*) calloc(1, sizeof(unionfind_t)); + uf->maxid = maxid; + uf->data = (struct ufrec*) malloc((maxid+1) * sizeof(struct ufrec)); + for (unsigned int i = 0; i <= maxid; i++) { + uf->data[i].size = 1; + uf->data[i].parent = i; + } + return uf; +} + +static inline void unionfind_destroy(unionfind_t *uf){ + free(uf->data); + free(uf); +} + +/* +static inline uint32_t unionfind_get_representative(unionfind_t *uf, uint32_t id) +{ + // base case: a node is its own parent + if (uf->data[id].parent == id) + return id; + + // otherwise, recurse + uint32_t root = unionfind_get_representative(uf, uf->data[id].parent); + + // short circuit the path. [XXX This write prevents tail recursion] + uf->data[id].parent = root; + + return root; +} + */ + +// this one seems to be every-so-slightly faster than the recursive +// version above. +static inline uint32_t unionfind_get_representative(unionfind_t *uf, uint32_t id){ + uint32_t root = id; + + // chase down the root + while (uf->data[root].parent != root) { + root = uf->data[root].parent; + } + + // go back and collapse the tree. + // + // XXX: on some of our workloads that have very shallow trees + // (e.g. image segmentation), we are actually faster not doing + // this... + while (uf->data[id].parent != root) { + uint32_t tmp = uf->data[id].parent; + uf->data[id].parent = root; + id = tmp; + } + + return root; +} + +static inline uint32_t unionfind_get_set_size(unionfind_t *uf, uint32_t id){ + uint32_t repid = unionfind_get_representative(uf, id); + return uf->data[repid].size; +} + +static inline uint32_t unionfind_connect(unionfind_t *uf, uint32_t aid, uint32_t bid){ + uint32_t aroot = unionfind_get_representative(uf, aid); + uint32_t broot = unionfind_get_representative(uf, bid); + + if (aroot == broot) + return aroot; + + // we don't perform "union by rank", but we perform a similar + // operation (but probably without the same asymptotic guarantee): + // We join trees based on the number of *elements* (as opposed to + // rank) contained within each tree. I.e., we use size as a proxy + // for rank. In my testing, it's often *faster* to use size than + // rank, perhaps because the rank of the tree isn't that critical + // if there are very few nodes in it. + uint32_t asize = uf->data[aroot].size; + uint32_t bsize = uf->data[broot].size; + + // optimization idea: We could shortcut some or all of the tree + // that is grafted onto the other tree. Pro: those nodes were just + // read and so are probably in cache. Con: it might end up being + // wasted effort -- the tree might be grafted onto another tree in + // a moment! + if (asize > bsize) { + uf->data[broot].parent = aroot; + uf->data[aroot].size += bsize; + return aroot; + } else { + uf->data[aroot].parent = broot; + uf->data[broot].size += asize; + return broot; + } +} +}} +#endif diff --git a/modules/objdetect/src/aruco/apriltag/zarray.hpp b/modules/objdetect/src/aruco/apriltag/zarray.hpp new file mode 100644 index 0000000000..4c05c925b6 --- /dev/null +++ b/modules/objdetect/src/aruco/apriltag/zarray.hpp @@ -0,0 +1,148 @@ +// This file is part of OpenCV project. +// It is subject to the license terms in the LICENSE file found in the top-level directory +// of this distribution and at http://opencv.org/license.html. +// +// Copyright (C) 2013-2016, The Regents of The University of Michigan. +// +// This software was developed in the APRIL Robotics Lab under the +// direction of Edwin Olson, ebolson@umich.edu. This software may be +// available under alternative licensing terms; contact the address above. +// +// The views and conclusions contained in the software and documentation are those +// of the authors and should not be interpreted as representing official policies, +// either expressed or implied, of the Regents of The University of Michigan. +#ifndef _OPENCV_ZARRAY_HPP_ +#define _OPENCV_ZARRAY_HPP_ + + +namespace cv { +namespace aruco { + + +struct sQuad{ + float p[4][2]; // corners +}; + +/** + * Defines a structure which acts as a resize-able array ala Java's ArrayList. + */ +typedef struct zarray zarray_t; +struct zarray{ + size_t el_sz; // size of each element + + int size; // how many elements? + int alloc; // we've allocated storage for how many elements? + char *data; +}; + +/** + * Creates and returns a variable array structure capable of holding elements of + * the specified size. It is the caller's responsibility to call zarray_destroy() + * on the returned array when it is no longer needed. + */ +inline static zarray_t *_zarray_create(size_t el_sz){ + zarray_t *za = (zarray_t*) calloc(1, sizeof(zarray_t)); + za->el_sz = el_sz; + return za; +} + +/** + * Frees all resources associated with the variable array structure which was + * created by zarray_create(). After calling, 'za' will no longer be valid for storage. + */ +inline static void _zarray_destroy(zarray_t *za){ + if (za == NULL) + return; + + if (za->data != NULL) + free(za->data); + memset(za, 0, sizeof(zarray_t)); + free(za); +} + +/** + * Retrieves the number of elements currently being contained by the passed + * array, which may be different from its capacity. The index of the last element + * in the array will be one less than the returned value. + */ +inline static int _zarray_size(const zarray_t *za){ + return za->size; +} + +/** + * Allocates enough internal storage in the supplied variable array structure to + * guarantee that the supplied number of elements (capacity) can be safely stored. + */ +inline static void _zarray_ensure_capacity(zarray_t *za, int capacity){ + if (capacity <= za->alloc) + return; + + while (za->alloc < capacity) { + za->alloc *= 2; + if (za->alloc < 8) + za->alloc = 8; + } + + za->data = (char*) realloc(za->data, za->alloc * za->el_sz); +} + +/** + * Adds a new element to the end of the supplied array, and sets its value + * (by copying) from the data pointed to by the supplied pointer 'p'. + * Automatically ensures that enough storage space is available for the new element. + */ +inline static void _zarray_add(zarray_t *za, const void *p){ + _zarray_ensure_capacity(za, za->size + 1); + + memcpy(&za->data[za->size*za->el_sz], p, za->el_sz); + za->size++; +} + +/** + * Retrieves the element from the supplied array located at the zero-based + * index of 'idx' and copies its value into the variable pointed to by the pointer + * 'p'. + */ +inline static void _zarray_get(const zarray_t *za, int idx, void *p){ + CV_DbgAssert(idx >= 0); + CV_DbgAssert(idx < za->size); + + memcpy(p, &za->data[idx*za->el_sz], za->el_sz); +} + +/** + * Similar to zarray_get(), but returns a "live" pointer to the internal + * storage, avoiding a memcpy. This pointer is not valid across + * operations which might move memory around (i.e. zarray_remove_value(), + * zarray_remove_index(), zarray_insert(), zarray_sort(), zarray_clear()). + * 'p' should be a pointer to the pointer which will be set to the internal address. + */ +inline static void _zarray_get_volatile(const zarray_t *za, int idx, void *p){ + CV_DbgAssert(idx >= 0); + CV_DbgAssert(idx < za->size); + + *((void**) p) = &za->data[idx*za->el_sz]; +} + +inline static void _zarray_truncate(zarray_t *za, int sz){ + za->size = sz; +} + +/** + * Sets the value of the current element at index 'idx' by copying its value from + * the data pointed to by 'p'. The previous value of the changed element will be + * copied into the data pointed to by 'outp' if it is not null. + */ +static inline void _zarray_set(zarray_t *za, int idx, const void *p, void *outp){ + CV_DbgAssert(idx >= 0); + CV_DbgAssert(idx < za->size); + + if (outp != NULL) + memcpy(outp, &za->data[idx*za->el_sz], za->el_sz); + + memcpy(&za->data[idx*za->el_sz], p, za->el_sz); +} + +} +} +#endif diff --git a/modules/objdetect/src/aruco/apriltag/zmaxheap.cpp b/modules/objdetect/src/aruco/apriltag/zmaxheap.cpp new file mode 100644 index 0000000000..5b0ac85dcb --- /dev/null +++ b/modules/objdetect/src/aruco/apriltag/zmaxheap.cpp @@ -0,0 +1,207 @@ +// This file is part of OpenCV project. +// It is subject to the license terms in the LICENSE file found in the top-level directory +// of this distribution and at http://opencv.org/license.html. +// +// Copyright (C) 2013-2016, The Regents of The University of Michigan. +// +// This software was developed in the APRIL Robotics Lab under the +// direction of Edwin Olson, ebolson@umich.edu. This software may be +// available under alternative licensing terms; contact the address above. +// +// The views and conclusions contained in the software and documentation are those +// of the authors and should not be interpreted as representing official policies, +// either expressed or implied, of the Regents of The University of Michigan. + +#include "../../precomp.hpp" +#include "zmaxheap.hpp" + + +// 0 +// 1 2 +// 3 4 5 6 +// 7 8 9 10 11 12 13 14 +// +// Children of node i: 2*i+1, 2*i+2 +// Parent of node i: (i-1) / 2 +// +// Heap property: a parent is greater than (or equal to) its children. + +#define MIN_CAPACITY 16 +namespace cv { +namespace aruco { +struct zmaxheap +{ + size_t el_sz; + + int size; + int alloc; + + float *values; + char *data; + + void (*swap)(zmaxheap_t *heap, int a, int b); +}; + +static inline void _swap_default(zmaxheap_t *heap, int a, int b) +{ + float t = heap->values[a]; + heap->values[a] = heap->values[b]; + heap->values[b] = t; + + cv::AutoBuffer tmp(heap->el_sz); + memcpy(tmp.data(), &heap->data[a*heap->el_sz], heap->el_sz); + memcpy(&heap->data[a*heap->el_sz], &heap->data[b*heap->el_sz], heap->el_sz); + memcpy(&heap->data[b*heap->el_sz], tmp.data(), heap->el_sz); +} + +static inline void _swap_pointer(zmaxheap_t *heap, int a, int b) +{ + float t = heap->values[a]; + heap->values[a] = heap->values[b]; + heap->values[b] = t; + + void **pp = (void**) heap->data; + void *tmp = pp[a]; + pp[a] = pp[b]; + pp[b] = tmp; +} + + +zmaxheap_t *zmaxheap_create(size_t el_sz) +{ + zmaxheap_t *heap = (zmaxheap_t*)calloc(1, sizeof(zmaxheap_t)); + heap->el_sz = el_sz; + + heap->swap = _swap_default; + + if (el_sz == sizeof(void*)) + heap->swap = _swap_pointer; + + return heap; +} + +void zmaxheap_destroy(zmaxheap_t *heap) +{ + free(heap->values); + free(heap->data); + memset(heap, 0, sizeof(zmaxheap_t)); + free(heap); +} + +static void _zmaxheap_ensure_capacity(zmaxheap_t *heap, int capacity) +{ + if (heap->alloc >= capacity) + return; + + int newcap = heap->alloc; + + while (newcap < capacity) { + if (newcap < MIN_CAPACITY) { + newcap = MIN_CAPACITY; + continue; + } + + newcap *= 2; + } + + heap->values = (float*)realloc(heap->values, newcap * sizeof(float)); + heap->data = (char*)realloc(heap->data, newcap * heap->el_sz); + heap->alloc = newcap; +} + +void zmaxheap_add(zmaxheap_t *heap, void *p, float v) +{ + _zmaxheap_ensure_capacity(heap, heap->size + 1); + + int idx = heap->size; + + heap->values[idx] = v; + memcpy(&heap->data[idx*heap->el_sz], p, heap->el_sz); + + heap->size++; + + while (idx > 0) { + + int parent = (idx - 1) / 2; + + // we're done! + if (heap->values[parent] >= v) + break; + + // else, swap and recurse upwards. + heap->swap(heap, idx, parent); + idx = parent; + } +} + +// Removes the item in the heap at the given index. Returns 1 if the +// item existed. 0 Indicates an invalid idx (heap is smaller than +// idx). This is mostly intended to be used by zmaxheap_remove_max. +static int zmaxheap_remove_index(zmaxheap_t *heap, int idx, void *p, float *v) +{ + if (idx >= heap->size) + return 0; + + // copy out the requested element from the heap. + if (v != NULL) + *v = heap->values[idx]; + if (p != NULL) + memcpy(p, &heap->data[idx*heap->el_sz], heap->el_sz); + + heap->size--; + + // If this element is already the last one, then there's nothing + // for us to do. + if (idx == heap->size) + return 1; + + // copy last element to first element. (which probably upsets + // the heap property). + heap->values[idx] = heap->values[heap->size]; + memcpy(&heap->data[idx*heap->el_sz], &heap->data[heap->el_sz * heap->size], heap->el_sz); + + // now fix the heap. Note, as we descend, we're "pushing down" + // the same node the entire time. Thus, while the index of the + // parent might change, the parent_score doesn't. + int parent = idx; + float parent_score = heap->values[idx]; + + // descend, fixing the heap. + while (parent < heap->size) { + + int left = 2*parent + 1; + int right = left + 1; + +// assert(parent_score == heap->values[parent]); + + float left_score = (left < heap->size) ? heap->values[left] : -INFINITY; + float right_score = (right < heap->size) ? heap->values[right] : -INFINITY; + + // put the biggest of (parent, left, right) as the parent. + + // already okay? + if (parent_score >= left_score && parent_score >= right_score) + break; + + // if we got here, then one of the children is bigger than the parent. + if (left_score >= right_score) { + CV_Assert(left < heap->size); + heap->swap(heap, parent, left); + parent = left; + } else { + // right_score can't be less than left_score if right_score is -INFINITY. + CV_Assert(right < heap->size); + heap->swap(heap, parent, right); + parent = right; + } + } + + return 1; +} + +int zmaxheap_remove_max(zmaxheap_t *heap, void *p, float *v) +{ + return zmaxheap_remove_index(heap, 0, p, v); +} + +}} diff --git a/modules/objdetect/src/aruco/apriltag/zmaxheap.hpp b/modules/objdetect/src/aruco/apriltag/zmaxheap.hpp new file mode 100644 index 0000000000..7d3fbc0811 --- /dev/null +++ b/modules/objdetect/src/aruco/apriltag/zmaxheap.hpp @@ -0,0 +1,38 @@ +// This file is part of OpenCV project. +// It is subject to the license terms in the LICENSE file found in the top-level directory +// of this distribution and at http://opencv.org/license.html. +// +// Copyright (C) 2013-2016, The Regents of The University of Michigan. +// +// This software was developed in the APRIL Robotics Lab under the +// direction of Edwin Olson, ebolson@umich.edu. This software may be +// available under alternative licensing terms; contact the address above. +// +// The views and conclusions contained in the software and documentation are those +// of the authors and should not be interpreted as representing official policies, +// either expressed or implied, of the Regents of The University of Michigan. +#ifndef _OPENCV_ZMAXHEAP_HPP_ +#define _OPENCV_ZMAXHEAP_HPP_ + +namespace cv { +namespace aruco { +typedef struct zmaxheap zmaxheap_t; + +typedef struct zmaxheap_iterator zmaxheap_iterator_t; +struct zmaxheap_iterator { + zmaxheap_t *heap; + int in, out; +}; + +zmaxheap_t *zmaxheap_create(size_t el_sz); + +void zmaxheap_destroy(zmaxheap_t *heap); + +void zmaxheap_add(zmaxheap_t *heap, void *p, float v); + +// returns 0 if the heap is empty, so you can do +// while (zmaxheap_remove_max(...)) { } +int zmaxheap_remove_max(zmaxheap_t *heap, void *p, float *v); + +}} +#endif diff --git a/modules/objdetect/src/aruco/aruco_board.cpp b/modules/objdetect/src/aruco/aruco_board.cpp new file mode 100644 index 0000000000..23bf4cf77f --- /dev/null +++ b/modules/objdetect/src/aruco/aruco_board.cpp @@ -0,0 +1,507 @@ +// This file is part of OpenCV project. +// It is subject to the license terms in the LICENSE file found in the top-level directory +// of this distribution and at http://opencv.org/license.html + +#include "../precomp.hpp" +#include +#include + +namespace cv { +namespace aruco { +using namespace std; + +struct Board::BoardImpl { + std::vector > objPoints; + Dictionary dictionary; + Point3f rightBottomBorder; + std::vector ids; + + BoardImpl() { + dictionary = Dictionary(getPredefinedDictionary(PredefinedDictionaryType::DICT_4X4_50)); + } +}; + +Board::Board(): boardImpl(makePtr()) {} + +Board::~Board() {} + +Ptr Board::create(InputArrayOfArrays objPoints, const Dictionary &dictionary, InputArray ids) { + CV_Assert(objPoints.total() == ids.total()); + CV_Assert(objPoints.type() == CV_32FC3 || objPoints.type() == CV_32FC1); + + vector > obj_points_vector; + Point3f rightBottomBorder = Point3f(0.f, 0.f, 0.f); + for (unsigned int i = 0; i < objPoints.total(); i++) { + vector corners; + Mat corners_mat = objPoints.getMat(i); + + if (corners_mat.type() == CV_32FC1) + corners_mat = corners_mat.reshape(3); + CV_Assert(corners_mat.total() == 4); + + for (int j = 0; j < 4; j++) { + const Point3f &corner = corners_mat.at(j); + corners.push_back(corner); + rightBottomBorder.x = std::max(rightBottomBorder.x, corner.x); + rightBottomBorder.y = std::max(rightBottomBorder.y, corner.y); + rightBottomBorder.z = std::max(rightBottomBorder.z, corner.z); + } + obj_points_vector.push_back(corners); + } + Board board; + Ptr res = makePtr(board); + ids.copyTo(res->boardImpl->ids); + res->boardImpl->objPoints = obj_points_vector; + res->boardImpl->dictionary = dictionary; + res->boardImpl->rightBottomBorder = rightBottomBorder; + return res; +} + +const Dictionary& Board::getDictionary() const { + return this->boardImpl->dictionary; +} + +const vector >& Board::getObjPoints() const { + return this->boardImpl->objPoints; +} + +const Point3f& Board::getRightBottomCorner() const { + return this->boardImpl->rightBottomBorder; +} + +const vector& Board::getIds() const { + return this->boardImpl->ids; +} + +/** @brief Implementation of draw planar board that accepts a raw Board pointer. + */ +void Board::generateImage(Size outSize, OutputArray img, int marginSize, int borderBits) const { + CV_Assert(!outSize.empty()); + CV_Assert(marginSize >= 0); + + img.create(outSize, CV_8UC1); + Mat out = img.getMat(); + out.setTo(Scalar::all(255)); + out.adjustROI(-marginSize, -marginSize, -marginSize, -marginSize); + + // calculate max and min values in XY plane + CV_Assert(this->getObjPoints().size() > 0); + float minX, maxX, minY, maxY; + minX = maxX = this->getObjPoints()[0][0].x; + minY = maxY = this->getObjPoints()[0][0].y; + + for(unsigned int i = 0; i < this->getObjPoints().size(); i++) { + for(int j = 0; j < 4; j++) { + minX = min(minX, this->getObjPoints()[i][j].x); + maxX = max(maxX, this->getObjPoints()[i][j].x); + minY = min(minY, this->getObjPoints()[i][j].y); + maxY = max(maxY, this->getObjPoints()[i][j].y); + } + } + + float sizeX = maxX - minX; + float sizeY = maxY - minY; + + // proportion transformations + float xReduction = sizeX / float(out.cols); + float yReduction = sizeY / float(out.rows); + + // determine the zone where the markers are placed + if(xReduction > yReduction) { + int nRows = int(sizeY / xReduction); + int rowsMargins = (out.rows - nRows) / 2; + out.adjustROI(-rowsMargins, -rowsMargins, 0, 0); + } else { + int nCols = int(sizeX / yReduction); + int colsMargins = (out.cols - nCols) / 2; + out.adjustROI(0, 0, -colsMargins, -colsMargins); + } + + // now paint each marker + Mat marker; + Point2f outCorners[3]; + Point2f inCorners[3]; + for(unsigned int m = 0; m < this->getObjPoints().size(); m++) { + // transform corners to markerZone coordinates + for(int j = 0; j < 3; j++) { + Point2f pf = Point2f(this->getObjPoints()[m][j].x, this->getObjPoints()[m][j].y); + // move top left to 0, 0 + pf -= Point2f(minX, minY); + pf.x = pf.x / sizeX * float(out.cols); + pf.y = pf.y / sizeY * float(out.rows); + outCorners[j] = pf; + } + + // get marker + Size dst_sz(outCorners[2] - outCorners[0]); // assuming CCW order + dst_sz.width = dst_sz.height = std::min(dst_sz.width, dst_sz.height); //marker should be square + getDictionary().generateImageMarker(this->getIds()[m], dst_sz.width, marker, borderBits); + + if((outCorners[0].y == outCorners[1].y) && (outCorners[1].x == outCorners[2].x)) { + // marker is aligned to image axes + marker.copyTo(out(Rect(outCorners[0], dst_sz))); + continue; + } + + // interpolate tiny marker to marker position in markerZone + inCorners[0] = Point2f(-0.5f, -0.5f); + inCorners[1] = Point2f(marker.cols - 0.5f, -0.5f); + inCorners[2] = Point2f(marker.cols - 0.5f, marker.rows - 0.5f); + + // remove perspective + Mat transformation = getAffineTransform(inCorners, outCorners); + warpAffine(marker, out, transformation, out.size(), INTER_LINEAR, + BORDER_TRANSPARENT); + } +} + +void Board::matchImagePoints(InputArray detectedCorners, InputArray detectedIds, + OutputArray _objPoints, OutputArray imgPoints) const { + CV_Assert(getIds().size() == getObjPoints().size()); + CV_Assert(detectedIds.total() == detectedCorners.total()); + + size_t nDetectedMarkers = detectedIds.total(); + + vector objPnts; + objPnts.reserve(nDetectedMarkers); + + vector imgPnts; + imgPnts.reserve(nDetectedMarkers); + + // look for detected markers that belong to the board and get their information + for(unsigned int i = 0; i < nDetectedMarkers; i++) { + int currentId = detectedIds.getMat().ptr< int >(0)[i]; + for(unsigned int j = 0; j < getIds().size(); j++) { + if(currentId == getIds()[j]) { + for(int p = 0; p < 4; p++) { + objPnts.push_back(getObjPoints()[j][p]); + imgPnts.push_back(detectedCorners.getMat(i).ptr(0)[p]); + } + } + } + } + + // create output + Mat(objPnts).copyTo(_objPoints); + Mat(imgPnts).copyTo(imgPoints); +} + +struct GridBoard::GridImpl { + GridImpl(){}; + // number of markers in X and Y directions + int sizeX = 3, sizeY = 3; + + // marker side length (normally in meters) + float markerLength = 1.f; + + // separation between markers in the grid + float markerSeparation = .5f; +}; + +GridBoard::GridBoard(): gridImpl(makePtr()) {} + +Ptr GridBoard::create(int markersX, int markersY, float markerLength, float markerSeparation, + const Dictionary &dictionary, InputArray ids) { + CV_Assert(markersX > 0 && markersY > 0 && markerLength > 0 && markerSeparation > 0); + GridBoard board; + Ptr res = makePtr(board); + res->gridImpl->sizeX = markersX; + res->gridImpl->sizeY = markersY; + res->gridImpl->markerLength = markerLength; + res->gridImpl->markerSeparation = markerSeparation; + res->boardImpl->dictionary = dictionary; + + size_t totalMarkers = (size_t) markersX * markersY; + CV_Assert(totalMarkers == ids.total()); + vector > objPoints; + objPoints.reserve(totalMarkers); + ids.copyTo(res->boardImpl->ids); + // calculate Board objPoints + for (int y = 0; y < markersY; y++) { + for (int x = 0; x < markersX; x++) { + vector corners(4); + corners[0] = Point3f(x * (markerLength + markerSeparation), + y * (markerLength + markerSeparation), 0); + corners[1] = corners[0] + Point3f(markerLength, 0, 0); + corners[2] = corners[0] + Point3f(markerLength, markerLength, 0); + corners[3] = corners[0] + Point3f(0, markerLength, 0); + objPoints.push_back(corners); + } + } + res->boardImpl->objPoints = objPoints; + res->boardImpl->rightBottomBorder = Point3f(markersX * markerLength + markerSeparation * (markersX - 1), + markersY * markerLength + markerSeparation * (markersY - 1), 0.f); + return res; +} + +Ptr GridBoard::create(int markersX, int markersY, float markerLength, float markerSeparation, + const Dictionary &dictionary, int firstMarker) { + vector ids(markersX*markersY); + std::iota(ids.begin(), ids.end(), firstMarker); + return GridBoard::create(markersX, markersY, markerLength, markerSeparation, dictionary, ids); +} + +void GridBoard::generateImage(Size outSize, OutputArray _img, int marginSize, int borderBits) const { + Board::generateImage(outSize, _img, marginSize, borderBits); +} + +Size GridBoard::getGridSize() const { + return Size(gridImpl->sizeX, gridImpl->sizeY); +} + +float GridBoard::getMarkerLength() const { + return gridImpl->markerLength; +} + +float GridBoard::getMarkerSeparation() const { + return gridImpl->markerSeparation; +} + +struct CharucoBoard::CharucoImpl : GridBoard::GridImpl { + // size of chessboard squares side (normally in meters) + float squareLength; + + // marker side length (normally in meters) + float markerLength; + + static void _getNearestMarkerCorners(CharucoBoard &board, float squareLength); + + // vector of chessboard 3D corners precalculated + std::vector chessboardCorners; + + // for each charuco corner, nearest marker id and nearest marker corner id of each marker + std::vector > nearestMarkerIdx; + std::vector > nearestMarkerCorners; +}; + +CharucoBoard::CharucoBoard(): charucoImpl(makePtr()) {} + +void CharucoBoard::generateImage(Size outSize, OutputArray _img, int marginSize, int borderBits) const { + CV_Assert(!outSize.empty()); + CV_Assert(marginSize >= 0); + + _img.create(outSize, CV_8UC1); + _img.setTo(255); + Mat out = _img.getMat(); + Mat noMarginsImg = + out.colRange(marginSize, out.cols - marginSize).rowRange(marginSize, out.rows - marginSize); + + double totalLengthX, totalLengthY; + totalLengthX = charucoImpl->squareLength * charucoImpl->sizeX; + totalLengthY = charucoImpl->squareLength * charucoImpl->sizeY; + + // proportional transformation + double xReduction = totalLengthX / double(noMarginsImg.cols); + double yReduction = totalLengthY / double(noMarginsImg.rows); + + // determine the zone where the chessboard is placed + Mat chessboardZoneImg; + if(xReduction > yReduction) { + int nRows = int(totalLengthY / xReduction); + int rowsMargins = (noMarginsImg.rows - nRows) / 2; + chessboardZoneImg = noMarginsImg.rowRange(rowsMargins, noMarginsImg.rows - rowsMargins); + } else { + int nCols = int(totalLengthX / yReduction); + int colsMargins = (noMarginsImg.cols - nCols) / 2; + chessboardZoneImg = noMarginsImg.colRange(colsMargins, noMarginsImg.cols - colsMargins); + } + + // determine the margins to draw only the markers + // take the minimum just to be sure + double squareSizePixels = min(double(chessboardZoneImg.cols) / double(charucoImpl->sizeX), + double(chessboardZoneImg.rows) / double(charucoImpl->sizeY)); + + double diffSquareMarkerLength = (charucoImpl->squareLength - charucoImpl->markerLength) / 2; + int diffSquareMarkerLengthPixels = + int(diffSquareMarkerLength * squareSizePixels / charucoImpl->squareLength); + + // draw markers + Mat markersImg; + Board::generateImage(chessboardZoneImg.size(), markersImg, diffSquareMarkerLengthPixels, borderBits); + markersImg.copyTo(chessboardZoneImg); + + // now draw black squares + for(int y = 0; y < charucoImpl->sizeY; y++) { + for(int x = 0; x < charucoImpl->sizeX; x++) { + + if(y % 2 != x % 2) continue; // white corner, dont do anything + + double startX, startY; + startX = squareSizePixels * double(x); + startY = squareSizePixels * double(y); + + Mat squareZone = chessboardZoneImg.rowRange(int(startY), int(startY + squareSizePixels)) + .colRange(int(startX), int(startX + squareSizePixels)); + + squareZone.setTo(0); + } + } +} + +/** + * Fill nearestMarkerIdx and nearestMarkerCorners arrays + */ +void CharucoBoard::CharucoImpl::_getNearestMarkerCorners(CharucoBoard &board, float squareLength) { + board.charucoImpl->nearestMarkerIdx.resize(board.charucoImpl->chessboardCorners.size()); + board.charucoImpl->nearestMarkerCorners.resize(board.charucoImpl->chessboardCorners.size()); + + unsigned int nMarkers = (unsigned int)board.getIds().size(); + unsigned int nCharucoCorners = (unsigned int)board.charucoImpl->chessboardCorners.size(); + for(unsigned int i = 0; i < nCharucoCorners; i++) { + double minDist = -1; // distance of closest markers + Point3f charucoCorner = board.charucoImpl->chessboardCorners[i]; + for(unsigned int j = 0; j < nMarkers; j++) { + // calculate distance from marker center to charuco corner + Point3f center = Point3f(0, 0, 0); + for(unsigned int k = 0; k < 4; k++) + center += board.getObjPoints()[j][k]; + center /= 4.; + double sqDistance; + Point3f distVector = charucoCorner - center; + sqDistance = distVector.x * distVector.x + distVector.y * distVector.y; + if(j == 0 || fabs(sqDistance - minDist) < cv::pow(0.01 * squareLength, 2)) { + // if same minimum distance (or first iteration), add to nearestMarkerIdx vector + board.charucoImpl->nearestMarkerIdx[i].push_back(j); + minDist = sqDistance; + } else if(sqDistance < minDist) { + // if finding a closest marker to the charuco corner + board.charucoImpl->nearestMarkerIdx[i].clear(); // remove any previous added marker + board.charucoImpl->nearestMarkerIdx[i].push_back(j); // add the new closest marker index + minDist = sqDistance; + } + } + // for each of the closest markers, search the marker corner index closer + // to the charuco corner + for(unsigned int j = 0; j < board.charucoImpl->nearestMarkerIdx[i].size(); j++) { + board.charucoImpl->nearestMarkerCorners[i].resize(board.charucoImpl->nearestMarkerIdx[i].size()); + double minDistCorner = -1; + for(unsigned int k = 0; k < 4; k++) { + double sqDistance; + Point3f distVector = charucoCorner - board.getObjPoints()[board.charucoImpl->nearestMarkerIdx[i][j]][k]; + sqDistance = distVector.x * distVector.x + distVector.y * distVector.y; + if(k == 0 || sqDistance < minDistCorner) { + // if this corner is closer to the charuco corner, assing its index + // to nearestMarkerCorners + minDistCorner = sqDistance; + board.charucoImpl->nearestMarkerCorners[i][j] = k; + } + } + } + } +} + +Ptr CharucoBoard::create(int squaresX, int squaresY, float squareLength, float markerLength, + const Dictionary &dictionary, InputArray ids) { + CV_Assert(squaresX > 1 && squaresY > 1 && markerLength > 0 && squareLength > markerLength); + CharucoBoard board; + Ptr res = makePtr(board); + + res->charucoImpl->sizeX = squaresX; + res->charucoImpl->sizeY = squaresY; + res->charucoImpl->squareLength = squareLength; + res->charucoImpl->markerLength = markerLength; + res->boardImpl->dictionary = dictionary; + vector > objPoints; + + float diffSquareMarkerLength = (squareLength - markerLength) / 2; + int totalMarkers = (int)(ids.total()); + ids.copyTo(res->boardImpl->ids); + // calculate Board objPoints + int nextId = 0; + for(int y = 0; y < squaresY; y++) { + for(int x = 0; x < squaresX; x++) { + + if(y % 2 == x % 2) continue; // black corner, no marker here + + vector corners(4); + corners[0] = Point3f(x * squareLength + diffSquareMarkerLength, + y * squareLength + diffSquareMarkerLength, 0); + corners[1] = corners[0] + Point3f(markerLength, 0, 0); + corners[2] = corners[0] + Point3f(markerLength, markerLength, 0); + corners[3] = corners[0] + Point3f(0, markerLength, 0); + objPoints.push_back(corners); + // first ids in dictionary + if (totalMarkers == 0) + res->boardImpl->ids.push_back(nextId); + nextId++; + } + } + if (totalMarkers > 0 && nextId != totalMarkers) + CV_Error(cv::Error::StsBadSize, "Size of ids must be equal to the number of markers: "+std::to_string(nextId)); + res->boardImpl->objPoints = objPoints; + + // now fill chessboardCorners + for(int y = 0; y < squaresY - 1; y++) { + for(int x = 0; x < squaresX - 1; x++) { + Point3f corner; + corner.x = (x + 1) * squareLength; + corner.y = (y + 1) * squareLength; + corner.z = 0; + res->charucoImpl->chessboardCorners.push_back(corner); + } + } + res->boardImpl->rightBottomBorder = Point3f(squaresX * squareLength, squaresY * squareLength, 0.f); + CharucoBoard::CharucoImpl::_getNearestMarkerCorners(*res, res->charucoImpl->squareLength); + return res; +} + +Size CharucoBoard::getChessboardSize() const { return Size(charucoImpl->sizeX, charucoImpl->sizeY); } + +float CharucoBoard::getSquareLength() const { return charucoImpl->squareLength; } + +float CharucoBoard::getMarkerLength() const { return charucoImpl->markerLength; } + +bool CharucoBoard::checkCharucoCornersCollinear(InputArray charucoIds) const { + unsigned int nCharucoCorners = (unsigned int)charucoIds.getMat().total(); + if (nCharucoCorners <= 2) + return true; + + // only test if there are 3 or more corners + CV_Assert(charucoImpl->chessboardCorners.size() >= charucoIds.getMat().total()); + + Vec point0(charucoImpl->chessboardCorners[charucoIds.getMat().at(0)].x, + charucoImpl->chessboardCorners[charucoIds.getMat().at(0)].y, 1); + + Vec point1(charucoImpl->chessboardCorners[charucoIds.getMat().at(1)].x, + charucoImpl->chessboardCorners[charucoIds.getMat().at(1)].y, 1); + + // create a line from the first two points. + Vec testLine = point0.cross(point1); + Vec testPoint(0, 0, 1); + + double divisor = sqrt(testLine[0]*testLine[0] + testLine[1]*testLine[1]); + CV_Assert(divisor != 0.0); + + // normalize the line with normal + testLine /= divisor; + + double dotProduct; + for (unsigned int i = 2; i < nCharucoCorners; i++){ + testPoint(0) = charucoImpl->chessboardCorners[charucoIds.getMat().at(i)].x; + testPoint(1) = charucoImpl->chessboardCorners[charucoIds.getMat().at(i)].y; + + // if testPoint is on testLine, dotProduct will be zero (or very, very close) + dotProduct = testPoint.dot(testLine); + + if (std::abs(dotProduct) > 1e-6){ + return false; + } + } + // no points found that were off of testLine, return true that all points collinear. + return true; +} + +std::vector CharucoBoard::getChessboardCorners() const { + return charucoImpl->chessboardCorners; +} + +std::vector > CharucoBoard::getNearestMarkerIdx() const { + return charucoImpl->nearestMarkerIdx; +} + +std::vector > CharucoBoard::getNearestMarkerCorners() const { + return charucoImpl->nearestMarkerCorners; +} + +} +} diff --git a/modules/objdetect/src/aruco/aruco_detector.cpp b/modules/objdetect/src/aruco/aruco_detector.cpp new file mode 100644 index 0000000000..c23545c6ad --- /dev/null +++ b/modules/objdetect/src/aruco/aruco_detector.cpp @@ -0,0 +1,1365 @@ +// This file is part of OpenCV project. +// It is subject to the license terms in the LICENSE file found in the top-level directory +// of this distribution and at http://opencv.org/license.html + +#include "../precomp.hpp" +#include + +#include "opencv2/objdetect/aruco_detector.hpp" +#include "opencv2/objdetect/aruco_board.hpp" +#include "apriltag/apriltag_quad_thresh.hpp" +#include "aruco_utils.hpp" +#include + +namespace cv { +namespace aruco { + +using namespace std; + +static inline bool readWrite(DetectorParameters ¶ms, const Ptr& readNode, + const Ptr& writeStorage = nullptr) { + CV_Assert(!readNode.empty() || !writeStorage.empty()); + bool check = false; + + check |= readWriteParameter("adaptiveThreshWinSizeMin", params.adaptiveThreshWinSizeMin, *readNode, *writeStorage); + check |= readWriteParameter("adaptiveThreshWinSizeMax", params.adaptiveThreshWinSizeMax, *readNode, *writeStorage); + check |= readWriteParameter("adaptiveThreshWinSizeStep", params.adaptiveThreshWinSizeStep, *readNode, *writeStorage); + check |= readWriteParameter("adaptiveThreshConstant", params.adaptiveThreshConstant, *readNode, *writeStorage); + check |= readWriteParameter("minMarkerPerimeterRate", params.minMarkerPerimeterRate, *readNode, *writeStorage); + check |= readWriteParameter("maxMarkerPerimeterRate", params.maxMarkerPerimeterRate, *readNode, *writeStorage); + check |= readWriteParameter("polygonalApproxAccuracyRate", params.polygonalApproxAccuracyRate, + *readNode, *writeStorage); + check |= readWriteParameter("minCornerDistanceRate", params.minCornerDistanceRate, *readNode, *writeStorage); + check |= readWriteParameter("minDistanceToBorder", params.minDistanceToBorder, *readNode, *writeStorage); + check |= readWriteParameter("minMarkerDistanceRate", params.minMarkerDistanceRate, *readNode, *writeStorage); + check |= readWriteParameter("cornerRefinementMethod", params.cornerRefinementMethod, *readNode, *writeStorage); + check |= readWriteParameter("cornerRefinementWinSize", params.cornerRefinementWinSize, *readNode, *writeStorage); + check |= readWriteParameter("cornerRefinementMaxIterations", params.cornerRefinementMaxIterations, + *readNode, *writeStorage); + check |= readWriteParameter("cornerRefinementMinAccuracy", params.cornerRefinementMinAccuracy, + *readNode, *writeStorage); + check |= readWriteParameter("markerBorderBits", params.markerBorderBits, *readNode, *writeStorage); + check |= readWriteParameter("perspectiveRemovePixelPerCell", params.perspectiveRemovePixelPerCell, + *readNode, *writeStorage); + check |= readWriteParameter("perspectiveRemoveIgnoredMarginPerCell", params.perspectiveRemoveIgnoredMarginPerCell, + *readNode, *writeStorage); + check |= readWriteParameter("maxErroneousBitsInBorderRate", params.maxErroneousBitsInBorderRate, + *readNode, *writeStorage); + check |= readWriteParameter("minOtsuStdDev", params.minOtsuStdDev, *readNode, *writeStorage); + check |= readWriteParameter("errorCorrectionRate", params.errorCorrectionRate, *readNode, *writeStorage); + // new aruco 3 functionality + check |= readWriteParameter("useAruco3Detection", params.useAruco3Detection, *readNode, *writeStorage); + check |= readWriteParameter("minSideLengthCanonicalImg", params.minSideLengthCanonicalImg, *readNode, *writeStorage); + check |= readWriteParameter("minMarkerLengthRatioOriginalImg", params.minMarkerLengthRatioOriginalImg, + *readNode, *writeStorage); + return check; +} + +bool DetectorParameters::readDetectorParameters(const FileNode& fn) { + if(fn.empty()) + return false; + Ptr pfn = makePtr(fn); + return readWrite(*this, pfn); +} + +bool DetectorParameters::writeDetectorParameters(const Ptr& fs, const String& name) { + if (fs.empty()) + return false; + if(name.empty()) + return writeDetectorParameters(*fs); + *fs << name << "{"; + bool res = writeDetectorParameters(*fs); + *fs << "}"; + return res; +} + +bool DetectorParameters::writeDetectorParameters(FileStorage &fs) { + if (!fs.isOpened()) + return false; + return readWrite(*this, nullptr, makePtr(fs)); +} + +static inline bool readWrite(RefineParameters& refineParameters, const Ptr& readNode, + const Ptr& writeStorage = nullptr) { + CV_Assert(!readNode.empty() || !writeStorage.empty()); + bool check = false; + + check |= readWriteParameter("minRepDistance", refineParameters.minRepDistance, *readNode, *writeStorage); + check |= readWriteParameter("errorCorrectionRate", refineParameters.errorCorrectionRate, *readNode, *writeStorage); + check |= readWriteParameter("checkAllOrders", refineParameters.checkAllOrders, *readNode, *writeStorage); + return check; +} + +RefineParameters::RefineParameters(float _minRepDistance, float _errorCorrectionRate, bool _checkAllOrders): + minRepDistance(_minRepDistance), errorCorrectionRate(_errorCorrectionRate), + checkAllOrders(_checkAllOrders){} + +bool RefineParameters::readRefineParameters(const FileNode &fn) { + if(fn.empty()) + return false; + Ptr pfn = makePtr(fn); + return readWrite(*this, pfn); +} + +bool RefineParameters::writeRefineParameters(FileStorage &fs) { + if(!fs.isOpened()) + return false; + return readWrite(*this, nullptr, makePtr(fs)); +} + +bool RefineParameters::writeRefineParameters(const Ptr& fs, const String& name) { + if(fs.empty()) + return false; + if(name.empty()) + return writeRefineParameters(*fs); + *fs << name << "{"; + bool res = writeRefineParameters(*fs); + *fs << "}"; + return res; +} + +/** + * @brief Threshold input image using adaptive thresholding + */ +static void _threshold(InputArray _in, OutputArray _out, int winSize, double constant) { + + CV_Assert(winSize >= 3); + if(winSize % 2 == 0) winSize++; // win size must be odd + adaptiveThreshold(_in, _out, 255, ADAPTIVE_THRESH_MEAN_C, THRESH_BINARY_INV, winSize, constant); +} + + +/** + * @brief Given a tresholded image, find the contours, calculate their polygonal approximation + * and take those that accomplish some conditions + */ +static void _findMarkerContours(const Mat &in, vector > &candidates, + vector > &contoursOut, double minPerimeterRate, + double maxPerimeterRate, double accuracyRate, + double minCornerDistanceRate, int minDistanceToBorder, int minSize) { + + CV_Assert(minPerimeterRate > 0 && maxPerimeterRate > 0 && accuracyRate > 0 && + minCornerDistanceRate >= 0 && minDistanceToBorder >= 0); + + // calculate maximum and minimum sizes in pixels + unsigned int minPerimeterPixels = + (unsigned int)(minPerimeterRate * max(in.cols, in.rows)); + unsigned int maxPerimeterPixels = + (unsigned int)(maxPerimeterRate * max(in.cols, in.rows)); + + // for aruco3 functionality + if (minSize != 0) { + minPerimeterPixels = 4*minSize; + } + + Mat contoursImg; + in.copyTo(contoursImg); + vector > contours; + findContours(contoursImg, contours, RETR_LIST, CHAIN_APPROX_NONE); + // now filter list of contours + for(unsigned int i = 0; i < contours.size(); i++) { + // check perimeter + if(contours[i].size() < minPerimeterPixels || contours[i].size() > maxPerimeterPixels) + continue; + + // check is square and is convex + vector approxCurve; + approxPolyDP(contours[i], approxCurve, double(contours[i].size()) * accuracyRate, true); + if(approxCurve.size() != 4 || !isContourConvex(approxCurve)) continue; + + // check min distance between corners + double minDistSq = + max(contoursImg.cols, contoursImg.rows) * max(contoursImg.cols, contoursImg.rows); + for(int j = 0; j < 4; j++) { + double d = (double)(approxCurve[j].x - approxCurve[(j + 1) % 4].x) * + (double)(approxCurve[j].x - approxCurve[(j + 1) % 4].x) + + (double)(approxCurve[j].y - approxCurve[(j + 1) % 4].y) * + (double)(approxCurve[j].y - approxCurve[(j + 1) % 4].y); + minDistSq = min(minDistSq, d); + } + double minCornerDistancePixels = double(contours[i].size()) * minCornerDistanceRate; + if(minDistSq < minCornerDistancePixels * minCornerDistancePixels) continue; + + // check if it is too near to the image border + bool tooNearBorder = false; + for(int j = 0; j < 4; j++) { + if(approxCurve[j].x < minDistanceToBorder || approxCurve[j].y < minDistanceToBorder || + approxCurve[j].x > contoursImg.cols - 1 - minDistanceToBorder || + approxCurve[j].y > contoursImg.rows - 1 - minDistanceToBorder) + tooNearBorder = true; + } + if(tooNearBorder) continue; + + // if it passes all the test, add to candidates vector + vector currentCandidate; + currentCandidate.resize(4); + for(int j = 0; j < 4; j++) { + currentCandidate[j] = Point2f((float)approxCurve[j].x, (float)approxCurve[j].y); + } + candidates.push_back(currentCandidate); + contoursOut.push_back(contours[i]); + } +} + + +/** + * @brief Assure order of candidate corners is clockwise direction + */ +static void _reorderCandidatesCorners(vector > &candidates) { + + for(unsigned int i = 0; i < candidates.size(); i++) { + double dx1 = candidates[i][1].x - candidates[i][0].x; + double dy1 = candidates[i][1].y - candidates[i][0].y; + double dx2 = candidates[i][2].x - candidates[i][0].x; + double dy2 = candidates[i][2].y - candidates[i][0].y; + double crossProduct = (dx1 * dy2) - (dy1 * dx2); + + if(crossProduct < 0.0) { // not clockwise direction + swap(candidates[i][1], candidates[i][3]); + } + } +} + +/** + * @brief to make sure that the corner's order of both candidates (default/white) is the same + */ +static vector alignContourOrder(Point2f corner, vector candidate) { + uint8_t r=0; + double min = norm( Vec2f( corner - candidate[0] ), NORM_L2SQR); + for(uint8_t pos=1; pos < 4; pos++) { + double nDiff = norm( Vec2f( corner - candidate[pos] ), NORM_L2SQR); + if(nDiff < min){ + r = pos; + min =nDiff; + } + } + std::rotate(candidate.begin(), candidate.begin() + r, candidate.end()); + return candidate; +} + +/** + * @brief Check candidates that are too close to each other, save the potential candidates + * (i.e. biggest/smallest contour) and remove the rest + */ +static void _filterTooCloseCandidates(const vector > &candidatesIn, + vector > > &candidatesSetOut, + const vector > &contoursIn, + vector > > &contoursSetOut, + double minMarkerDistanceRate, bool detectInvertedMarker) { + + CV_Assert(minMarkerDistanceRate >= 0); + vector candGroup; + candGroup.resize(candidatesIn.size(), -1); + vector > groupedCandidates; + for(unsigned int i = 0; i < candidatesIn.size(); i++) { + bool isSingleContour = true; + for(unsigned int j = i + 1; j < candidatesIn.size(); j++) { + + int minimumPerimeter = min((int)contoursIn[i].size(), (int)contoursIn[j].size() ); + + // fc is the first corner considered on one of the markers, 4 combinations are possible + for(int fc = 0; fc < 4; fc++) { + double distSq = 0; + for(int c = 0; c < 4; c++) { + // modC is the corner considering first corner is fc + int modC = (c + fc) % 4; + distSq += (candidatesIn[i][modC].x - candidatesIn[j][c].x) * + (candidatesIn[i][modC].x - candidatesIn[j][c].x) + + (candidatesIn[i][modC].y - candidatesIn[j][c].y) * + (candidatesIn[i][modC].y - candidatesIn[j][c].y); + } + distSq /= 4.; + + // if mean square distance is too low, remove the smaller one of the two markers + double minMarkerDistancePixels = double(minimumPerimeter) * minMarkerDistanceRate; + if(distSq < minMarkerDistancePixels * minMarkerDistancePixels) { + isSingleContour = false; + // i and j are not related to a group + if(candGroup[i]<0 && candGroup[j]<0){ + // mark candidates with their corresponding group number + candGroup[i] = candGroup[j] = (int)groupedCandidates.size(); + + // create group + vector grouped; + grouped.push_back(i); + grouped.push_back(j); + groupedCandidates.push_back( grouped ); + } + // i is related to a group + else if(candGroup[i] > -1 && candGroup[j] == -1){ + int group = candGroup[i]; + candGroup[j] = group; + + // add to group + groupedCandidates[group].push_back( j ); + } + // j is related to a group + else if(candGroup[j] > -1 && candGroup[i] == -1){ + int group = candGroup[j]; + candGroup[i] = group; + + // add to group + groupedCandidates[group].push_back( i ); + } + } + } + } + if (isSingleContour && candGroup[i] < 0) + { + candGroup[i] = (int)groupedCandidates.size(); + vector grouped; + grouped.push_back(i); + grouped.push_back(i); // step "save possible candidates" require minimum 2 elements + groupedCandidates.push_back(grouped); + } + } + + // save possible candidates + candidatesSetOut.clear(); + contoursSetOut.clear(); + + vector > biggerCandidates; + vector > biggerContours; + vector > smallerCandidates; + vector > smallerContours; + + // save possible candidates + for(unsigned int i = 0; i < groupedCandidates.size(); i++) { + unsigned int smallerIdx = groupedCandidates[i][0]; + unsigned int biggerIdx = smallerIdx; + double smallerArea = contourArea(candidatesIn[smallerIdx]); + double biggerArea = smallerArea; + + // evaluate group elements + for(unsigned int j = 1; j < groupedCandidates[i].size(); j++) { + unsigned int currIdx = groupedCandidates[i][j]; + double currArea = contourArea(candidatesIn[currIdx]); + + // check if current contour is bigger + if(currArea >= biggerArea) { + biggerIdx = currIdx; + biggerArea = currArea; + } + + // check if current contour is smaller + if(currArea < smallerArea && detectInvertedMarker) { + smallerIdx = currIdx; + smallerArea = currArea; + } + } + + // add contours and candidates + biggerCandidates.push_back(candidatesIn[biggerIdx]); + biggerContours.push_back(contoursIn[biggerIdx]); + if(detectInvertedMarker) { + smallerCandidates.push_back(alignContourOrder(candidatesIn[biggerIdx][0], candidatesIn[smallerIdx])); + smallerContours.push_back(contoursIn[smallerIdx]); + } + } + // to preserve the structure :: candidateSet< defaultCandidates, whiteCandidates > + // default candidates + candidatesSetOut.push_back(biggerCandidates); + contoursSetOut.push_back(biggerContours); + // white candidates + candidatesSetOut.push_back(smallerCandidates); + contoursSetOut.push_back(smallerContours); +} + +/** + * @brief Initial steps on finding square candidates + */ +static void _detectInitialCandidates(const Mat &grey, vector > &candidates, + vector > &contours, + const DetectorParameters ¶ms) { + + CV_Assert(params.adaptiveThreshWinSizeMin >= 3 && params.adaptiveThreshWinSizeMax >= 3); + CV_Assert(params.adaptiveThreshWinSizeMax >= params.adaptiveThreshWinSizeMin); + CV_Assert(params.adaptiveThreshWinSizeStep > 0); + + // number of window sizes (scales) to apply adaptive thresholding + int nScales = (params.adaptiveThreshWinSizeMax - params.adaptiveThreshWinSizeMin) / + params.adaptiveThreshWinSizeStep + 1; + + vector > > candidatesArrays((size_t) nScales); + vector > > contoursArrays((size_t) nScales); + + ////for each value in the interval of thresholding window sizes + parallel_for_(Range(0, nScales), [&](const Range& range) { + const int begin = range.start; + const int end = range.end; + + for (int i = begin; i < end; i++) { + int currScale = params.adaptiveThreshWinSizeMin + i * params.adaptiveThreshWinSizeStep; + // threshold + Mat thresh; + _threshold(grey, thresh, currScale, params.adaptiveThreshConstant); + + // detect rectangles + _findMarkerContours(thresh, candidatesArrays[i], contoursArrays[i], + params.minMarkerPerimeterRate, params.maxMarkerPerimeterRate, + params.polygonalApproxAccuracyRate, params.minCornerDistanceRate, + params.minDistanceToBorder, params.minSideLengthCanonicalImg); + } + }); + // join candidates + for(int i = 0; i < nScales; i++) { + for(unsigned int j = 0; j < candidatesArrays[i].size(); j++) { + candidates.push_back(candidatesArrays[i][j]); + contours.push_back(contoursArrays[i][j]); + } + } +} + + +/** + * @brief Detect square candidates in the input image + */ +static void _detectCandidates(InputArray _grayImage, vector > >& candidatesSetOut, + vector > >& contoursSetOut, const DetectorParameters &_params) { + Mat grey = _grayImage.getMat(); + CV_DbgAssert(grey.total() != 0); + CV_DbgAssert(grey.type() == CV_8UC1); + + /// 1. DETECT FIRST SET OF CANDIDATES + vector > candidates; + vector > contours; + _detectInitialCandidates(grey, candidates, contours, _params); + /// 2. SORT CORNERS + _reorderCandidatesCorners(candidates); + + /// 3. FILTER OUT NEAR CANDIDATE PAIRS + // save the outter/inner border (i.e. potential candidates) + _filterTooCloseCandidates(candidates, candidatesSetOut, contours, contoursSetOut, + _params.minMarkerDistanceRate, _params.detectInvertedMarker); +} + + +/** + * @brief Given an input image and candidate corners, extract the bits of the candidate, including + * the border bits + */ +static Mat _extractBits(InputArray _image, const vector& corners, int markerSize, + int markerBorderBits, int cellSize, double cellMarginRate, double minStdDevOtsu) { + CV_Assert(_image.getMat().channels() == 1); + CV_Assert(corners.size() == 4ull); + CV_Assert(markerBorderBits > 0 && cellSize > 0 && cellMarginRate >= 0 && cellMarginRate <= 1); + CV_Assert(minStdDevOtsu >= 0); + + // number of bits in the marker + int markerSizeWithBorders = markerSize + 2 * markerBorderBits; + int cellMarginPixels = int(cellMarginRate * cellSize); + + Mat resultImg; // marker image after removing perspective + int resultImgSize = markerSizeWithBorders * cellSize; + Mat resultImgCorners(4, 1, CV_32FC2); + resultImgCorners.ptr(0)[0] = Point2f(0, 0); + resultImgCorners.ptr(0)[1] = Point2f((float)resultImgSize - 1, 0); + resultImgCorners.ptr(0)[2] = + Point2f((float)resultImgSize - 1, (float)resultImgSize - 1); + resultImgCorners.ptr(0)[3] = Point2f(0, (float)resultImgSize - 1); + + // remove perspective + Mat transformation = getPerspectiveTransform(corners, resultImgCorners); + warpPerspective(_image, resultImg, transformation, Size(resultImgSize, resultImgSize), + INTER_NEAREST); + + // output image containing the bits + Mat bits(markerSizeWithBorders, markerSizeWithBorders, CV_8UC1, Scalar::all(0)); + + // check if standard deviation is enough to apply Otsu + // if not enough, it probably means all bits are the same color (black or white) + Mat mean, stddev; + // Remove some border just to avoid border noise from perspective transformation + Mat innerRegion = resultImg.colRange(cellSize / 2, resultImg.cols - cellSize / 2) + .rowRange(cellSize / 2, resultImg.rows - cellSize / 2); + meanStdDev(innerRegion, mean, stddev); + if(stddev.ptr< double >(0)[0] < minStdDevOtsu) { + // all black or all white, depending on mean value + if(mean.ptr< double >(0)[0] > 127) + bits.setTo(1); + else + bits.setTo(0); + return bits; + } + + // now extract code, first threshold using Otsu + threshold(resultImg, resultImg, 125, 255, THRESH_BINARY | THRESH_OTSU); + + // for each cell + for(int y = 0; y < markerSizeWithBorders; y++) { + for(int x = 0; x < markerSizeWithBorders; x++) { + int Xstart = x * (cellSize) + cellMarginPixels; + int Ystart = y * (cellSize) + cellMarginPixels; + Mat square = resultImg(Rect(Xstart, Ystart, cellSize - 2 * cellMarginPixels, + cellSize - 2 * cellMarginPixels)); + // count white pixels on each cell to assign its value + size_t nZ = (size_t) countNonZero(square); + if(nZ > square.total() / 2) bits.at(y, x) = 1; + } + } + + return bits; +} + + + +/** + * @brief Return number of erroneous bits in border, i.e. number of white bits in border. + */ +static int _getBorderErrors(const Mat &bits, int markerSize, int borderSize) { + + int sizeWithBorders = markerSize + 2 * borderSize; + + CV_Assert(markerSize > 0 && bits.cols == sizeWithBorders && bits.rows == sizeWithBorders); + + int totalErrors = 0; + for(int y = 0; y < sizeWithBorders; y++) { + for(int k = 0; k < borderSize; k++) { + if(bits.ptr(y)[k] != 0) totalErrors++; + if(bits.ptr(y)[sizeWithBorders - 1 - k] != 0) totalErrors++; + } + } + for(int x = borderSize; x < sizeWithBorders - borderSize; x++) { + for(int k = 0; k < borderSize; k++) { + if(bits.ptr(k)[x] != 0) totalErrors++; + if(bits.ptr(sizeWithBorders - 1 - k)[x] != 0) totalErrors++; + } + } + return totalErrors; +} + + +/** + * @brief Tries to identify one candidate given the dictionary + * @return candidate typ. zero if the candidate is not valid, + * 1 if the candidate is a black candidate (default candidate) + * 2 if the candidate is a white candidate + */ +static uint8_t _identifyOneCandidate(const Dictionary& dictionary, InputArray _image, + const vector& _corners, int& idx, + const DetectorParameters& params, int& rotation, + const float scale = 1.f) { + CV_DbgAssert(_corners.size() == 4); + CV_DbgAssert(_image.getMat().total() != 0); + CV_DbgAssert(params.markerBorderBits > 0); + uint8_t typ=1; + // get bits + // scale corners to the correct size to search on the corresponding image pyramid + vector scaled_corners(4); + for (int i = 0; i < 4; ++i) { + scaled_corners[i].x = _corners[i].x * scale; + scaled_corners[i].y = _corners[i].y * scale; + } + + Mat candidateBits = + _extractBits(_image, scaled_corners, dictionary.markerSize, params.markerBorderBits, + params.perspectiveRemovePixelPerCell, + params.perspectiveRemoveIgnoredMarginPerCell, params.minOtsuStdDev); + + // analyze border bits + int maximumErrorsInBorder = + int(dictionary.markerSize * dictionary.markerSize * params.maxErroneousBitsInBorderRate); + int borderErrors = + _getBorderErrors(candidateBits, dictionary.markerSize, params.markerBorderBits); + + // check if it is a white marker + if(params.detectInvertedMarker){ + // to get from 255 to 1 + Mat invertedImg = ~candidateBits-254; + int invBError = _getBorderErrors(invertedImg, dictionary.markerSize, params.markerBorderBits); + // white marker + if(invBError maximumErrorsInBorder) return 0; // border is wrong + + // take only inner bits + Mat onlyBits = + candidateBits.rowRange(params.markerBorderBits, + candidateBits.rows - params.markerBorderBits) + .colRange(params.markerBorderBits, candidateBits.cols - params.markerBorderBits); + + // try to indentify the marker + if(!dictionary.identify(onlyBits, idx, rotation, params.errorCorrectionRate)) + return 0; + + return typ; +} + +/** + * @brief rotate the initial corner to get to the right position + */ +static void correctCornerPosition(vector& _candidate, int rotate){ + std::rotate(_candidate.begin(), _candidate.begin() + 4 - rotate, _candidate.end()); +} + +static size_t _findOptPyrImageForCanonicalImg( + const vector& img_pyr, + const int scaled_width, + const int cur_perimeter, + const int min_perimeter) { + CV_Assert(scaled_width > 0); + size_t optLevel = 0; + float dist = std::numeric_limits::max(); + for (size_t i = 0; i < img_pyr.size(); ++i) { + const float scale = img_pyr[i].cols / static_cast(scaled_width); + const float perimeter_scaled = cur_perimeter * scale; + // instead of std::abs() favor the larger pyramid level by checking if the distance is postive + // will slow down the algorithm but find more corners in the end + const float new_dist = perimeter_scaled - min_perimeter; + if (new_dist < dist && new_dist > 0.f) { + dist = new_dist; + optLevel = i; + } + } + return optLevel; +} + +/** + * @brief Identify square candidates according to a marker dictionary + */ + +static void _identifyCandidates(InputArray grey, + const vector& image_pyr, + vector > >& _candidatesSet, + vector > >& _contoursSet, const Dictionary &_dictionary, + vector >& _accepted, vector >& _contours, vector& ids, + const DetectorParameters ¶ms, + OutputArrayOfArrays _rejected = noArray()) { + CV_DbgAssert(grey.getMat().total() != 0); + CV_DbgAssert(grey.getMat().type() == CV_8UC1); + int ncandidates = (int)_candidatesSet[0].size(); + vector > accepted; + vector > rejected; + vector > contours; + + vector idsTmp(ncandidates, -1); + vector rotated(ncandidates, 0); + vector validCandidates(ncandidates, 0); + + //// Analyze each of the candidates + parallel_for_(Range(0, ncandidates), [&](const Range &range) { + const int begin = range.start; + const int end = range.end; + + vector >& candidates = params.detectInvertedMarker ? _candidatesSet[1] : _candidatesSet[0]; + vector >& contourS = params.detectInvertedMarker ? _contoursSet[1] : _contoursSet[0]; + + for(int i = begin; i < end; i++) { + int currId = -1; + // implements equation (4) + if (params.useAruco3Detection) { + const int perimeterOfContour = static_cast(contourS[i].size()); + const int min_perimeter = params.minSideLengthCanonicalImg * 4; + const size_t nearestImgId = _findOptPyrImageForCanonicalImg(image_pyr, grey.cols(), perimeterOfContour, min_perimeter); + const float scale = image_pyr[nearestImgId].cols / static_cast(grey.cols()); + + validCandidates[i] = _identifyOneCandidate(_dictionary, image_pyr[nearestImgId], candidates[i], currId, params, rotated[i], scale); + } + else { + validCandidates[i] = _identifyOneCandidate(_dictionary, grey, candidates[i], currId, params, rotated[i]); + } + + if(validCandidates[i] > 0) + idsTmp[i] = currId; + } + }); + + for(int i = 0; i < ncandidates; i++) { + if(validCandidates[i] > 0) { + // to choose the right set of candidates :: 0 for default, 1 for white markers + uint8_t set = validCandidates[i]-1; + + // shift corner positions to the correct rotation + correctCornerPosition(_candidatesSet[set][i], rotated[i]); + + if( !params.detectInvertedMarker && validCandidates[i] == 2 ) + continue; + + // add valid candidate + accepted.push_back(_candidatesSet[set][i]); + ids.push_back(idsTmp[i]); + + contours.push_back(_contoursSet[set][i]); + + } else { + rejected.push_back(_candidatesSet[0][i]); + } + } + + // parse output + _accepted = accepted; + + _contours= contours; + + if(_rejected.needed()) { + _copyVector2Output(rejected, _rejected); + } +} + +/** + * Line fitting A * B = C :: Called from function refineCandidateLines + * @param nContours, contour-container + */ +static Point3f _interpolate2Dline(const vector& nContours){ + CV_Assert(nContours.size() >= 2); + float minX, minY, maxX, maxY; + minX = maxX = nContours[0].x; + minY = maxY = nContours[0].y; + + for(unsigned int i = 0; i< nContours.size(); i++){ + minX = nContours[i].x < minX ? nContours[i].x : minX; + minY = nContours[i].y < minY ? nContours[i].y : minY; + maxX = nContours[i].x > maxX ? nContours[i].x : maxX; + maxY = nContours[i].y > maxY ? nContours[i].y : maxY; + } + + Mat A = Mat::ones((int)nContours.size(), 2, CV_32F); // Coefficient Matrix (N x 2) + Mat B((int)nContours.size(), 1, CV_32F); // Variables Matrix (N x 1) + Mat C; // Constant + + if(maxX - minX > maxY - minY){ + for(unsigned int i =0; i < nContours.size(); i++){ + A.at(i,0)= nContours[i].x; + B.at(i,0)= nContours[i].y; + } + + solve(A, B, C, DECOMP_NORMAL); + + return Point3f(C.at(0, 0), -1., C.at(1, 0)); + } + else{ + for(unsigned int i =0; i < nContours.size(); i++){ + A.at(i,0)= nContours[i].y; + B.at(i,0)= nContours[i].x; + } + + solve(A, B, C, DECOMP_NORMAL); + + return Point3f(-1., C.at(0, 0), C.at(1, 0)); + } + +} + +/** + * Find the Point where the lines crosses :: Called from function refineCandidateLines + * @param nLine1 + * @param nLine2 + * @return Crossed Point + */ +static Point2f _getCrossPoint(Point3f nLine1, Point3f nLine2){ + Matx22f A(nLine1.x, nLine1.y, nLine2.x, nLine2.y); + Vec2f B(-nLine1.z, -nLine2.z); + return Vec2f(A.solve(B).val); +} + +/** + * Refine Corners using the contour vector :: Called from function detectMarkers + * @param nContours, contour-container + * @param nCorners, candidate Corners + * @param camMatrix, cameraMatrix input 3x3 floating-point camera matrix + * @param distCoeff, distCoeffs vector of distortion coefficient + */ +static void _refineCandidateLines(vector& nContours, vector& nCorners){ + vector contour2f(nContours.begin(), nContours.end()); + /* 5 groups :: to group the edges + * 4 - classified by its corner + * extra group - (temporary) if contours do not begin with a corner + */ + vector cntPts[5]; + int cornerIndex[4]={-1}; + int group=4; + + for ( unsigned int i =0; i < nContours.size(); i++ ) { + for(unsigned int j=0; j<4; j++){ + if ( nCorners[j] == contour2f[i] ){ + cornerIndex[j] = i; + group=j; + } + } + cntPts[group].push_back(contour2f[i]); + } + for (int i = 0; i < 4; i++) + { + CV_Assert(cornerIndex[i] != -1); + } + // saves extra group into corresponding + if( !cntPts[4].empty() ){ + for( unsigned int i=0; i < cntPts[4].size() ; i++ ) + cntPts[group].push_back(cntPts[4].at(i)); + cntPts[4].clear(); + } + + //Evaluate contour direction :: using the position of the detected corners + int inc=1; + + inc = ( (cornerIndex[0] > cornerIndex[1]) && (cornerIndex[3] > cornerIndex[0]) ) ? -1:inc; + inc = ( (cornerIndex[2] > cornerIndex[3]) && (cornerIndex[1] > cornerIndex[2]) ) ? -1:inc; + + // calculate the line :: who passes through the grouped points + Point3f lines[4]; + for(int i=0; i<4; i++){ + lines[i]=_interpolate2Dline(cntPts[i]); + } + + /* + * calculate the corner :: where the lines crosses to each other + * clockwise direction no clockwise direction + * 0 1 + * .---. 1 .---. 2 + * | | | | + * 3 .___. 0 .___. + * 2 3 + */ + for(int i=0; i < 4; i++){ + if(inc<0) + nCorners[i] = _getCrossPoint(lines[ i ], lines[ (i+1)%4 ]); // 01 12 23 30 + else + nCorners[i] = _getCrossPoint(lines[ i ], lines[ (i+3)%4 ]); // 30 01 12 23 + } +} + +static inline void findCornerInPyrImage(const float scale_init, const int closest_pyr_image_idx, + const vector& grey_pyramid, Mat corners, + const DetectorParameters& params) { + // scale them to the closest pyramid level + if (scale_init != 1.f) + corners *= scale_init; // scale_init * scale_pyr + for (int idx = closest_pyr_image_idx - 1; idx >= 0; --idx) { + // scale them to new pyramid level + corners *= 2.f; // *= scale_pyr; + // use larger win size for larger images + const int subpix_win_size = std::max(grey_pyramid[idx].cols, grey_pyramid[idx].rows) > 1080 ? 5 : 3; + cornerSubPix(grey_pyramid[idx], corners, + Size(subpix_win_size, subpix_win_size), + Size(-1, -1), + TermCriteria(TermCriteria::MAX_ITER | TermCriteria::EPS, + params.cornerRefinementMaxIterations, + params.cornerRefinementMinAccuracy)); + } +} + +struct ArucoDetector::ArucoDetectorImpl { + /// dictionary indicates the type of markers that will be searched + Dictionary dictionary; + + /// marker detection parameters, check DetectorParameters docs to see available settings + DetectorParameters detectorParams; + + /// marker refine parameters + RefineParameters refineParams; + ArucoDetectorImpl() {} + + ArucoDetectorImpl(const Dictionary &_dictionary, const DetectorParameters &_detectorParams, + const RefineParameters& _refineParams): dictionary(_dictionary), + detectorParams(_detectorParams), refineParams(_refineParams) {} + +}; + +ArucoDetector::ArucoDetector(const Dictionary &_dictionary, + const DetectorParameters &_detectorParams, + const RefineParameters& _refineParams) { + arucoDetectorImpl = makePtr(_dictionary, _detectorParams, _refineParams); +} + +void ArucoDetector::detectMarkers(InputArray _image, OutputArrayOfArrays _corners, OutputArray _ids, + OutputArrayOfArrays _rejectedImgPoints) { + CV_Assert(!_image.empty()); + DetectorParameters& detectorParams = arucoDetectorImpl->detectorParams; + const Dictionary& dictionary = arucoDetectorImpl->dictionary; + + CV_Assert(detectorParams.markerBorderBits > 0); + // check that the parameters are set correctly if Aruco3 is used + CV_Assert(!(detectorParams.useAruco3Detection == true && + detectorParams.minSideLengthCanonicalImg == 0 && + detectorParams.minMarkerLengthRatioOriginalImg == 0.0)); + + Mat grey; + _convertToGrey(_image.getMat(), grey); + + // Aruco3 functionality is the extension of Aruco. + // The description can be found in: + // [1] Speeded up detection of squared fiducial markers, 2018, FJ Romera-Ramirez et al. + // if Aruco3 functionality if not wanted + // change some parameters to be sure to turn it off + if (!detectorParams.useAruco3Detection) { + detectorParams.minMarkerLengthRatioOriginalImg = 0.0; + detectorParams.minSideLengthCanonicalImg = 0; + } + else { + // always turn on corner refinement in case of Aruco3, due to upsampling + detectorParams.cornerRefinementMethod = CORNER_REFINE_SUBPIX; + // only CORNER_REFINE_SUBPIX implement correctly for useAruco3Detection + // Todo: update other CORNER_REFINE methods + } + + /// Step 0: equation (2) from paper [1] + const float fxfy = (!detectorParams.useAruco3Detection ? 1.f : detectorParams.minSideLengthCanonicalImg / + (detectorParams.minSideLengthCanonicalImg + std::max(grey.cols, grey.rows)* + detectorParams.minMarkerLengthRatioOriginalImg)); + + /// Step 1: create image pyramid. Section 3.4. in [1] + vector grey_pyramid; + int closest_pyr_image_idx = 0, num_levels = 0; + //// Step 1.1: resize image with equation (1) from paper [1] + if (detectorParams.useAruco3Detection) { + const float scale_pyr = 2.f; + const float img_area = static_cast(grey.rows*grey.cols); + const float min_area_marker = static_cast(detectorParams.minSideLengthCanonicalImg* + detectorParams.minSideLengthCanonicalImg); + // find max level + num_levels = static_cast(log2(img_area / min_area_marker)/scale_pyr); + // the closest pyramid image to the downsampled segmentation image + // will later be used as start index for corner upsampling + const float scale_img_area = img_area * fxfy * fxfy; + closest_pyr_image_idx = cvRound(log2(img_area / scale_img_area)/scale_pyr); + } + buildPyramid(grey, grey_pyramid, num_levels); + + // resize to segmentation image + // in this reduces size the contours will be detected + if (fxfy != 1.f) + resize(grey, grey, Size(cvRound(fxfy * grey.cols), cvRound(fxfy * grey.rows))); + + /// STEP 2: Detect marker candidates + vector > candidates; + vector > contours; + vector ids; + + vector > > candidatesSet; + vector > > contoursSet; + + /// STEP 2.a Detect marker candidates :: using AprilTag + if(detectorParams.cornerRefinementMethod == CORNER_REFINE_APRILTAG){ + _apriltag(grey, detectorParams, candidates, contours); + + candidatesSet.push_back(candidates); + contoursSet.push_back(contours); + } + /// STEP 2.b Detect marker candidates :: traditional way + else + _detectCandidates(grey, candidatesSet, contoursSet, detectorParams); + + /// STEP 2: Check candidate codification (identify markers) + _identifyCandidates(grey, grey_pyramid, candidatesSet, contoursSet, dictionary, + candidates, contours, ids, detectorParams, _rejectedImgPoints); + + /// STEP 3: Corner refinement :: use corner subpix + if (detectorParams.cornerRefinementMethod == CORNER_REFINE_SUBPIX) { + CV_Assert(detectorParams.cornerRefinementWinSize > 0 && detectorParams.cornerRefinementMaxIterations > 0 && + detectorParams.cornerRefinementMinAccuracy > 0); + // Do subpixel estimation. In Aruco3 start on the lowest pyramid level and upscale the corners + parallel_for_(Range(0, (int)candidates.size()), [&](const Range& range) { + const int begin = range.start; + const int end = range.end; + + for (int i = begin; i < end; i++) { + if (detectorParams.useAruco3Detection) { + const float scale_init = (float) grey_pyramid[closest_pyr_image_idx].cols / grey.cols; + findCornerInPyrImage(scale_init, closest_pyr_image_idx, grey_pyramid, Mat(candidates[i]), detectorParams); + } + else + cornerSubPix(grey, Mat(candidates[i]), + Size(detectorParams.cornerRefinementWinSize, detectorParams.cornerRefinementWinSize), + Size(-1, -1), + TermCriteria(TermCriteria::MAX_ITER | TermCriteria::EPS, + detectorParams.cornerRefinementMaxIterations, + detectorParams.cornerRefinementMinAccuracy)); + } + }); + } + + /// STEP 3, Optional : Corner refinement :: use contour container + if (detectorParams.cornerRefinementMethod == CORNER_REFINE_CONTOUR){ + + if (!_ids.empty()) { + + // do corner refinement using the contours for each detected markers + parallel_for_(Range(0, (int)candidates.size()), [&](const Range& range) { + for (int i = range.start; i < range.end; i++) { + _refineCandidateLines(contours[i], candidates[i]); + } + }); + } + } + + if (detectorParams.cornerRefinementMethod != CORNER_REFINE_SUBPIX && fxfy != 1.f) { + // only CORNER_REFINE_SUBPIX implement correctly for useAruco3Detection + // Todo: update other CORNER_REFINE methods + + // scale to orignal size, this however will lead to inaccurate detections! + for (auto &vecPoints : candidates) + for (auto &point : vecPoints) + point *= 1.f/fxfy; + } + + // copy to output arrays + _copyVector2Output(candidates, _corners); + Mat(ids).copyTo(_ids); +} + +/** + * Project board markers that are not included in the list of detected markers + */ +static void _projectUndetectedMarkers(const Ptr &_board, InputOutputArrayOfArrays _detectedCorners, + InputOutputArray _detectedIds, InputArray _cameraMatrix, InputArray _distCoeffs, + vector >& _undetectedMarkersProjectedCorners, + OutputArray _undetectedMarkersIds) { + // first estimate board pose with the current avaible markers + Mat rvec, tvec; + int boardDetectedMarkers = 0; + { + CV_Assert(_detectedCorners.total() == _detectedIds.total()); + // get object and image points for the solvePnP function + Mat detectedObjPoints, imgPoints; + _board->matchImagePoints(_detectedCorners, _detectedIds, detectedObjPoints, imgPoints); + CV_Assert(imgPoints.total() == detectedObjPoints.total()); + if(detectedObjPoints.total() > 0) // 0 of the detected markers in board + { + solvePnP(detectedObjPoints, imgPoints, _cameraMatrix, _distCoeffs, rvec, tvec); + // divide by four since all the four corners are concatenated in the array for each marker + boardDetectedMarkers = static_cast(detectedObjPoints.total()) / 4; + } + } + + // at least one marker from board so rvec and tvec are valid + if(boardDetectedMarkers == 0) return; + + // search undetected markers and project them using the previous pose + vector > undetectedCorners; + vector undetectedIds; + for(unsigned int i = 0; i < _board->getIds().size(); i++) { + int foundIdx = -1; + for(unsigned int j = 0; j < _detectedIds.total(); j++) { + if(_board->getIds()[i] == _detectedIds.getMat().ptr()[j]) { + foundIdx = j; + break; + } + } + + // not detected + if(foundIdx == -1) { + undetectedCorners.push_back(vector()); + undetectedIds.push_back(_board->getIds()[i]); + projectPoints(_board->getObjPoints()[i], rvec, tvec, _cameraMatrix, _distCoeffs, + undetectedCorners.back()); + } + } + // parse output + Mat(undetectedIds).copyTo(_undetectedMarkersIds); + _undetectedMarkersProjectedCorners = undetectedCorners; +} + +/** + * Interpolate board markers that are not included in the list of detected markers using + * global homography + */ +static void _projectUndetectedMarkers(const Ptr &_board, InputOutputArrayOfArrays _detectedCorners, + InputOutputArray _detectedIds, + vector >& _undetectedMarkersProjectedCorners, + OutputArray _undetectedMarkersIds) { + // check board points are in the same plane, if not, global homography cannot be applied + CV_Assert(_board->getObjPoints().size() > 0); + CV_Assert(_board->getObjPoints()[0].size() > 0); + float boardZ = _board->getObjPoints()[0][0].z; + for(unsigned int i = 0; i < _board->getObjPoints().size(); i++) { + for(unsigned int j = 0; j < _board->getObjPoints()[i].size(); j++) + CV_Assert(boardZ == _board->getObjPoints()[i][j].z); + } + + vector detectedMarkersObj2DAll; // Object coordinates (without Z) of all the detected + // marker corners in a single vector + vector imageCornersAll; // Image corners of all detected markers in a single vector + vector > undetectedMarkersObj2D; // Object coordinates (without Z) of all + // missing markers in different vectors + vector undetectedMarkersIds; // ids of missing markers + // find markers included in board, and missing markers from board. Fill the previous vectors + for(unsigned int j = 0; j < _board->getIds().size(); j++) { + bool found = false; + for(unsigned int i = 0; i < _detectedIds.total(); i++) { + if(_detectedIds.getMat().ptr()[i] == _board->getIds()[j]) { + for(int c = 0; c < 4; c++) { + imageCornersAll.push_back(_detectedCorners.getMat(i).ptr()[c]); + detectedMarkersObj2DAll.push_back( + Point2f(_board->getObjPoints()[j][c].x, _board->getObjPoints()[j][c].y)); + } + found = true; + break; + } + } + if(!found) { + undetectedMarkersObj2D.push_back(vector()); + for(int c = 0; c < 4; c++) { + undetectedMarkersObj2D.back().push_back( + Point2f(_board->getObjPoints()[j][c].x, _board->getObjPoints()[j][c].y)); + } + undetectedMarkersIds.push_back(_board->getIds()[j]); + } + } + if(imageCornersAll.size() == 0) return; + + // get homography from detected markers + Mat transformation = findHomography(detectedMarkersObj2DAll, imageCornersAll); + + _undetectedMarkersProjectedCorners.resize(undetectedMarkersIds.size()); + + // for each undetected marker, apply transformation + for(unsigned int i = 0; i < undetectedMarkersObj2D.size(); i++) { + perspectiveTransform(undetectedMarkersObj2D[i], _undetectedMarkersProjectedCorners[i], transformation); + } + Mat(undetectedMarkersIds).copyTo(_undetectedMarkersIds); +} + +void ArucoDetector::refineDetectedMarkers(InputArray _image, const Ptr &_board, + InputOutputArrayOfArrays _detectedCorners, InputOutputArray _detectedIds, + InputOutputArrayOfArrays _rejectedCorners, InputArray _cameraMatrix, + InputArray _distCoeffs, OutputArray _recoveredIdxs) { + DetectorParameters& detectorParams = arucoDetectorImpl->detectorParams; + const Dictionary& dictionary = arucoDetectorImpl->dictionary; + RefineParameters& refineParams = arucoDetectorImpl->refineParams; + CV_Assert(refineParams.minRepDistance > 0); + + if(_detectedIds.total() == 0 || _rejectedCorners.total() == 0) return; + + // get projections of missing markers in the board + vector > undetectedMarkersCorners; + vector undetectedMarkersIds; + if(_cameraMatrix.total() != 0) { + // reproject based on camera projection model + _projectUndetectedMarkers(_board, _detectedCorners, _detectedIds, _cameraMatrix, _distCoeffs, + undetectedMarkersCorners, undetectedMarkersIds); + + } else { + // reproject based on global homography + _projectUndetectedMarkers(_board, _detectedCorners, _detectedIds, undetectedMarkersCorners, + undetectedMarkersIds); + } + + // list of missing markers indicating if they have been assigned to a candidate + vector alreadyIdentified(_rejectedCorners.total(), false); + + // maximum bits that can be corrected + int maxCorrectionRecalculated = + int(double(dictionary.maxCorrectionBits) * refineParams.errorCorrectionRate); + + Mat grey; + _convertToGrey(_image, grey); + + // vector of final detected marker corners and ids + vector > finalAcceptedCorners; + vector finalAcceptedIds; + // fill with the current markers + finalAcceptedCorners.resize(_detectedCorners.total()); + finalAcceptedIds.resize(_detectedIds.total()); + for(unsigned int i = 0; i < _detectedIds.total(); i++) { + finalAcceptedCorners[i] = _detectedCorners.getMat(i).clone(); + finalAcceptedIds[i] = _detectedIds.getMat().ptr()[i]; + } + vector recoveredIdxs; // original indexes of accepted markers in _rejectedCorners + + // for each missing marker, try to find a correspondence + for(unsigned int i = 0; i < undetectedMarkersIds.size(); i++) { + + // best match at the moment + int closestCandidateIdx = -1; + double closestCandidateDistance = refineParams.minRepDistance * refineParams.minRepDistance + 1; + Mat closestRotatedMarker; + + for(unsigned int j = 0; j < _rejectedCorners.total(); j++) { + if(alreadyIdentified[j]) continue; + + // check distance + double minDistance = closestCandidateDistance + 1; + bool valid = false; + int validRot = 0; + for(int c = 0; c < 4; c++) { // first corner in rejected candidate + double currentMaxDistance = 0; + for(int k = 0; k < 4; k++) { + Point2f rejCorner = _rejectedCorners.getMat(j).ptr()[(c + k) % 4]; + Point2f distVector = undetectedMarkersCorners[i][k] - rejCorner; + double cornerDist = distVector.x * distVector.x + distVector.y * distVector.y; + currentMaxDistance = max(currentMaxDistance, cornerDist); + } + // if distance is better than current best distance + if(currentMaxDistance < closestCandidateDistance) { + valid = true; + validRot = c; + minDistance = currentMaxDistance; + } + if(!refineParams.checkAllOrders) break; + } + + if(!valid) continue; + + // apply rotation + Mat rotatedMarker; + if(refineParams.checkAllOrders) { + rotatedMarker = Mat(4, 1, CV_32FC2); + for(int c = 0; c < 4; c++) + rotatedMarker.ptr()[c] = + _rejectedCorners.getMat(j).ptr()[(c + 4 + validRot) % 4]; + } + else rotatedMarker = _rejectedCorners.getMat(j); + + // last filter, check if inner code is close enough to the assigned marker code + int codeDistance = 0; + // if errorCorrectionRate, dont check code + if(refineParams.errorCorrectionRate >= 0) { + + // extract bits + Mat bits = _extractBits( + grey, rotatedMarker, dictionary.markerSize, detectorParams.markerBorderBits, + detectorParams.perspectiveRemovePixelPerCell, + detectorParams.perspectiveRemoveIgnoredMarginPerCell, detectorParams.minOtsuStdDev); + + Mat onlyBits = + bits.rowRange(detectorParams.markerBorderBits, bits.rows - detectorParams.markerBorderBits) + .colRange(detectorParams.markerBorderBits, bits.rows - detectorParams.markerBorderBits); + + codeDistance = + dictionary.getDistanceToId(onlyBits, undetectedMarkersIds[i], false); + } + + // if everythin is ok, assign values to current best match + if(refineParams.errorCorrectionRate < 0 || codeDistance < maxCorrectionRecalculated) { + closestCandidateIdx = j; + closestCandidateDistance = minDistance; + closestRotatedMarker = rotatedMarker; + } + } + + // if at least one good match, we have rescue the missing marker + if(closestCandidateIdx >= 0) { + + // subpixel refinement + if(detectorParams.cornerRefinementMethod == CORNER_REFINE_SUBPIX) { + CV_Assert(detectorParams.cornerRefinementWinSize > 0 && + detectorParams.cornerRefinementMaxIterations > 0 && + detectorParams.cornerRefinementMinAccuracy > 0); + cornerSubPix(grey, closestRotatedMarker, + Size(detectorParams.cornerRefinementWinSize, detectorParams.cornerRefinementWinSize), + Size(-1, -1), TermCriteria(TermCriteria::MAX_ITER | TermCriteria::EPS, + detectorParams.cornerRefinementMaxIterations, + detectorParams.cornerRefinementMinAccuracy)); + } + + // remove from rejected + alreadyIdentified[closestCandidateIdx] = true; + + // add to detected + finalAcceptedCorners.push_back(closestRotatedMarker); + finalAcceptedIds.push_back(undetectedMarkersIds[i]); + + // add the original index of the candidate + recoveredIdxs.push_back(closestCandidateIdx); + } + } + + // parse output + if(finalAcceptedIds.size() != _detectedIds.total()) { + // parse output + Mat(finalAcceptedIds).copyTo(_detectedIds); + _copyVector2Output(finalAcceptedCorners, _detectedCorners); + + // recalculate _rejectedCorners based on alreadyIdentified + vector > finalRejected; + for(unsigned int i = 0; i < alreadyIdentified.size(); i++) { + if(!alreadyIdentified[i]) { + finalRejected.push_back(_rejectedCorners.getMat(i).clone()); + } + } + _copyVector2Output(finalRejected, _rejectedCorners); + + if(_recoveredIdxs.needed()) { + Mat(recoveredIdxs).copyTo(_recoveredIdxs); + } + } +} + +void ArucoDetector::write(FileStorage &fs) const { + Ptr pfs = makePtr(fs); + arucoDetectorImpl->dictionary.writeDictionary(pfs); + arucoDetectorImpl->detectorParams.writeDetectorParameters(fs); + arucoDetectorImpl->refineParams.writeRefineParameters(fs); +} + +void ArucoDetector::read(const FileNode &fn) { + arucoDetectorImpl->dictionary.readDictionary(fn); + arucoDetectorImpl->detectorParams.readDetectorParameters(fn); + arucoDetectorImpl->refineParams.readRefineParameters(fn); +} + +const Dictionary& ArucoDetector::getDictionary() const { + return arucoDetectorImpl->dictionary; +} + +void ArucoDetector::setDictionary(const Dictionary& dictionary) { + arucoDetectorImpl->dictionary = dictionary; +} + +const DetectorParameters& ArucoDetector::getDetectorParameters() const { + return arucoDetectorImpl->detectorParams; +} + +void ArucoDetector::setDetectorParameters(const DetectorParameters& detectorParameters) { + arucoDetectorImpl->detectorParams = detectorParameters; +} + +const RefineParameters& ArucoDetector::getRefineParameters() const { + return arucoDetectorImpl->refineParams; +} + +void ArucoDetector::setRefineParameters(const RefineParameters& refineParameters) { + arucoDetectorImpl->refineParams = refineParameters; +} + +void drawDetectedMarkers(InputOutputArray _image, InputArrayOfArrays _corners, + InputArray _ids, Scalar borderColor) { + CV_Assert(_image.getMat().total() != 0 && + (_image.getMat().channels() == 1 || _image.getMat().channels() == 3)); + CV_Assert((_corners.total() == _ids.total()) || _ids.total() == 0); + + // calculate colors + Scalar textColor, cornerColor; + textColor = cornerColor = borderColor; + swap(textColor.val[0], textColor.val[1]); // text color just sawp G and R + swap(cornerColor.val[1], cornerColor.val[2]); // corner color just sawp G and B + + int nMarkers = (int)_corners.total(); + for(int i = 0; i < nMarkers; i++) { + Mat currentMarker = _corners.getMat(i); + CV_Assert(currentMarker.total() == 4 && currentMarker.type() == CV_32FC2); + + // draw marker sides + for(int j = 0; j < 4; j++) { + Point2f p0, p1; + p0 = currentMarker.ptr(0)[j]; + p1 = currentMarker.ptr(0)[(j + 1) % 4]; + line(_image, p0, p1, borderColor, 1); + } + // draw first corner mark + rectangle(_image, currentMarker.ptr(0)[0] - Point2f(3, 3), + currentMarker.ptr(0)[0] + Point2f(3, 3), cornerColor, 1, LINE_AA); + + // draw ID + if(_ids.total() != 0) { + Point2f cent(0, 0); + for(int p = 0; p < 4; p++) + cent += currentMarker.ptr(0)[p]; + cent = cent / 4.; + stringstream s; + s << "id=" << _ids.getMat().ptr(0)[i]; + putText(_image, s.str(), cent, FONT_HERSHEY_SIMPLEX, 0.5, textColor, 2); + } + } +} + +void generateImageMarker(const Dictionary &dictionary, int id, int sidePixels, OutputArray _img, int borderBits) { + dictionary.generateImageMarker(id, sidePixels, _img, borderBits); +} + +} +} diff --git a/modules/objdetect/src/aruco/aruco_dictionary.cpp b/modules/objdetect/src/aruco/aruco_dictionary.cpp new file mode 100644 index 0000000000..a0177acfee --- /dev/null +++ b/modules/objdetect/src/aruco/aruco_dictionary.cpp @@ -0,0 +1,441 @@ +// This file is part of OpenCV project. +// It is subject to the license terms in the LICENSE file found in the top-level directory +// of this distribution and at http://opencv.org/license.html + +#include "../precomp.hpp" +#include "opencv2/core/hal/hal.hpp" + +#include "aruco_utils.hpp" +#include "predefined_dictionaries.hpp" +#include "apriltag/predefined_dictionaries_apriltag.hpp" +#include + +namespace cv { +namespace aruco { + +using namespace std; + +Dictionary::Dictionary(): markerSize(0), maxCorrectionBits(0) {} + + +Dictionary::Dictionary(const Mat &_bytesList, int _markerSize, int _maxcorr) { + markerSize = _markerSize; + maxCorrectionBits = _maxcorr; + bytesList = _bytesList; +} + + +bool Dictionary::readDictionary(const cv::FileNode& fn) { + int nMarkers = 0, _markerSize = 0; + if (fn.empty() || !readParameter("nmarkers", nMarkers, fn) || !readParameter("markersize", _markerSize, fn)) + return false; + Mat bytes(0, 0, CV_8UC1), marker(_markerSize, _markerSize, CV_8UC1); + std::string markerString; + for (int i = 0; i < nMarkers; i++) { + std::ostringstream ostr; + ostr << i; + if (!readParameter("marker_" + ostr.str(), markerString, fn)) + return false; + for (int j = 0; j < (int) markerString.size(); j++) + marker.at(j) = (markerString[j] == '0') ? 0 : 1; + bytes.push_back(Dictionary::getByteListFromBits(marker)); + } + int _maxCorrectionBits = 0; + readParameter("maxCorrectionBits", _maxCorrectionBits, fn); + *this = Dictionary(bytes, _markerSize, _maxCorrectionBits); + return true; +} + +void Dictionary::writeDictionary(FileStorage &fs) { + fs << "nmarkers" << bytesList.rows; + fs << "markersize" << markerSize; + fs << "maxCorrectionBits" << maxCorrectionBits; + for (int i = 0; i < bytesList.rows; i++) { + Mat row = bytesList.row(i);; + Mat bitMarker = getBitsFromByteList(row, markerSize); + std::ostringstream ostr; + ostr << i; + string markerName = "marker_" + ostr.str(); + string marker; + for (int j = 0; j < markerSize * markerSize; j++) + marker.push_back(bitMarker.at(j) + '0'); + fs << markerName << marker; + } +} + +void Dictionary::writeDictionary(Ptr& fs, const String &name) { + if(name.empty()) + return writeDictionary(*fs); + *fs << name << "{"; + writeDictionary(*fs); + *fs << "}"; +} + + +bool Dictionary::identify(const Mat &onlyBits, int &idx, int &rotation, double maxCorrectionRate) const { + CV_Assert(onlyBits.rows == markerSize && onlyBits.cols == markerSize); + + int maxCorrectionRecalculed = int(double(maxCorrectionBits) * maxCorrectionRate); + + // get as a byte list + Mat candidateBytes = getByteListFromBits(onlyBits); + + idx = -1; // by default, not found + + // search closest marker in dict + for(int m = 0; m < bytesList.rows; m++) { + int currentMinDistance = markerSize * markerSize + 1; + int currentRotation = -1; + for(unsigned int r = 0; r < 4; r++) { + int currentHamming = cv::hal::normHamming( + bytesList.ptr(m)+r*candidateBytes.cols, + candidateBytes.ptr(), + candidateBytes.cols); + + if(currentHamming < currentMinDistance) { + currentMinDistance = currentHamming; + currentRotation = r; + } + } + + // if maxCorrection is fulfilled, return this one + if(currentMinDistance <= maxCorrectionRecalculed) { + idx = m; + rotation = currentRotation; + break; + } + } + + return idx != -1; +} + + +int Dictionary::getDistanceToId(InputArray bits, int id, bool allRotations) const { + + CV_Assert(id >= 0 && id < bytesList.rows); + + unsigned int nRotations = 4; + if(!allRotations) nRotations = 1; + + Mat candidateBytes = getByteListFromBits(bits.getMat()); + int currentMinDistance = int(bits.total() * bits.total()); + for(unsigned int r = 0; r < nRotations; r++) { + int currentHamming = cv::hal::normHamming( + bytesList.ptr(id) + r*candidateBytes.cols, + candidateBytes.ptr(), + candidateBytes.cols); + + if(currentHamming < currentMinDistance) { + currentMinDistance = currentHamming; + } + } + return currentMinDistance; +} + + +void Dictionary::generateImageMarker(int id, int sidePixels, OutputArray _img, int borderBits) const { + CV_Assert(sidePixels >= (markerSize + 2*borderBits)); + CV_Assert(id < bytesList.rows); + CV_Assert(borderBits > 0); + + _img.create(sidePixels, sidePixels, CV_8UC1); + + // create small marker with 1 pixel per bin + Mat tinyMarker(markerSize + 2 * borderBits, markerSize + 2 * borderBits, CV_8UC1, + Scalar::all(0)); + Mat innerRegion = tinyMarker.rowRange(borderBits, tinyMarker.rows - borderBits) + .colRange(borderBits, tinyMarker.cols - borderBits); + // put inner bits + Mat bits = 255 * getBitsFromByteList(bytesList.rowRange(id, id + 1), markerSize); + CV_Assert(innerRegion.total() == bits.total()); + bits.copyTo(innerRegion); + + // resize tiny marker to output size + cv::resize(tinyMarker, _img.getMat(), _img.getMat().size(), 0, 0, INTER_NEAREST); +} + + +Mat Dictionary::getByteListFromBits(const Mat &bits) { + // integer ceil + int nbytes = (bits.cols * bits.rows + 8 - 1) / 8; + + Mat candidateByteList(1, nbytes, CV_8UC4, Scalar::all(0)); + unsigned char currentBit = 0; + int currentByte = 0; + + // the 4 rotations + uchar* rot0 = candidateByteList.ptr(); + uchar* rot1 = candidateByteList.ptr() + 1*nbytes; + uchar* rot2 = candidateByteList.ptr() + 2*nbytes; + uchar* rot3 = candidateByteList.ptr() + 3*nbytes; + + for(int row = 0; row < bits.rows; row++) { + for(int col = 0; col < bits.cols; col++) { + // circular shift + rot0[currentByte] <<= 1; + rot1[currentByte] <<= 1; + rot2[currentByte] <<= 1; + rot3[currentByte] <<= 1; + // set bit + rot0[currentByte] |= bits.at(row, col); + rot1[currentByte] |= bits.at(col, bits.cols - 1 - row); + rot2[currentByte] |= bits.at(bits.rows - 1 - row, bits.cols - 1 - col); + rot3[currentByte] |= bits.at(bits.rows - 1 - col, row); + currentBit++; + if(currentBit == 8) { + // next byte + currentBit = 0; + currentByte++; + } + } + } + return candidateByteList; +} + + +Mat Dictionary::getBitsFromByteList(const Mat &byteList, int markerSize) { + CV_Assert(byteList.total() > 0 && + byteList.total() >= (unsigned int)markerSize * markerSize / 8 && + byteList.total() <= (unsigned int)markerSize * markerSize / 8 + 1); + Mat bits(markerSize, markerSize, CV_8UC1, Scalar::all(0)); + + unsigned char base2List[] = { 128, 64, 32, 16, 8, 4, 2, 1 }; + int currentByteIdx = 0; + // we only need the bytes in normal rotation + unsigned char currentByte = byteList.ptr()[0]; + int currentBit = 0; + for(int row = 0; row < bits.rows; row++) { + for(int col = 0; col < bits.cols; col++) { + if(currentByte >= base2List[currentBit]) { + bits.at(row, col) = 1; + currentByte -= base2List[currentBit]; + } + currentBit++; + if(currentBit == 8) { + currentByteIdx++; + currentByte = byteList.ptr()[currentByteIdx]; + // if not enough bits for one more byte, we are in the end + // update bit position accordingly + if(8 * (currentByteIdx + 1) > (int)bits.total()) + currentBit = 8 * (currentByteIdx + 1) - (int)bits.total(); + else + currentBit = 0; // ok, bits enough for next byte + } + } + } + return bits; +} + + +Dictionary getPredefinedDictionary(PredefinedDictionaryType name) { + // DictionaryData constructors calls + // moved out of globals so construted on first use, which allows lazy-loading of opencv dll + static const Dictionary DICT_ARUCO_DATA = Dictionary(Mat(1024, (5 * 5 + 7) / 8, CV_8UC4, (uchar*)DICT_ARUCO_BYTES), 5, 0); + + static const Dictionary DICT_4X4_50_DATA = Dictionary(Mat(50, (4 * 4 + 7) / 8, CV_8UC4, (uchar*)DICT_4X4_1000_BYTES), 4, 1); + static const Dictionary DICT_4X4_100_DATA = Dictionary(Mat(100, (4 * 4 + 7) / 8, CV_8UC4, (uchar*)DICT_4X4_1000_BYTES), 4, 1); + static const Dictionary DICT_4X4_250_DATA = Dictionary(Mat(250, (4 * 4 + 7) / 8, CV_8UC4, (uchar*)DICT_4X4_1000_BYTES), 4, 1); + static const Dictionary DICT_4X4_1000_DATA = Dictionary(Mat(1000, (4 * 4 + 7) / 8, CV_8UC4, (uchar*)DICT_4X4_1000_BYTES), 4, 0); + + static const Dictionary DICT_5X5_50_DATA = Dictionary(Mat(50, (5 * 5 + 7) / 8, CV_8UC4, (uchar*)DICT_5X5_1000_BYTES), 5, 3); + static const Dictionary DICT_5X5_100_DATA = Dictionary(Mat(100, (5 * 5 + 7) / 8, CV_8UC4, (uchar*)DICT_5X5_1000_BYTES), 5, 3); + static const Dictionary DICT_5X5_250_DATA = Dictionary(Mat(250, (5 * 5 + 7) / 8, CV_8UC4, (uchar*)DICT_5X5_1000_BYTES), 5, 2); + static const Dictionary DICT_5X5_1000_DATA = Dictionary(Mat(1000, (5 * 5 + 7) / 8, CV_8UC4, (uchar*)DICT_5X5_1000_BYTES), 5, 2); + + static const Dictionary DICT_6X6_50_DATA = Dictionary(Mat(50, (6 * 6 + 7) / 8, CV_8UC4, (uchar*)DICT_6X6_1000_BYTES), 6, 6); + static const Dictionary DICT_6X6_100_DATA = Dictionary(Mat(100, (6 * 6 + 7) / 8, CV_8UC4, (uchar*)DICT_6X6_1000_BYTES), 6, 5); + static const Dictionary DICT_6X6_250_DATA = Dictionary(Mat(250, (6 * 6 + 7) / 8, CV_8UC4, (uchar*)DICT_6X6_1000_BYTES), 6, 5); + static const Dictionary DICT_6X6_1000_DATA = Dictionary(Mat(1000, (6 * 6 + 7) / 8, CV_8UC4, (uchar*)DICT_6X6_1000_BYTES), 6, 4); + + static const Dictionary DICT_7X7_50_DATA = Dictionary(Mat(50, (7 * 7 + 7) / 8, CV_8UC4, (uchar*)DICT_7X7_1000_BYTES), 7, 9); + static const Dictionary DICT_7X7_100_DATA = Dictionary(Mat(100, (7 * 7 + 7) / 8, CV_8UC4, (uchar*)DICT_7X7_1000_BYTES), 7, 8); + static const Dictionary DICT_7X7_250_DATA = Dictionary(Mat(250, (7 * 7 + 7) / 8, CV_8UC4, (uchar*)DICT_7X7_1000_BYTES), 7, 8); + static const Dictionary DICT_7X7_1000_DATA = Dictionary(Mat(1000, (7 * 7 + 7) / 8, CV_8UC4, (uchar*)DICT_7X7_1000_BYTES), 7, 6); + + static const Dictionary DICT_APRILTAG_16h5_DATA = Dictionary(Mat(30, (4 * 4 + 7) / 8, CV_8UC4, (uchar*)DICT_APRILTAG_16h5_BYTES), 4, 0); + static const Dictionary DICT_APRILTAG_25h9_DATA = Dictionary(Mat(35, (5 * 5 + 7) / 8, CV_8UC4, (uchar*)DICT_APRILTAG_25h9_BYTES), 5, 0); + static const Dictionary DICT_APRILTAG_36h10_DATA = Dictionary(Mat(2320, (6 * 6 + 7) / 8, CV_8UC4, (uchar*)DICT_APRILTAG_36h10_BYTES), 6, 0); + static const Dictionary DICT_APRILTAG_36h11_DATA = Dictionary(Mat(587, (6 * 6 + 7) / 8, CV_8UC4, (uchar*)DICT_APRILTAG_36h11_BYTES), 6, 0); + + switch(name) { + + case DICT_ARUCO_ORIGINAL: + return Dictionary(DICT_ARUCO_DATA); + + case DICT_4X4_50: + return Dictionary(DICT_4X4_50_DATA); + case DICT_4X4_100: + return Dictionary(DICT_4X4_100_DATA); + case DICT_4X4_250: + return Dictionary(DICT_4X4_250_DATA); + case DICT_4X4_1000: + return Dictionary(DICT_4X4_1000_DATA); + + case DICT_5X5_50: + return Dictionary(DICT_5X5_50_DATA); + case DICT_5X5_100: + return Dictionary(DICT_5X5_100_DATA); + case DICT_5X5_250: + return Dictionary(DICT_5X5_250_DATA); + case DICT_5X5_1000: + return Dictionary(DICT_5X5_1000_DATA); + + case DICT_6X6_50: + return Dictionary(DICT_6X6_50_DATA); + case DICT_6X6_100: + return Dictionary(DICT_6X6_100_DATA); + case DICT_6X6_250: + return Dictionary(DICT_6X6_250_DATA); + case DICT_6X6_1000: + return Dictionary(DICT_6X6_1000_DATA); + + case DICT_7X7_50: + return Dictionary(DICT_7X7_50_DATA); + case DICT_7X7_100: + return Dictionary(DICT_7X7_100_DATA); + case DICT_7X7_250: + return Dictionary(DICT_7X7_250_DATA); + case DICT_7X7_1000: + return Dictionary(DICT_7X7_1000_DATA); + + case DICT_APRILTAG_16h5: + return Dictionary(DICT_APRILTAG_16h5_DATA); + case DICT_APRILTAG_25h9: + return Dictionary(DICT_APRILTAG_25h9_DATA); + case DICT_APRILTAG_36h10: + return Dictionary(DICT_APRILTAG_36h10_DATA); + case DICT_APRILTAG_36h11: + return Dictionary(DICT_APRILTAG_36h11_DATA); + + } + return Dictionary(DICT_4X4_50_DATA); +} + + +Dictionary getPredefinedDictionary(int dict) { + return getPredefinedDictionary(PredefinedDictionaryType(dict)); +} + + +/** + * @brief Generates a random marker Mat of size markerSize x markerSize + */ +static Mat _generateRandomMarker(int markerSize, RNG &rng) { + Mat marker(markerSize, markerSize, CV_8UC1, Scalar::all(0)); + for(int i = 0; i < markerSize; i++) { + for(int j = 0; j < markerSize; j++) { + unsigned char bit = (unsigned char) (rng.uniform(0,2)); + marker.at(i, j) = bit; + } + } + return marker; +} + +/** + * @brief Calculate selfDistance of the codification of a marker Mat. Self distance is the Hamming + * distance of the marker to itself in the other rotations. + * See S. Garrido-Jurado, R. Muñoz-Salinas, F. J. Madrid-Cuevas, and M. J. MarĂ­n-JimĂ©nez. 2014. + * "Automatic generation and detection of highly reliable fiducial markers under occlusion". + * Pattern Recogn. 47, 6 (June 2014), 2280-2292. DOI=10.1016/j.patcog.2014.01.005 + */ +static int _getSelfDistance(const Mat &marker) { + Mat bytes = Dictionary::getByteListFromBits(marker); + int minHamming = (int)marker.total() + 1; + for(int r = 1; r < 4; r++) { + int currentHamming = cv::hal::normHamming(bytes.ptr(), bytes.ptr() + bytes.cols*r, bytes.cols); + if(currentHamming < minHamming) minHamming = currentHamming; + } + return minHamming; +} + + +Dictionary extendDictionary(int nMarkers, int markerSize, const Dictionary &baseDictionary, int randomSeed) { + RNG rng((uint64)(randomSeed)); + + Dictionary out = Dictionary(Mat(), markerSize); + out.markerSize = markerSize; + + // theoretical maximum intermarker distance + // See S. Garrido-Jurado, R. Muñoz-Salinas, F. J. Madrid-Cuevas, and M. J. MarĂ­n-JimĂ©nez. 2014. + // "Automatic generation and detection of highly reliable fiducial markers under occlusion". + // Pattern Recogn. 47, 6 (June 2014), 2280-2292. DOI=10.1016/j.patcog.2014.01.005 + int C = (int)std::floor(float(markerSize * markerSize) / 4.f); + int tau = 2 * (int)std::floor(float(C) * 4.f / 3.f); + + // if baseDictionary is provided, calculate its intermarker distance + if(baseDictionary.bytesList.rows > 0) { + CV_Assert(baseDictionary.markerSize == markerSize); + out.bytesList = baseDictionary.bytesList.clone(); + + int minDistance = markerSize * markerSize + 1; + for(int i = 0; i < out.bytesList.rows; i++) { + Mat markerBytes = out.bytesList.rowRange(i, i + 1); + Mat markerBits = Dictionary::getBitsFromByteList(markerBytes, markerSize); + minDistance = min(minDistance, _getSelfDistance(markerBits)); + for(int j = i + 1; j < out.bytesList.rows; j++) { + minDistance = min(minDistance, out.getDistanceToId(markerBits, j)); + } + } + tau = minDistance; + } + + // current best option + int bestTau = 0; + Mat bestMarker; + + // after these number of unproductive iterations, the best option is accepted + const int maxUnproductiveIterations = 5000; + int unproductiveIterations = 0; + + while(out.bytesList.rows < nMarkers) { + Mat currentMarker = _generateRandomMarker(markerSize, rng); + + int selfDistance = _getSelfDistance(currentMarker); + int minDistance = selfDistance; + + // if self distance is better or equal than current best option, calculate distance + // to previous accepted markers + if(selfDistance >= bestTau) { + for(int i = 0; i < out.bytesList.rows; i++) { + int currentDistance = out.getDistanceToId(currentMarker, i); + minDistance = min(currentDistance, minDistance); + if(minDistance <= bestTau) { + break; + } + } + } + + // if distance is high enough, accept the marker + if(minDistance >= tau) { + unproductiveIterations = 0; + bestTau = 0; + Mat bytes = Dictionary::getByteListFromBits(currentMarker); + out.bytesList.push_back(bytes); + } else { + unproductiveIterations++; + + // if distance is not enough, but is better than the current best option + if(minDistance > bestTau) { + bestTau = minDistance; + bestMarker = currentMarker; + } + + // if number of unproductive iterarions has been reached, accept the current best option + if(unproductiveIterations == maxUnproductiveIterations) { + unproductiveIterations = 0; + tau = bestTau; + bestTau = 0; + Mat bytes = Dictionary::getByteListFromBits(bestMarker); + out.bytesList.push_back(bytes); + } + } + } + + // update the maximum number of correction bits for the generated dictionary + out.maxCorrectionBits = (tau - 1) / 2; + + return out; +} + +} +} diff --git a/modules/objdetect/src/aruco/aruco_utils.cpp b/modules/objdetect/src/aruco/aruco_utils.cpp new file mode 100644 index 0000000000..4c0d2dc3f7 --- /dev/null +++ b/modules/objdetect/src/aruco/aruco_utils.cpp @@ -0,0 +1,50 @@ +// This file is part of OpenCV project. +// It is subject to the license terms in the LICENSE file found in the top-level directory +// of this distribution and at http://opencv.org/license.html + +#include "../precomp.hpp" +#include "aruco_utils.hpp" + +namespace cv { +namespace aruco { +using namespace std; + +void _copyVector2Output(vector > &vec, OutputArrayOfArrays out, const float scale) { + out.create((int)vec.size(), 1, CV_32FC2); + if(out.isMatVector()) { + for (unsigned int i = 0; i < vec.size(); i++) { + out.create(4, 1, CV_32FC2, i); + Mat &m = out.getMatRef(i); + Mat(Mat(vec[i]).t()*scale).copyTo(m); + } + } + else if(out.isUMatVector()) { + for (unsigned int i = 0; i < vec.size(); i++) { + out.create(4, 1, CV_32FC2, i); + UMat &m = out.getUMatRef(i); + Mat(Mat(vec[i]).t()*scale).copyTo(m); + } + } + else if(out.kind() == _OutputArray::STD_VECTOR_VECTOR){ + for (unsigned int i = 0; i < vec.size(); i++) { + out.create(4, 1, CV_32FC2, i); + Mat m = out.getMat(i); + Mat(Mat(vec[i]).t()*scale).copyTo(m); + } + } + else { + CV_Error(cv::Error::StsNotImplemented, + "Only Mat vector, UMat vector, and vector OutputArrays are currently supported."); + } +} + +void _convertToGrey(InputArray _in, OutputArray _out) { + CV_Assert(_in.type() == CV_8UC1 || _in.type() == CV_8UC3); + if(_in.type() == CV_8UC3) + cvtColor(_in, _out, COLOR_BGR2GRAY); + else + _in.copyTo(_out); +} + +} +} diff --git a/modules/objdetect/src/aruco/aruco_utils.hpp b/modules/objdetect/src/aruco/aruco_utils.hpp new file mode 100644 index 0000000000..e3aa62051a --- /dev/null +++ b/modules/objdetect/src/aruco/aruco_utils.hpp @@ -0,0 +1,43 @@ +// This file is part of OpenCV project. +// It is subject to the license terms in the LICENSE file found in the top-level directory +// of this distribution and at http://opencv.org/license.html +#ifndef __OPENCV_OBJDETECT_ARUCO_UTILS_HPP__ +#define __OPENCV_OBJDETECT_ARUCO_UTILS_HPP__ + +#include +#include + +namespace cv { +namespace aruco { + +/** + * @brief Copy the contents of a corners vector to an OutputArray, settings its size. + */ +void _copyVector2Output(std::vector > &vec, OutputArrayOfArrays out, const float scale = 1.f); + +/** + * @brief Convert input image to gray if it is a 3-channels image + */ +void _convertToGrey(InputArray _in, OutputArray _out); + +template +inline bool readParameter(const std::string& name, T& parameter, const FileNode& node) +{ + if (!node.empty() && !node[name].empty()) { + node[name] >> parameter; + return true; + } + return false; +} + +template +inline bool readWriteParameter(const std::string& name, T& parameter, const FileNode& readNode, FileStorage& writeStorage) { + if (!readNode.empty()) + return readParameter(name, parameter, readNode); + writeStorage << name << parameter; + return true; +} + +} +} +#endif diff --git a/modules/objdetect/src/aruco/predefined_dictionaries.hpp b/modules/objdetect/src/aruco/predefined_dictionaries.hpp new file mode 100644 index 0000000000..f343183059 --- /dev/null +++ b/modules/objdetect/src/aruco/predefined_dictionaries.hpp @@ -0,0 +1,20127 @@ +// This file is part of OpenCV project. +// It is subject to the license terms in the LICENSE file found in the top-level directory +// of this distribution and at http://opencv.org/license.html + +namespace { + + + +/** + * Dictionaries are stored as a list of bytes in its four rotations + * On each rotation, the marker is divided in bytes assuming a row-major order + * This format allows a faster marker identification. + * For a dictionary composed by M markers of NxN bits, the structure dimensions should be: + * const char name[nMarkers][4rotations][nBytes], or more specifically: + * const char name[M][4][ceil(NxN/8)] + * The element [i][j][k] represents the k-th byte of the i-th marker in the dictionary + * in its j-th rotation. + * Each rotation implies a 90 degree rotation of the marker in anticlockwise direction. + */ + +static unsigned char DICT_ARUCO_BYTES[][4][4] = { + { { 132, 33, 8, 0 }, + { 0, 0, 15, 1 }, + { 8, 66, 16, 1 }, + { 248, 0, 0, 0 }, }, + { { 132, 33, 11, 1 }, + { 8, 66, 15, 1 }, + { 232, 66, 16, 1 }, + { 248, 33, 8, 0 }, }, + { { 132, 33, 4, 1 }, + { 8, 0, 31, 0 }, + { 144, 66, 16, 1 }, + { 124, 0, 8, 0 }, }, + { { 132, 33, 7, 0 }, + { 0, 66, 31, 0 }, + { 112, 66, 16, 1 }, + { 124, 33, 0, 0 }, }, + { { 132, 33, 120, 0 }, + { 16, 132, 15, 1 }, + { 15, 66, 16, 1 }, + { 248, 16, 132, 0 }, }, + { { 132, 33, 123, 1 }, + { 24, 198, 15, 1 }, + { 239, 66, 16, 1 }, + { 248, 49, 140, 0 }, }, + { { 132, 33, 116, 1 }, + { 24, 132, 31, 0 }, + { 151, 66, 16, 1 }, + { 124, 16, 140, 0 }, }, + { { 132, 33, 119, 0 }, + { 16, 198, 31, 0 }, + { 119, 66, 16, 1 }, + { 124, 49, 132, 0 }, }, + { { 132, 32, 152, 0 }, + { 16, 0, 46, 1 }, + { 12, 130, 16, 1 }, + { 186, 0, 4, 0 }, }, + { { 132, 32, 155, 1 }, + { 24, 66, 46, 1 }, + { 236, 130, 16, 1 }, + { 186, 33, 12, 0 }, }, + { { 132, 32, 148, 1 }, + { 24, 0, 62, 0 }, + { 148, 130, 16, 1 }, + { 62, 0, 12, 0 }, }, + { { 132, 32, 151, 0 }, + { 16, 66, 62, 0 }, + { 116, 130, 16, 1 }, + { 62, 33, 4, 0 }, }, + { { 132, 32, 232, 0 }, + { 0, 132, 46, 1 }, + { 11, 130, 16, 1 }, + { 186, 16, 128, 0 }, }, + { { 132, 32, 235, 1 }, + { 8, 198, 46, 1 }, + { 235, 130, 16, 1 }, + { 186, 49, 136, 0 }, }, + { { 132, 32, 228, 1 }, + { 8, 132, 62, 0 }, + { 147, 130, 16, 1 }, + { 62, 16, 136, 0 }, }, + { { 132, 32, 231, 0 }, + { 0, 198, 62, 0 }, + { 115, 130, 16, 1 }, + { 62, 49, 128, 0 }, }, + { { 132, 47, 8, 0 }, + { 33, 8, 15, 1 }, + { 8, 122, 16, 1 }, + { 248, 8, 66, 0 }, }, + { { 132, 47, 11, 1 }, + { 41, 74, 15, 1 }, + { 232, 122, 16, 1 }, + { 248, 41, 74, 0 }, }, + { { 132, 47, 4, 1 }, + { 41, 8, 31, 0 }, + { 144, 122, 16, 1 }, + { 124, 8, 74, 0 }, }, + { { 132, 47, 7, 0 }, + { 33, 74, 31, 0 }, + { 112, 122, 16, 1 }, + { 124, 41, 66, 0 }, }, + { { 132, 47, 120, 0 }, + { 49, 140, 15, 1 }, + { 15, 122, 16, 1 }, + { 248, 24, 198, 0 }, }, + { { 132, 47, 123, 1 }, + { 57, 206, 15, 1 }, + { 239, 122, 16, 1 }, + { 248, 57, 206, 0 }, }, + { { 132, 47, 116, 1 }, + { 57, 140, 31, 0 }, + { 151, 122, 16, 1 }, + { 124, 24, 206, 0 }, }, + { { 132, 47, 119, 0 }, + { 49, 206, 31, 0 }, + { 119, 122, 16, 1 }, + { 124, 57, 198, 0 }, }, + { { 132, 46, 152, 0 }, + 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11, 156, 231, 0 }, + { 131, 222, 240, 0 }, }, + { { 115, 156, 235, 1 }, + { 15, 255, 224, 1 }, + { 235, 156, 231, 0 }, + { 131, 255, 248, 0 }, }, + { { 115, 156, 228, 1 }, + { 15, 189, 240, 0 }, + { 147, 156, 231, 0 }, + { 7, 222, 248, 0 }, }, + { { 115, 156, 231, 0 }, + { 7, 255, 240, 0 }, + { 115, 156, 231, 0 }, + { 7, 255, 240, 0 }, }, +}; + +static unsigned char DICT_4X4_1000_BYTES[][4][2] = + { { { 181, 50 }, + { 235, 72 }, + { 76, 173 }, + { 18, 215 }, }, + { { 15, 154 }, + { 101, 71 }, + { 89, 240 }, + { 226, 166 }, }, + { { 51, 45 }, + { 222, 17 }, + { 180, 204 }, + { 136, 123 }, }, + { { 153, 70 }, + { 193, 60 }, + { 98, 153 }, + { 60, 131 }, }, + { { 84, 158 }, + { 161, 211 }, + { 121, 42 }, + { 203, 133 }, }, + { { 121, 205 }, + { 216, 183 }, + { 179, 158 }, + { 237, 27 }, }, + { { 158, 46 }, + { 135, 93 }, + { 116, 121 }, + { 186, 225 }, }, + { { 196, 242 }, + { 35, 234 }, + { 79, 35 }, + { 87, 196 }, }, + { { 254, 218 }, + { 173, 239 }, + { 91, 127 }, + { 247, 181 }, }, + { { 207, 86 }, + { 101, 252 }, + { 106, 243 }, + { 63, 166 }, }, + { { 249, 145 }, + { 248, 142 }, + { 137, 159 }, + { 113, 31 }, }, + { { 17, 167 }, + { 211, 18 }, + { 229, 136 }, + { 72, 203 }, }, + { { 14, 183 }, + { 55, 86 }, + { 237, 112 }, + { 106, 236 }, }, + { { 42, 15 }, + { 29, 21 }, + { 240, 84 }, + { 168, 184 }, }, + { { 36, 177 }, + { 58, 66 }, + { 141, 36 }, + { 66, 92 }, }, + { { 38, 62 }, + { 47, 81 }, + { 124, 100 }, + { 138, 244 }, }, + { { 70, 101 }, + { 22, 240 }, + { 166, 98 }, + { 15, 104 }, }, + { { 102, 0 }, + { 12, 192 }, + { 0, 102 }, + { 3, 48 }, }, + { { 108, 94 }, + { 41, 245 }, + { 122, 54 }, + { 175, 148 }, }, + { { 118, 175 }, + { 159, 211 }, + { 245, 110 }, + { 203, 249 }, }, + { { 134, 139 }, + { 21, 75 }, + { 209, 97 }, + { 210, 168 }, }, + { { 176, 43 }, + { 155, 9 }, + { 212, 13 }, + { 144, 217 }, }, + { { 204, 213 }, + { 48, 254 }, + { 171, 51 }, + { 127, 12 }, }, + { { 221, 130 }, + { 193, 206 }, + { 65, 187 }, + { 115, 131 }, }, + { { 254, 71 }, + { 157, 252 }, + { 226, 127 }, + { 63, 185 }, }, + { { 148, 113 }, + { 178, 104 }, + { 142, 41 }, + { 22, 77 }, }, + { { 172, 228 }, + { 10, 126 }, + { 39, 53 }, + { 126, 80 }, }, + { { 165, 84 }, + { 104, 120 }, + { 42, 165 }, + { 30, 22 }, }, + { { 33, 35 }, + { 91, 0 }, + { 196, 132 }, + { 0, 218 }, }, + { { 52, 111 }, + { 155, 113 }, + { 246, 44 }, + { 142, 217 }, }, + { { 68, 21 }, + { 48, 208 }, + { 168, 34 }, + { 11, 12 }, }, + { { 87, 178 }, + { 231, 194 }, + { 77, 234 }, + { 67, 231 }, }, + { { 158, 207 }, + { 149, 127 }, + { 243, 121 }, + { 254, 169 }, }, + { { 240, 203 }, + { 153, 171 }, + { 211, 15 }, + { 213, 153 }, }, + { { 8, 174 }, + { 3, 23 }, + { 117, 16 }, + { 232, 192 }, }, + { { 9, 41 }, + { 82, 5 }, + { 148, 144 }, + { 160, 74 }, }, + { { 24, 117 }, + { 178, 52 }, + { 174, 24 }, + { 44, 77 }, }, + { { 4, 255 }, + { 51, 115 }, + { 255, 32 }, + { 206, 204 }, }, + { { 13, 246 }, + { 99, 118 }, + { 111, 176 }, + { 110, 198 }, }, + { { 28, 90 }, + { 161, 101 }, + { 90, 56 }, + { 166, 133 }, }, + { { 23, 24 }, + { 228, 65 }, + { 24, 232 }, + { 130, 39 }, }, + { { 42, 40 }, + { 14, 5 }, + { 20, 84 }, + { 160, 112 }, }, + { { 50, 140 }, + { 140, 19 }, + { 49, 76 }, + { 200, 49 }, }, + { { 56, 178 }, + { 171, 6 }, + { 77, 28 }, + { 96, 213 }, }, + { { 36, 232 }, + { 10, 99 }, + { 23, 36 }, + { 198, 80 }, }, + { { 46, 235 }, + { 31, 103 }, + { 215, 116 }, + { 230, 248 }, }, + { { 45, 63 }, + { 123, 85 }, + { 252, 180 }, + { 170, 222 }, }, + { { 75, 100 }, + { 70, 180 }, + { 38, 210 }, + { 45, 98 }, }, + { { 80, 46 }, + { 131, 145 }, + { 116, 10 }, + { 137, 193 }, }, + { { 80, 19 }, + { 177, 128 }, + { 200, 10 }, + { 1, 141 }, }, + { { 81, 148 }, + { 224, 146 }, + { 41, 138 }, + { 73, 7 }, }, + { { 85, 104 }, + { 194, 225 }, + { 22, 170 }, + { 135, 67 }, }, + { { 93, 65 }, + { 208, 228 }, + { 130, 186 }, + { 39, 11 }, }, + { { 95, 151 }, + { 245, 214 }, + { 233, 250 }, + { 107, 175 }, }, + { { 104, 1 }, + { 24, 132 }, + { 128, 22 }, + { 33, 24 }, }, + { { 104, 103 }, + { 27, 180 }, + { 230, 22 }, + { 45, 216 }, }, + { { 97, 36 }, + { 74, 144 }, + { 36, 134 }, + { 9, 82 }, }, + { { 97, 233 }, + { 90, 163 }, + { 151, 134 }, + { 197, 90 }, }, + { { 107, 18 }, + { 109, 132 }, + { 72, 214 }, + { 33, 182 }, }, + { { 111, 229 }, + { 94, 246 }, + { 167, 246 }, + { 111, 122 }, }, + { { 103, 223 }, + { 125, 243 }, + { 251, 230 }, + { 207, 190 }, }, + { { 126, 27 }, + { 189, 197 }, + { 216, 126 }, + { 163, 189 }, }, + { { 128, 160 }, + { 2, 10 }, + { 5, 1 }, + { 80, 64 }, }, + { { 131, 68 }, + { 68, 56 }, + { 34, 193 }, + { 28, 34 }, }, + { { 139, 162 }, + { 71, 14 }, + { 69, 209 }, + { 112, 226 }, }, + { { 147, 122 }, + { 231, 41 }, + { 94, 201 }, + { 148, 231 }, }, + { { 132, 108 }, + { 2, 121 }, + { 54, 33 }, + { 158, 64 }, }, + { { 133, 42 }, + { 67, 73 }, + { 84, 161 }, + { 146, 194 }, }, + { { 133, 156 }, + { 96, 91 }, + { 57, 161 }, + { 218, 6 }, }, + { { 156, 137 }, + { 144, 79 }, + { 145, 57 }, + { 242, 9 }, }, + { { 159, 161 }, + { 214, 78 }, + { 133, 249 }, + { 114, 107 }, }, + { { 187, 124 }, + { 238, 61 }, + { 62, 221 }, + { 188, 119 }, }, + { { 188, 4 }, + { 136, 92 }, + { 32, 61 }, + { 58, 17 }, }, + { { 182, 91 }, + { 189, 105 }, + { 218, 109 }, + { 150, 189 }, }, + { { 191, 200 }, + { 204, 111 }, + { 19, 253 }, + { 246, 51 }, }, + { { 183, 171 }, + { 223, 75 }, + { 213, 237 }, + { 210, 251 }, }, + { { 202, 31 }, + { 53, 157 }, + { 248, 83 }, + { 185, 172 }, }, + { { 201, 98 }, + { 67, 172 }, + { 70, 147 }, + { 53, 194 }, }, + { { 217, 88 }, + { 224, 173 }, + { 26, 155 }, + { 181, 7 }, }, + { { 211, 213 }, + { 244, 186 }, + { 171, 203 }, + { 93, 47 }, }, + { { 204, 152 }, + { 32, 207 }, + { 25, 51 }, + { 243, 4 }, }, + { { 199, 160 }, + { 70, 202 }, + { 5, 227 }, + { 83, 98 }, }, + { { 197, 55 }, + { 115, 216 }, + { 236, 163 }, + { 27, 206 }, }, + { { 233, 93 }, + { 120, 189 }, + { 186, 151 }, + { 189, 30 }, }, + { { 249, 37 }, + { 218, 156 }, + { 164, 159 }, + { 57, 91 }, }, + { { 251, 187 }, + { 255, 143 }, + { 221, 223 }, + { 241, 255 }, }, + { { 238, 42 }, + { 15, 205 }, + { 84, 119 }, + { 179, 240 }, }, + { { 247, 77 }, + { 220, 249 }, + { 178, 239 }, + { 159, 59 }, }, + { { 53, 117 }, + { 250, 112 }, + { 174, 172 }, + { 14, 95 }, }, + { { 138, 173 }, + { 22, 31 }, + { 181, 81 }, + { 248, 104 }, }, + { { 118, 23 }, + { 189, 208 }, + { 232, 110 }, + { 11, 189 }, }, + { { 10, 207 }, + { 21, 55 }, + { 243, 80 }, + { 236, 168 }, }, + { { 6, 75 }, + { 21, 97 }, + { 210, 96 }, + { 134, 168 }, }, + { { 45, 193 }, + { 88, 102 }, + { 131, 180 }, + { 102, 26 }, }, + { { 73, 216 }, + { 96, 167 }, + { 27, 146 }, + { 229, 6 }, }, + { { 67, 244 }, + { 102, 178 }, + { 47, 194 }, + { 77, 102 }, }, + { { 79, 54 }, + { 103, 212 }, + { 108, 242 }, + { 43, 230 }, }, + { { 79, 211 }, + { 117, 230 }, + { 203, 242 }, + { 103, 174 }, }, + { { 105, 228 }, + { 74, 182 }, + { 39, 150 }, + { 109, 82 }, }, + { { 112, 199 }, + { 153, 178 }, + { 227, 14 }, + { 77, 153 }, }, + { { 122, 110 }, + { 143, 181 }, + { 118, 94 }, + { 173, 241 }, }, + { { 180, 234 }, + { 139, 107 }, + { 87, 45 }, + { 214, 209 }, }, + { { 237, 79 }, + { 89, 253 }, + { 242, 183 }, + { 191, 154 }, }, + { { 252, 231 }, + { 155, 254 }, + { 231, 63 }, + { 127, 217 }, }, + { { 254, 166 }, + { 143, 222 }, + { 101, 127 }, + { 123, 241 }, }, + { { 0, 37 }, + { 18, 16 }, + { 164, 0 }, + { 8, 72 }, }, + { { 0, 67 }, + { 17, 32 }, + { 194, 0 }, + { 4, 136 }, }, + { { 10, 136 }, + { 4, 7 }, + { 17, 80 }, + { 224, 32 }, }, + { { 10, 134 }, + { 5, 22 }, + { 97, 80 }, + { 104, 160 }, }, + { { 2, 111 }, + { 23, 49 }, + { 246, 64 }, + { 140, 232 }, }, + { { 0, 28 }, + { 32, 17 }, + { 56, 0 }, + { 136, 4 }, }, + { { 0, 151 }, + { 49, 18 }, + { 233, 0 }, + { 72, 140 }, }, + { { 8, 55 }, + { 51, 20 }, + { 236, 16 }, + { 40, 204 }, }, + { { 10, 49 }, + { 54, 4 }, + { 140, 80 }, + { 32, 108 }, }, + { { 9, 198 }, + { 65, 54 }, + { 99, 144 }, + { 108, 130 }, }, + { { 11, 1 }, + { 84, 4 }, + { 128, 208 }, + { 32, 42 }, }, + { { 9, 251 }, + { 115, 39 }, + { 223, 144 }, + { 228, 206 }, }, + { { 11, 88 }, + { 100, 37 }, + { 26, 208 }, + { 164, 38 }, }, + { { 16, 130 }, + { 129, 2 }, + { 65, 8 }, + { 64, 129 }, }, + { { 24, 45 }, + { 146, 21 }, + { 180, 24 }, + { 168, 73 }, }, + { { 16, 120 }, + { 162, 33 }, + { 30, 8 }, + { 132, 69 }, }, + { { 16, 115 }, + { 179, 32 }, + { 206, 8 }, + { 4, 205 }, }, + { { 18, 116 }, + { 166, 48 }, + { 46, 72 }, + { 12, 101 }, }, + { { 18, 177 }, + { 182, 2 }, + { 141, 72 }, + { 64, 109 }, }, + { { 26, 249 }, + { 182, 39 }, + { 159, 88 }, + { 228, 109 }, }, + { { 19, 6 }, + { 197, 16 }, + { 96, 200 }, + { 8, 163 }, }, + { { 12, 14 }, + { 1, 85 }, + { 112, 48 }, + { 170, 128 }, }, + { { 12, 241 }, + { 50, 102 }, + { 143, 48 }, + { 102, 76 }, }, + { { 4, 51 }, + { 51, 64 }, + { 204, 32 }, + { 2, 204 }, }, + { { 12, 159 }, + { 49, 87 }, + { 249, 48 }, + { 234, 140 }, }, + { { 14, 242 }, + { 39, 102 }, + { 79, 112 }, + { 102, 228 }, }, + { { 14, 253 }, + { 54, 119 }, + { 191, 112 }, + { 238, 108 }, }, + { { 7, 76 }, + { 68, 113 }, + { 50, 224 }, + { 142, 34 }, }, + { { 15, 164 }, + { 70, 86 }, + { 37, 240 }, + { 106, 98 }, }, + { { 7, 47 }, + { 87, 81 }, + { 244, 224 }, + { 138, 234 }, }, + { { 5, 181 }, + { 114, 82 }, + { 173, 160 }, + { 74, 78 }, }, + { { 15, 145 }, + { 116, 70 }, + { 137, 240 }, + { 98, 46 }, }, + { { 7, 219 }, + { 117, 99 }, + { 219, 224 }, + { 198, 174 }, }, + { { 30, 228 }, + { 134, 118 }, + { 39, 120 }, + { 110, 97 }, }, + { { 20, 57 }, + { 178, 65 }, + { 156, 40 }, + { 130, 77 }, }, + { { 29, 128 }, + { 192, 70 }, + { 1, 184 }, + { 98, 3 }, }, + { { 21, 200 }, + { 192, 99 }, + { 19, 168 }, + { 198, 3 }, }, + { { 31, 139 }, + { 213, 71 }, + { 209, 248 }, + { 226, 171 }, }, + { { 21, 186 }, + { 227, 67 }, + { 93, 168 }, + { 194, 199 }, }, + { { 29, 177 }, + { 242, 70 }, + { 141, 184 }, + { 98, 79 }, }, + { { 32, 128 }, + { 8, 2 }, + { 1, 4 }, + { 64, 16 }, }, + { { 40, 233 }, + { 26, 39 }, + { 151, 20 }, + { 228, 88 }, }, + { { 34, 162 }, + { 15, 2 }, + { 69, 68 }, + { 64, 240 }, }, + { { 40, 83 }, + { 57, 36 }, + { 202, 20 }, + { 36, 156 }, }, + { { 42, 240 }, + { 46, 38 }, + { 15, 84 }, + { 100, 116 }, }, + { { 34, 247 }, + { 63, 50 }, + { 239, 68 }, + { 76, 252 }, }, + { { 41, 64 }, + { 72, 36 }, + { 2, 148 }, + { 36, 18 }, }, + { { 33, 70 }, + { 73, 48 }, + { 98, 132 }, + { 12, 146 }, }, + { { 41, 185 }, + { 122, 7 }, + { 157, 148 }, + { 224, 94 }, }, + { { 43, 156 }, + { 108, 23 }, + { 57, 212 }, + { 232, 54 }, }, + { { 43, 178 }, + { 111, 6 }, + { 77, 212 }, + { 96, 246 }, }, + { { 56, 202 }, + { 137, 39 }, + { 83, 28 }, + { 228, 145 }, }, + { { 56, 46 }, + { 139, 21 }, + { 116, 28 }, + { 168, 209 }, }, + { { 48, 7 }, + { 153, 16 }, + { 224, 12 }, + { 8, 153 }, }, + { { 56, 231 }, + { 155, 54 }, + { 231, 28 }, + { 108, 217 }, }, + { { 58, 73 }, + { 156, 37 }, + { 146, 92 }, + { 164, 57 }, }, + { { 58, 101 }, + { 158, 52 }, + { 166, 92 }, + { 44, 121 }, }, + { { 50, 93 }, + { 188, 49 }, + { 186, 76 }, + { 140, 61 }, }, + { { 59, 136 }, + { 204, 7 }, + { 17, 220 }, + { 224, 51 }, }, + { { 57, 29 }, + { 248, 21 }, + { 184, 156 }, + { 168, 31 }, }, + { { 59, 211 }, + { 253, 38 }, + { 203, 220 }, + { 100, 191 }, }, + { { 38, 71 }, + { 29, 112 }, + { 226, 100 }, + { 14, 184 }, }, + { { 39, 128 }, + { 76, 66 }, + { 1, 228 }, + { 66, 50 }, }, + { { 47, 170 }, + { 79, 71 }, + { 85, 244 }, + { 226, 242 }, }, + { { 45, 20 }, + { 104, 84 }, + { 40, 180 }, + { 42, 22 }, }, + { { 37, 222 }, + { 105, 115 }, + { 123, 164 }, + { 206, 150 }, }, + { { 37, 83 }, + { 121, 96 }, + { 202, 164 }, + { 6, 158 }, }, + { { 47, 119 }, + { 127, 116 }, + { 238, 244 }, + { 46, 254 }, }, + { { 52, 72 }, + { 136, 97 }, + { 18, 44 }, + { 134, 17 }, }, + { { 60, 168 }, + { 138, 71 }, + { 21, 60 }, + { 226, 81 }, }, + { { 60, 65 }, + { 152, 100 }, + { 130, 60 }, + { 38, 25 }, }, + { { 52, 13 }, + { 152, 81 }, + { 176, 44 }, + { 138, 25 }, }, + { { 52, 251 }, + { 187, 99 }, + { 223, 44 }, + { 198, 221 }, }, + { { 54, 154 }, + { 173, 67 }, + { 89, 108 }, + { 194, 181 }, }, + { { 61, 224 }, + { 202, 102 }, + { 7, 188 }, + { 102, 83 }, }, + { { 53, 106 }, + { 203, 97 }, + { 86, 172 }, + { 134, 211 }, }, + { { 61, 9 }, + { 216, 69 }, + { 144, 188 }, + { 162, 27 }, }, + { { 61, 237 }, + { 218, 119 }, + { 183, 188 }, + { 238, 91 }, }, + { { 63, 196 }, + { 204, 118 }, + { 35, 252 }, + { 110, 51 }, }, + { { 63, 108 }, + { 206, 117 }, + { 54, 252 }, + { 174, 115 }, }, + { { 55, 206 }, + { 205, 115 }, + { 115, 236 }, + { 206, 179 }, }, + { { 61, 92 }, + { 232, 117 }, + { 58, 188 }, + { 174, 23 }, }, + { { 61, 118 }, + { 235, 116 }, + { 110, 188 }, + { 46, 215 }, }, + { { 55, 176 }, + { 238, 66 }, + { 13, 236 }, + { 66, 119 }, }, + { { 63, 23 }, + { 253, 84 }, + { 232, 252 }, + { 42, 191 }, }, + { { 63, 255 }, + { 255, 119 }, + { 255, 252 }, + { 238, 255 }, }, + { { 72, 229 }, + { 18, 182 }, + { 167, 18 }, + { 109, 72 }, }, + { { 66, 104 }, + { 6, 161 }, + { 22, 66 }, + { 133, 96 }, }, + { { 74, 45 }, + { 22, 149 }, + { 180, 82 }, + { 169, 104 }, }, + { { 65, 96 }, + { 66, 160 }, + { 6, 130 }, + { 5, 66 }, }, + { { 73, 81 }, + { 112, 164 }, + { 138, 146 }, + { 37, 14 }, }, + { { 65, 221 }, + { 112, 179 }, + { 187, 130 }, + { 205, 14 }, }, + { { 75, 223 }, + { 117, 183 }, + { 251, 210 }, + { 237, 174 }, }, + { { 88, 79 }, + { 145, 181 }, + { 242, 26 }, + { 173, 137 }, }, + { { 90, 72 }, + { 132, 165 }, + { 18, 90 }, + { 165, 33 }, }, + { { 88, 22 }, + { 161, 148 }, + { 104, 26 }, + { 41, 133 }, }, + { { 80, 93 }, + { 176, 177 }, + { 186, 10 }, + { 141, 13 }, }, + { { 90, 250 }, + { 167, 167 }, + { 95, 90 }, + { 229, 229 }, }, + { { 90, 181 }, + { 182, 150 }, + { 173, 90 }, + { 105, 109 }, }, + { { 81, 35 }, + { 211, 128 }, + { 196, 138 }, + { 1, 203 }, }, + { { 91, 138 }, + { 197, 135 }, + { 81, 218 }, + { 225, 163 }, }, + { { 89, 25 }, + { 240, 133 }, + { 152, 154 }, + { 161, 15 }, }, + { { 81, 53 }, + { 242, 144 }, + { 172, 138 }, + { 9, 79 }, }, + { { 76, 105 }, + { 18, 229 }, + { 150, 50 }, + { 167, 72 }, }, + { { 70, 193 }, + { 20, 226 }, + { 131, 98 }, + { 71, 40 }, }, + { { 78, 11 }, + { 21, 197 }, + { 208, 114 }, + { 163, 168 }, }, + { { 68, 95 }, + { 49, 241 }, + { 250, 34 }, + { 143, 140 }, }, + { { 78, 89 }, + { 52, 229 }, + { 154, 114 }, + { 167, 44 }, }, + { { 77, 131 }, + { 81, 198 }, + { 193, 178 }, + { 99, 138 }, }, + { { 77, 125 }, + { 114, 245 }, + { 190, 178 }, + { 175, 78 }, }, + { { 71, 216 }, + { 100, 227 }, + { 27, 226 }, + { 199, 38 }, }, + { { 71, 115 }, + { 119, 224 }, + { 206, 226 }, + { 7, 238 }, }, + { { 92, 133 }, + { 144, 214 }, + { 161, 58 }, + { 107, 9 }, }, + { { 94, 68 }, + { 132, 244 }, + { 34, 122 }, + { 47, 33 }, }, + { { 86, 43 }, + { 151, 193 }, + { 212, 106 }, + { 131, 233 }, }, + { { 92, 187 }, + { 179, 199 }, + { 221, 58 }, + { 227, 205 }, }, + { { 85, 195 }, + { 209, 226 }, + { 195, 170 }, + { 71, 139 }, }, + { { 95, 110 }, + { 199, 245 }, + { 118, 250 }, + { 175, 227 }, }, + { { 95, 235 }, + { 215, 231 }, + { 215, 250 }, + { 231, 235 }, }, + { { 93, 18 }, + { 225, 196 }, + { 72, 186 }, + { 35, 135 }, }, + { { 85, 94 }, + { 225, 241 }, + { 122, 170 }, + { 143, 135 }, }, + { { 98, 112 }, + { 46, 160 }, + { 14, 70 }, + { 5, 116 }, }, + { { 98, 21 }, + { 60, 144 }, + { 168, 70 }, + { 9, 60 }, }, + { { 97, 194 }, + { 73, 162 }, + { 67, 134 }, + { 69, 146 }, }, + { { 107, 32 }, + { 78, 132 }, + { 4, 214 }, + { 33, 114 }, }, + { { 99, 69 }, + { 92, 176 }, + { 162, 198 }, + { 13, 58 }, }, + { { 107, 92 }, + { 108, 181 }, + { 58, 214 }, + { 173, 54 }, }, + { { 107, 91 }, + { 125, 165 }, + { 218, 214 }, + { 165, 190 }, }, + { { 120, 12 }, + { 136, 149 }, + { 48, 30 }, + { 169, 17 }, }, + { { 122, 207 }, + { 157, 183 }, + { 243, 94 }, + { 237, 185 }, }, + { { 120, 127 }, + { 187, 181 }, + { 254, 30 }, + { 173, 221 }, }, + { { 121, 128 }, + { 200, 134 }, + { 1, 158 }, + { 97, 19 }, }, + { { 113, 229 }, + { 218, 178 }, + { 167, 142 }, + { 77, 91 }, }, + { { 113, 116 }, + { 234, 176 }, + { 46, 142 }, + { 13, 87 }, }, + { { 121, 182 }, + { 235, 150 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+ { { 166, 192 }, + { 12, 106 }, + { 3, 101 }, + { 86, 48 }, }, + { { 174, 224 }, + { 14, 110 }, + { 7, 117 }, + { 118, 112 }, }, + { { 166, 35 }, + { 31, 72 }, + { 196, 101 }, + { 18, 248 }, }, + { { 173, 232 }, + { 74, 111 }, + { 23, 181 }, + { 246, 82 }, }, + { { 165, 204 }, + { 72, 123 }, + { 51, 165 }, + { 222, 18 }, }, + { { 167, 236 }, + { 78, 123 }, + { 55, 229 }, + { 222, 114 }, }, + { { 173, 124 }, + { 106, 125 }, + { 62, 181 }, + { 190, 86 }, }, + { { 165, 26 }, + { 105, 73 }, + { 88, 165 }, + { 146, 150 }, }, + { { 165, 145 }, + { 120, 74 }, + { 137, 165 }, + { 82, 30 }, }, + { { 173, 25 }, + { 120, 77 }, + { 152, 181 }, + { 178, 30 }, }, + { { 165, 151 }, + { 121, 90 }, + { 233, 165 }, + { 90, 158 }, }, + { { 180, 109 }, + { 154, 121 }, + { 182, 45 }, + { 158, 89 }, }, + { { 190, 203 }, + { 157, 111 }, + { 211, 125 }, + { 246, 185 }, }, + { { 188, 58 }, + { 171, 77 }, + { 92, 61 }, + { 178, 213 }, }, + { { 188, 245 }, + { 186, 126 }, + { 175, 61 }, + { 126, 93 }, }, + { { 190, 189 }, + { 190, 95 }, + { 189, 125 }, + { 250, 125 }, }, + { { 190, 243 }, + { 191, 110 }, + { 207, 125 }, + { 118, 253 }, }, + { { 181, 37 }, + { 218, 88 }, + { 164, 173 }, + { 26, 91 }, }, + { { 181, 143 }, + { 217, 91 }, + { 241, 173 }, + { 218, 155 }, }, + { { 183, 104 }, + { 206, 105 }, + { 22, 237 }, + { 150, 115 }, }, + { { 191, 228 }, + { 206, 126 }, + { 39, 253 }, + { 126, 115 }, }, + { { 189, 254 }, + { 235, 127 }, + { 127, 189 }, + { 254, 215 }, }, + { { 189, 157 }, + { 248, 95 }, + { 185, 189 }, + { 250, 31 }, }, + { { 181, 245 }, + { 250, 122 }, + { 175, 173 }, + { 94, 95 }, }, + { { 181, 243 }, + { 251, 106 }, + { 207, 173 }, + { 86, 223 }, }, + { { 191, 176 }, + { 238, 78 }, + { 13, 253 }, + { 114, 119 }, }, + { { 183, 90 }, + { 237, 105 }, + { 90, 237 }, + { 150, 183 }, }, + { { 191, 62 }, + { 239, 93 }, + { 124, 253 }, + { 186, 247 }, }, + { { 183, 57 }, + { 254, 73 }, + { 156, 237 }, + { 146, 127 }, }, + { { 191, 213 }, + { 252, 126 }, + { 171, 253 }, + { 126, 63 }, }, + { { 183, 29 }, + { 252, 89 }, + { 184, 237 }, + { 154, 63 }, }, + { { 191, 53 }, + { 254, 92 }, + { 172, 253 }, + { 58, 127 }, }, + { { 183, 127 }, + { 255, 121 }, + { 254, 237 }, + { 158, 255 }, }, + { { 200, 1 }, + { 16, 140 }, + { 128, 19 }, + { 49, 8 }, }, + { { 192, 165 }, + { 18, 154 }, + { 165, 3 }, + { 89, 72 }, }, + { { 194, 130 }, + { 5, 138 }, + { 65, 67 }, + { 81, 160 }, }, + { { 200, 189 }, + { 50, 159 }, + { 189, 19 }, + { 249, 76 }, }, + { { 194, 252 }, + { 38, 187 }, + { 63, 67 }, + { 221, 100 }, }, + { { 202, 145 }, + { 52, 142 }, + { 137, 83 }, + { 113, 44 }, }, + { { 194, 91 }, + { 53, 169 }, + { 218, 67 }, + { 149, 172 }, }, + { { 201, 68 }, + { 64, 188 }, + { 34, 147 }, + { 61, 2 }, }, + { { 193, 42 }, + { 67, 137 }, + { 84, 131 }, + { 145, 194 }, }, + { { 195, 192 }, + { 68, 170 }, + { 3, 195 }, + { 85, 34 }, }, + { { 201, 122 }, + { 99, 173 }, + { 94, 147 }, + { 181, 198 }, }, + { { 193, 185 }, + { 114, 139 }, + { 157, 131 }, + { 209, 78 }, }, + { { 201, 117 }, + { 114, 188 }, + { 174, 147 }, + { 61, 78 }, }, + { { 193, 247 }, + { 115, 186 }, + { 239, 131 }, + { 93, 206 }, }, + { { 203, 177 }, + { 118, 142 }, + { 141, 211 }, + { 113, 110 }, }, + { { 208, 108 }, + { 130, 185 }, + { 54, 11 }, + { 157, 65 }, }, + { { 216, 135 }, + { 145, 158 }, + { 225, 27 }, + { 121, 137 }, }, + { { 208, 175 }, + { 147, 155 }, + { 245, 11 }, + { 217, 201 }, }, + { { 218, 196 }, + { 132, 190 }, + { 35, 91 }, + { 125, 33 }, }, + { { 210, 12 }, + { 132, 153 }, + { 48, 75 }, + { 153, 33 }, }, + { { 218, 9 }, + { 148, 141 }, + { 144, 91 }, + { 177, 41 }, }, + { { 208, 48 }, + { 162, 136 }, + { 12, 11 }, + { 17, 69 }, }, + { { 216, 148 }, + { 160, 158 }, + { 41, 27 }, + { 121, 5 }, }, + { { 208, 58 }, + { 163, 137 }, + { 92, 11 }, + { 145, 197 }, }, + { { 208, 182 }, + { 163, 154 }, + { 109, 11 }, + { 89, 197 }, }, + { { 208, 117 }, + { 178, 184 }, + { 174, 11 }, + { 29, 77 }, }, + { { 210, 118 }, + { 167, 184 }, + { 110, 75 }, + { 29, 229 }, }, + { { 218, 93 }, + { 180, 189 }, + { 186, 91 }, + { 189, 45 }, }, + { { 218, 53 }, + { 182, 156 }, + { 172, 91 }, + { 57, 109 }, }, + { { 210, 23 }, + { 181, 152 }, + { 232, 75 }, + { 25, 173 }, }, + { { 217, 2 }, + { 193, 140 }, + { 64, 155 }, + { 49, 131 }, }, + { { 211, 232 }, + { 198, 171 }, + { 23, 203 }, + { 213, 99 }, }, + { { 211, 229 }, + { 214, 186 }, + { 167, 203 }, + { 93, 107 }, }, + { { 209, 154 }, + { 225, 139 }, + { 89, 139 }, + { 209, 135 }, }, + { { 209, 246 }, + { 227, 186 }, + { 111, 139 }, + { 93, 199 }, }, + { { 209, 81 }, + { 240, 168 }, + { 138, 139 }, + { 21, 15 }, }, + { { 219, 20 }, + { 228, 156 }, + { 40, 219 }, + { 57, 39 }, }, + { { 211, 62 }, + { 231, 153 }, + { 124, 203 }, + { 153, 231 }, }, + { { 211, 211 }, + { 245, 170 }, + { 203, 203 }, + { 85, 175 }, }, + { { 196, 96 }, + { 2, 232 }, + { 6, 35 }, + { 23, 64 }, }, + { { 204, 167 }, + { 19, 222 }, + { 229, 51 }, + { 123, 200 }, }, + { { 198, 66 }, + { 5, 232 }, + { 66, 99 }, + { 23, 160 }, }, + { { 198, 71 }, + { 21, 248 }, + { 226, 99 }, + { 31, 168 }, }, + { { 206, 231 }, + { 23, 254 }, + { 231, 115 }, + { 127, 232 }, }, + { { 196, 92 }, + { 32, 249 }, + { 58, 35 }, + { 159, 4 }, }, + { { 204, 29 }, + { 48, 221 }, + { 184, 51 }, + { 187, 12 }, }, + { { 204, 53 }, + { 50, 220 }, + { 172, 51 }, + { 59, 76 }, }, + { { 198, 188 }, + { 38, 219 }, + { 61, 99 }, + { 219, 100 }, }, + { { 205, 168 }, + { 66, 207 }, + { 21, 179 }, + { 243, 66 }, }, + { { 197, 12 }, + { 64, 217 }, + { 48, 163 }, + { 155, 2 }, }, + { { 197, 228 }, + { 66, 250 }, + { 39, 163 }, + { 95, 66 }, }, + { { 197, 194 }, + { 65, 234 }, + { 67, 163 }, + { 87, 130 }, }, + { { 205, 45 }, + { 82, 221 }, + { 180, 179 }, + { 187, 74 }, }, + { { 205, 89 }, + { 112, 237 }, + { 154, 179 }, + { 183, 14 }, }, + { { 205, 149 }, + { 112, 222 }, + { 169, 179 }, + { 123, 14 }, }, + { { 197, 147 }, + { 113, 202 }, + { 201, 163 }, + { 83, 142 }, }, + { { 199, 95 }, + { 117, 249 }, + { 250, 227 }, + { 159, 174 }, }, + { { 212, 197 }, + { 144, 250 }, + { 163, 43 }, + { 95, 9 }, }, + { { 222, 136 }, + { 132, 207 }, + { 17, 123 }, + { 243, 33 }, }, + { { 214, 36 }, + { 134, 216 }, + { 36, 107 }, + { 27, 97 }, }, + { { 222, 236 }, + { 134, 255 }, + { 55, 123 }, + { 255, 97 }, }, + { { 214, 226 }, + { 135, 234 }, + { 71, 107 }, + { 87, 225 }, }, + { { 222, 198 }, + { 133, 254 }, + { 99, 123 }, + { 127, 161 }, }, + { { 222, 35 }, + { 151, 204 }, + { 196, 123 }, + { 51, 233 }, }, + { { 220, 220 }, + { 160, 255 }, + { 59, 59 }, + { 255, 5 }, }, + { { 220, 26 }, + { 161, 205 }, + { 88, 59 }, + { 179, 133 }, }, + { { 212, 17 }, + { 176, 200 }, + { 136, 43 }, + { 19, 13 }, }, + { { 222, 84 }, + { 164, 252 }, + { 42, 123 }, + { 63, 37 }, }, + { { 214, 148 }, + { 164, 218 }, + { 41, 107 }, + { 91, 37 }, }, + { { 222, 157 }, + { 180, 223 }, + { 185, 123 }, + { 251, 45 }, }, + { { 221, 129 }, + { 208, 206 }, + { 129, 187 }, + { 115, 11 }, }, + { { 213, 165 }, + { 210, 218 }, + { 165, 171 }, + { 91, 75 }, }, + { { 215, 172 }, + { 198, 219 }, + { 53, 235 }, + { 219, 99 }, }, + { { 215, 102 }, + { 199, 248 }, + { 102, 235 }, + { 31, 227 }, }, + { { 223, 169 }, + { 214, 207 }, + { 149, 251 }, + { 243, 107 }, }, + { { 213, 220 }, + { 224, 251 }, + { 59, 171 }, + { 223, 7 }, }, + { { 221, 31 }, + { 241, 221 }, + { 248, 187 }, + { 187, 143 }, }, + { { 223, 240 }, + { 230, 238 }, + { 15, 251 }, + { 119, 103 }, }, + { { 226, 72 }, + { 12, 169 }, + { 18, 71 }, + { 149, 48 }, }, + { { 226, 232 }, + { 14, 171 }, + { 23, 71 }, + { 213, 112 }, }, + { { 226, 7 }, + { 29, 152 }, + { 224, 71 }, + { 25, 184 }, }, + { { 224, 93 }, + { 56, 185 }, + { 186, 7 }, + { 157, 28 }, }, + { { 234, 245 }, + { 62, 190 }, + { 175, 87 }, + { 125, 124 }, }, + { { 235, 38 }, + { 79, 156 }, + { 100, 215 }, + { 57, 242 }, }, + { { 235, 237 }, + { 94, 191 }, + { 183, 215 }, + { 253, 122 }, }, + { { 225, 82 }, + { 105, 168 }, + { 74, 135 }, + { 21, 150 }, }, + { { 225, 126 }, + { 107, 185 }, + { 126, 135 }, + { 157, 214 }, }, + { { 233, 219 }, + { 121, 175 }, + { 219, 151 }, + { 245, 158 }, }, + { { 248, 6 }, + { 137, 156 }, + { 96, 31 }, + { 57, 145 }, }, + { { 240, 238 }, + { 139, 187 }, + { 119, 15 }, + { 221, 209 }, }, + { { 248, 161 }, + { 154, 142 }, + { 133, 31 }, + { 113, 89 }, }, + { { 250, 0 }, + { 140, 140 }, + { 0, 95 }, + { 49, 49 }, }, + { { 250, 194 }, + { 141, 174 }, + { 67, 95 }, + { 117, 177 }, }, + { { 240, 155 }, + { 185, 139 }, + { 217, 15 }, + { 209, 157 }, }, + { { 250, 244 }, + { 174, 190 }, + { 47, 95 }, + { 125, 117 }, }, + { { 250, 60 }, + { 174, 157 }, + { 60, 95 }, + { 185, 117 }, }, + { { 242, 252 }, + { 174, 187 }, + { 63, 79 }, + { 221, 117 }, }, + { { 242, 189 }, + { 190, 155 }, + { 189, 79 }, + { 217, 125 }, }, + { { 242, 147 }, + { 189, 138 }, + { 201, 79 }, + { 81, 189 }, }, + { { 241, 96 }, + { 202, 168 }, + { 6, 143 }, + { 21, 83 }, }, + { { 249, 236 }, + { 202, 191 }, + { 55, 159 }, + { 253, 83 }, }, + { { 241, 70 }, + { 201, 184 }, + { 98, 143 }, + { 29, 147 }, }, + { { 249, 225 }, + { 218, 174 }, + { 135, 159 }, + { 117, 91 }, }, + { { 243, 72 }, + { 204, 169 }, + { 18, 207 }, + { 149, 51 }, }, + { { 243, 174 }, + { 207, 155 }, + { 117, 207 }, + { 217, 243 }, }, + { { 243, 193 }, + { 220, 170 }, + { 131, 207 }, + { 85, 59 }, }, + { { 243, 139 }, + { 221, 139 }, + { 209, 207 }, + { 209, 187 }, }, + { { 243, 167 }, + { 223, 154 }, + { 229, 207 }, + { 89, 251 }, }, + { { 241, 115 }, + { 251, 168 }, + { 206, 143 }, + { 21, 223 }, }, + { { 241, 151 }, + { 249, 154 }, + { 233, 143 }, + { 89, 159 }, }, + { { 243, 244 }, + { 238, 186 }, + { 47, 207 }, + { 93, 119 }, }, + { { 251, 50 }, + { 239, 140 }, + { 76, 223 }, + { 49, 247 }, }, + { { 228, 7 }, + { 25, 216 }, + { 224, 39 }, + { 27, 152 }, }, + { { 230, 77 }, + { 28, 249 }, + { 178, 103 }, + { 159, 56 }, }, + { { 236, 85 }, + { 56, 252 }, + { 170, 55 }, + { 63, 28 }, }, + { { 237, 192 }, + { 72, 238 }, + { 3, 183 }, + { 119, 18 }, }, + { { 237, 133 }, + { 88, 222 }, + { 161, 183 }, + { 123, 26 }, }, + { { 239, 162 }, + { 79, 206 }, + { 69, 247 }, + { 115, 242 }, }, + { { 231, 78 }, + { 77, 249 }, + { 114, 231 }, + { 159, 178 }, }, + { { 229, 213 }, + { 120, 250 }, + { 171, 167 }, + { 95, 30 }, }, + { { 239, 80 }, + { 108, 236 }, + { 10, 247 }, + { 55, 54 }, }, + { { 244, 34 }, + { 139, 200 }, + { 68, 47 }, + { 19, 209 }, }, + { { 244, 137 }, + { 152, 203 }, + { 145, 47 }, + { 211, 25 }, }, + { { 244, 41 }, + { 154, 201 }, + { 148, 47 }, + { 147, 89 }, }, + { { 246, 106 }, + { 143, 233 }, + { 86, 111 }, + { 151, 241 }, }, + { { 254, 11 }, + { 157, 205 }, + { 208, 127 }, + { 179, 185 }, }, + { { 254, 111 }, + { 159, 253 }, + { 246, 127 }, + { 191, 249 }, }, + { { 244, 149 }, + { 184, 218 }, + { 169, 47 }, + { 91, 29 }, }, + { { 244, 53 }, + { 186, 216 }, + { 172, 47 }, + { 27, 93 }, }, + { { 244, 31 }, + { 185, 217 }, + { 248, 47 }, + { 155, 157 }, }, + { { 246, 176 }, + { 174, 202 }, + { 13, 111 }, + { 83, 117 }, }, + { { 245, 232 }, + { 202, 235 }, + { 23, 175 }, + { 215, 83 }, }, + { { 245, 197 }, + { 216, 250 }, + { 163, 175 }, + { 95, 27 }, }, + { { 253, 35 }, + { 219, 204 }, + { 196, 191 }, + { 51, 219 }, }, + { { 255, 192 }, + { 204, 238 }, + { 3, 255 }, + { 119, 51 }, }, + { { 247, 204 }, + { 204, 251 }, + { 51, 239 }, + { 223, 51 }, }, + { { 247, 233 }, + { 222, 235 }, + { 151, 239 }, + { 215, 123 }, }, + { { 245, 188 }, + { 234, 219 }, + { 61, 175 }, + { 219, 87 }, }, + { { 253, 246 }, + { 235, 254 }, + { 111, 191 }, + { 127, 215 }, }, + { { 245, 217 }, + { 248, 235 }, + { 155, 175 }, + { 215, 31 }, }, + { { 253, 151 }, + { 249, 222 }, + { 233, 191 }, + { 123, 159 }, }, + { { 253, 63 }, + { 251, 221 }, + { 252, 191 }, + { 187, 223 }, }, + { { 255, 156 }, + { 236, 223 }, + { 57, 255 }, + { 251, 55 }, }, + { { 255, 90 }, + { 237, 237 }, + { 90, 255 }, + { 183, 183 }, }, + { { 247, 254 }, + { 239, 251 }, + { 127, 239 }, + { 223, 247 }, }, + { { 255, 17 }, + { 252, 204 }, + { 136, 255 }, + { 51, 63 }, }, + { { 247, 191 }, + { 255, 219 }, + { 253, 239 }, + { 219, 255 }, }, }; + +static unsigned char DICT_5X5_1000_BYTES[][4][4] = + { { { 162, 217, 94, 0 }, + { 82, 46, 217, 1 }, + { 61, 77, 162, 1 }, + { 205, 186, 37, 0 }, }, + { { 14, 3, 115, 0 }, + { 176, 198, 133, 0 }, + { 103, 96, 56, 0 }, + { 80, 177, 134, 1 }, }, + { { 215, 135, 110, 1 }, + { 47, 151, 157, 1 }, + { 187, 112, 245, 1 }, + { 220, 244, 250, 0 }, }, + { { 129, 202, 251, 1 }, + { 122, 222, 40, 1 }, + { 239, 169, 192, 1 }, + { 138, 61, 175, 0 }, }, + { { 215, 90, 146, 0 }, + { 116, 27, 236, 0 }, + { 36, 173, 117, 1 }, + { 27, 236, 23, 0 }, }, + { { 234, 4, 22, 1 }, + { 153, 35, 152, 0 }, + { 180, 16, 43, 1 }, + { 12, 226, 76, 1 }, }, + { { 105, 235, 246, 0 }, + { 242, 191, 51, 0 }, + { 55, 235, 203, 0 }, + { 102, 126, 167, 1 }, }, + { { 113, 10, 53, 1 }, + { 60, 249, 16, 0 }, + { 214, 40, 71, 0 }, + { 4, 79, 158, 0 }, }, + { { 134, 176, 153, 0 }, + { 18, 64, 238, 1 }, + { 76, 134, 176, 1 }, + { 187, 129, 36, 0 }, }, + { { 152, 159, 210, 1 }, + { 191, 14, 105, 0 }, + { 165, 252, 140, 1 }, + { 75, 56, 126, 1 }, }, + { { 158, 119, 1, 1 }, + { 237, 64, 207, 0 }, + { 192, 119, 60, 1 }, + { 121, 129, 91, 1 }, }, + { { 209, 109, 96, 0 }, + { 69, 157, 11, 0 }, + { 3, 91, 69, 1 }, + { 104, 92, 209, 0 }, }, + { { 243, 21, 136, 1 }, + { 13, 49, 233, 1 }, + { 136, 212, 103, 1 }, + { 203, 198, 88, 0 }, }, + { { 47, 56, 179, 0 }, + { 144, 250, 230, 0 }, + { 102, 142, 122, 0 }, + { 51, 175, 132, 1 }, }, + { { 254, 126, 84, 0 }, + { 245, 45, 222, 0 }, + { 21, 63, 63, 1 }, + { 61, 218, 87, 1 }, }, + { { 40, 241, 191, 1 }, + { 218, 226, 115, 1 }, + { 254, 199, 138, 0 }, + { 231, 35, 173, 1 }, }, + { { 75, 211, 172, 0 }, + { 226, 145, 241, 1 }, + { 26, 229, 233, 0 }, + { 199, 196, 163, 1 }, }, + { { 95, 81, 55, 1 }, + { 220, 211, 213, 0 }, + { 246, 69, 125, 0 }, + { 85, 229, 157, 1 }, }, + { { 123, 38, 226, 0 }, + { 165, 183, 162, 0 }, + { 35, 178, 111, 0 }, + { 34, 246, 210, 1 }, }, + { { 131, 14, 244, 0 }, + { 49, 156, 184, 0 }, + { 23, 184, 96, 1 }, + { 14, 156, 198, 0 }, }, + { { 150, 237, 58, 1 }, + { 95, 138, 143, 1 }, + { 174, 91, 180, 1 }, + { 248, 168, 253, 0 }, }, + { { 168, 114, 32, 0 }, + { 224, 160, 74, 0 }, + { 2, 39, 10, 1 }, + { 41, 2, 131, 1 }, }, + { { 181, 134, 80, 1 }, + { 63, 52, 12, 0 }, + { 133, 48, 214, 1 }, + { 24, 22, 126, 0 }, }, + { { 93, 9, 111, 0 }, + { 132, 223, 21, 1 }, + { 123, 72, 93, 0 }, + { 212, 125, 144, 1 }, }, + { { 206, 104, 17, 1 }, + { 216, 73, 142, 0 }, + { 196, 11, 57, 1 }, + { 56, 201, 13, 1 }, }, + { { 210, 204, 185, 0 }, + { 87, 201, 168, 1 }, + { 78, 153, 165, 1 }, + { 138, 201, 245, 0 }, }, + { { 225, 231, 69, 1 }, + { 107, 117, 27, 0 }, + { 209, 115, 195, 1 }, + { 108, 87, 107, 0 }, }, + { { 17, 33, 35, 0 }, + { 4, 210, 3, 0 }, + { 98, 66, 68, 0 }, + { 96, 37, 144, 0 }, }, + { { 29, 203, 57, 0 }, + { 246, 216, 5, 1 }, + { 78, 105, 220, 0 }, + { 208, 13, 183, 1 }, }, + { { 18, 17, 29, 1 }, + { 28, 64, 209, 1 }, + { 220, 68, 36, 0 }, + { 197, 129, 28, 0 }, }, + { { 19, 155, 183, 0 }, + { 54, 218, 241, 0 }, + { 118, 236, 228, 0 }, + { 71, 173, 182, 0 }, }, + { { 27, 68, 57, 1 }, + { 221, 208, 128, 1 }, + { 206, 17, 108, 0 }, + { 128, 133, 221, 1 }, }, + { { 32, 104, 103, 0 }, + { 64, 238, 18, 0 }, + { 115, 11, 2, 0 }, + { 36, 59, 129, 0 }, }, + { { 37, 85, 100, 0 }, + { 65, 180, 85, 0 }, + { 19, 85, 82, 0 }, + { 85, 22, 193, 0 }, }, + { { 35, 33, 221, 0 }, + { 16, 116, 179, 1 }, + { 93, 194, 98, 0 }, + { 230, 151, 4, 0 }, }, + { { 61, 55, 245, 0 }, + { 181, 244, 119, 0 }, + { 87, 246, 94, 0 }, + { 119, 23, 214, 1 }, }, + { { 76, 197, 86, 0 }, + { 211, 7, 21, 0 }, + { 53, 81, 153, 0 }, + { 84, 112, 101, 1 }, }, + { { 65, 104, 128, 1 }, + { 72, 25, 34, 0 }, + { 128, 139, 65, 0 }, + { 34, 76, 9, 0 }, }, + { { 77, 86, 142, 1 }, + { 233, 19, 116, 1 }, + { 184, 181, 89, 0 }, + { 151, 100, 75, 1 }, }, + { { 67, 30, 57, 0 }, + { 49, 217, 192, 1 }, + { 78, 60, 97, 0 }, + { 129, 205, 198, 0 }, }, + { { 86, 148, 18, 1 }, + { 31, 3, 196, 0 }, + { 164, 20, 181, 0 }, + { 17, 224, 124, 0 }, }, + { { 82, 151, 207, 0 }, + { 39, 71, 241, 1 }, 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{ 120, 137, 170, 1 }, + { 142, 171, 33, 1 }, }, + { { 167, 110, 148, 1 }, + { 121, 56, 190, 0 }, + { 148, 187, 114, 1 }, + { 62, 142, 79, 0 }, }, + { { 175, 4, 36, 1 }, + { 137, 176, 156, 0 }, + { 146, 16, 122, 1 }, + { 28, 134, 200, 1 }, }, + { { 176, 65, 44, 0 }, + { 68, 160, 25, 1 }, + { 26, 65, 6, 1 }, + { 204, 2, 145, 0 }, }, + { { 176, 208, 227, 0 }, + { 70, 230, 104, 0 }, + { 99, 133, 134, 1 }, + { 11, 51, 177, 0 }, }, + { { 176, 237, 129, 1 }, + { 79, 104, 43, 0 }, + { 192, 219, 134, 1 }, + { 106, 11, 121, 0 }, }, + { { 180, 231, 236, 0 }, + { 103, 164, 63, 1 }, + { 27, 243, 150, 1 }, + { 254, 18, 243, 0 }, }, + { { 184, 160, 236, 1 }, + { 142, 164, 58, 1 }, + { 155, 130, 142, 1 }, + { 174, 18, 184, 1 }, }, + { { 184, 188, 60, 1 }, + { 159, 168, 90, 1 }, + { 158, 30, 142, 1 }, + { 173, 10, 252, 1 }, }, + { { 177, 102, 224, 1 }, + { 109, 180, 42, 0 }, + { 131, 179, 70, 1 }, + { 42, 22, 219, 0 }, }, + { { 189, 49, 10, 1 }, + { 140, 50, 79, 1 }, + { 168, 70, 94, 1 }, + { 249, 38, 24, 1 }, }, + { { 189, 63, 186, 1 }, + { 189, 186, 111, 1 }, + { 174, 254, 94, 1 }, + { 251, 46, 222, 1 }, }, + { { 185, 190, 220, 0 }, + { 183, 60, 122, 1 }, + { 29, 190, 206, 1 }, + { 175, 30, 118, 1 }, }, + { { 178, 58, 240, 1 }, + { 60, 172, 234, 0 }, + { 135, 174, 38, 1 }, + { 43, 154, 158, 0 }, }, + { { 182, 207, 169, 0 }, + { 103, 232, 173, 1 }, + { 74, 249, 182, 1 }, + { 218, 139, 243, 0 }, }, + { { 186, 35, 226, 1 }, + { 172, 166, 171, 0 }, + { 163, 226, 46, 1 }, + { 106, 178, 154, 1 }, }, + { { 183, 36, 171, 1 }, + { 13, 242, 174, 1 }, + { 234, 146, 118, 1 }, + { 186, 167, 216, 0 }, }, + { { 183, 41, 251, 0 }, + { 20, 254, 175, 1 }, + { 111, 202, 118, 1 }, + { 250, 191, 148, 0 }, }, + { { 179, 174, 8, 0 }, + { 39, 56, 138, 1 }, + { 8, 58, 230, 1 }, + { 168, 142, 114, 0 }, }, + { { 183, 86, 202, 1 }, + { 109, 54, 236, 1 }, + { 169, 181, 118, 1 }, + { 155, 182, 91, 0 }, }, + { { 191, 168, 244, 0 }, + { 150, 188, 190, 0 }, + { 23, 138, 254, 1 }, + { 62, 158, 180, 1 }, }, + { { 191, 148, 18, 1 }, + { 159, 50, 204, 0 }, + { 164, 20, 254, 1 }, + { 25, 166, 124, 1 }, }, + { { 191, 122, 64, 1 }, + { 236, 60, 206, 0 }, + { 129, 47, 126, 1 }, + { 57, 158, 27, 1 }, }, + { { 196, 133, 200, 0 }, + { 3, 5, 45, 1 }, + { 9, 208, 145, 1 }, + { 218, 80, 96, 0 }, }, + { { 192, 14, 9, 1 }, + { 41, 73, 8, 1 }, + { 200, 56, 1, 1 }, + { 136, 73, 74, 0 }, }, + { { 192, 112, 254, 0 }, + { 80, 135, 122, 1 }, + { 63, 135, 1, 1 }, + { 175, 112, 133, 0 }, }, + { { 204, 116, 17, 0 }, + { 209, 65, 78, 0 }, + { 68, 23, 25, 1 }, + { 57, 65, 69, 1 }, }, + { { 193, 8, 90, 1 }, + { 24, 31, 8, 1 }, + { 173, 8, 65, 1 }, + { 136, 124, 12, 0 }, }, + { { 193, 47, 130, 1 }, + { 41, 27, 43, 0 }, + { 160, 250, 65, 1 }, + { 106, 108, 74, 0 }, }, + { { 193, 35, 120, 0 }, + { 48, 149, 11, 1 }, + { 15, 98, 65, 1 }, + { 232, 84, 134, 0 }, }, + { { 198, 52, 219, 1 }, + { 25, 71, 238, 1 }, + { 237, 150, 49, 1 }, + { 187, 241, 76, 0 }, }, + { { 198, 164, 244, 1 }, + { 27, 133, 190, 0 }, + { 151, 146, 177, 1 }, + { 62, 208, 236, 0 }, }, + { { 194, 228, 25, 0 }, + { 83, 65, 138, 1 }, + { 76, 19, 161, 1 }, + { 168, 193, 101, 0 }, }, + { { 195, 29, 35, 0 }, + { 1, 219, 201, 0 }, + { 98, 92, 97, 1 }, + { 73, 237, 192, 0 }, }, + { { 195, 242, 196, 1 }, + { 106, 21, 250, 0 }, + { 145, 167, 225, 1 }, + { 47, 212, 43, 0 }, }, + { { 199, 95, 223, 0 }, + { 113, 95, 253, 1 }, + { 125, 253, 113, 1 }, + { 223, 253, 71, 0 }, }, + { { 203, 101, 189, 0 }, + { 209, 209, 187, 1 }, + { 94, 211, 105, 1 }, + { 238, 197, 197, 1 }, }, + { { 203, 199, 15, 1 }, + { 235, 83, 153, 1 }, + { 248, 113, 233, 1 }, + { 204, 229, 107, 1 }, }, + { { 207, 246, 185, 0 }, + { 243, 209, 238, 1 }, + { 78, 183, 249, 1 }, + { 187, 197, 231, 1 }, }, + { { 212, 84, 239, 0 }, + { 69, 199, 124, 1 }, + { 123, 149, 21, 1 }, + { 159, 113, 209, 0 }, }, + { { 212, 251, 220, 0 }, + { 118, 13, 127, 1 }, + { 29, 239, 149, 1 }, + { 255, 88, 55, 0 }, }, + { { 220, 232, 84, 0 }, + { 214, 13, 30, 0 }, + { 21, 11, 157, 1 }, + { 60, 88, 53, 1 }, }, + { { 213, 177, 150, 0 }, + { 22, 19, 127, 0 }, + { 52, 198, 213, 1 }, + { 127, 100, 52, 0 }, }, + { { 209, 159, 7, 1 }, + { 47, 91, 89, 0 }, + { 240, 124, 197, 1 }, + { 77, 109, 122, 0 }, }, + { { 209, 93, 126, 1 }, + { 93, 159, 89, 1 }, + { 191, 93, 69, 1 }, + { 205, 124, 221, 0 }, }, + { { 217, 164, 134, 1 }, + { 143, 19, 58, 0 }, + { 176, 146, 205, 1 }, + { 46, 100, 120, 1 }, }, + { { 221, 9, 48, 1 }, + { 156, 153, 13, 0 }, + { 134, 72, 93, 1 }, + { 88, 76, 156, 1 }, }, + { { 217, 180, 57, 1 }, + { 159, 209, 74, 1 }, + { 206, 22, 205, 1 }, + { 169, 69, 252, 1 }, }, + { { 221, 171, 105, 1 }, + { 174, 221, 15, 1 }, + { 203, 106, 221, 1 }, + { 248, 93, 186, 1 }, }, + { { 217, 203, 66, 0 }, + { 230, 31, 9, 0 }, + { 33, 105, 205, 1 }, + { 72, 124, 51, 1 }, }, + { { 210, 33, 13, 0 }, + { 4, 65, 155, 1 }, + { 88, 66, 37, 1 }, + { 236, 193, 16, 0 }, }, + { { 214, 73, 4, 0 }, + { 68, 9, 157, 0 }, + { 16, 73, 53, 1 }, + { 92, 200, 17, 0 }, }, + { { 210, 216, 219, 0 }, + { 86, 79, 232, 1 }, + { 109, 141, 165, 1 }, + { 139, 249, 53, 0 }, }, + { { 218, 63, 69, 1 }, + { 173, 77, 219, 0 }, + { 209, 126, 45, 1 }, + { 109, 217, 90, 1 }, }, + { { 218, 125, 218, 0 }, + { 213, 15, 235, 1 }, + { 45, 223, 45, 1 }, + { 235, 248, 85, 1 }, }, + { { 218, 211, 230, 0 }, + { 230, 135, 249, 0 }, + { 51, 229, 173, 1 }, + { 79, 240, 179, 1 }, }, + { { 211, 51, 189, 0 }, + { 52, 209, 251, 1 }, + { 94, 230, 101, 1 }, + { 239, 197, 150, 0 }, }, + { { 215, 225, 237, 1 }, + { 78, 213, 191, 1 }, + { 219, 195, 245, 1 }, + { 254, 213, 185, 0 }, }, + { { 219, 197, 122, 0 }, + { 215, 151, 137, 1 }, + { 47, 81, 237, 1 }, + { 200, 244, 245, 1 }, }, + { { 224, 128, 59, 1 }, + { 26, 227, 8, 1 }, + { 238, 0, 131, 1 }, + { 136, 99, 172, 0 }, }, + { { 224, 207, 105, 1 }, + { 107, 237, 9, 1 }, + { 203, 121, 131, 1 }, + { 200, 91, 235, 0 }, }, + { { 228, 71, 48, 1 }, + { 121, 161, 13, 0 }, + { 134, 113, 19, 1 }, + { 88, 66, 207, 0 }, }, + { { 232, 29, 86, 1 }, + { 153, 47, 89, 0 }, + { 181, 92, 11, 1 }, + { 77, 122, 76, 1 }, }, + { { 232, 243, 72, 1 }, + { 234, 37, 75, 1 }, + { 137, 103, 139, 1 }, + { 233, 82, 43, 1 }, }, + { { 232, 254, 175, 0 }, + { 227, 235, 122, 1 }, + { 122, 191, 139, 1 }, + { 175, 107, 227, 1 }, }, + { { 236, 231, 159, 0 }, + { 243, 99, 63, 1 }, + { 124, 243, 155, 1 }, + { 254, 99, 103, 1 }, }, + { { 225, 60, 212, 1 }, + { 25, 61, 122, 0 }, + { 149, 158, 67, 1 }, + { 47, 94, 76, 0 }, }, + { { 229, 204, 106, 1 }, + { 75, 191, 12, 1 }, + { 171, 25, 211, 1 }, + { 152, 126, 233, 0 }, }, + { { 233, 175, 154, 0 }, + { 179, 59, 43, 1 }, + { 44, 250, 203, 1 }, + { 234, 110, 102, 1 }, }, + { { 227, 0, 237, 0 }, + { 0, 245, 184, 1 }, + { 91, 128, 99, 1 }, + { 142, 215, 128, 0 }, }, + { { 231, 177, 14, 0 }, + { 2, 51, 223, 1 }, + { 56, 70, 243, 1 }, + { 253, 230, 32, 0 }, }, + { { 227, 192, 126, 0 }, + { 82, 183, 152, 1 }, + { 63, 1, 227, 1 }, + { 140, 246, 165, 0 }, }, + { { 235, 140, 163, 0 }, + { 131, 251, 168, 0 }, + { 98, 152, 235, 1 }, + { 10, 239, 224, 1 }, }, + { { 235, 159, 109, 1 }, + { 171, 253, 217, 1 }, + { 219, 124, 235, 1 }, + { 205, 223, 234, 1 }, }, + { { 239, 65, 11, 0 }, + { 192, 115, 141, 1 }, + { 104, 65, 123, 1 }, + { 216, 231, 1, 1 }, }, + { { 239, 194, 195, 0 }, + { 226, 119, 172, 0 }, + { 97, 161, 251, 1 }, + { 26, 247, 35, 1 }, }, + { { 240, 168, 32, 0 }, + { 6, 169, 10, 0 }, + { 2, 10, 135, 1 }, + { 40, 74, 176, 0 }, }, + { { 244, 25, 211, 0 }, + { 20, 111, 109, 0 }, + { 101, 204, 23, 1 }, + { 91, 123, 20, 0 }, }, + { { 244, 133, 191, 1 }, + { 31, 227, 61, 1 }, + { 254, 208, 151, 1 }, + { 222, 99, 252, 0 }, }, + { { 240, 106, 204, 0 }, + { 100, 45, 58, 1 }, + { 25, 171, 7, 1 }, + { 174, 90, 19, 0 }, }, + { { 240, 123, 107, 1 }, + { 108, 239, 75, 1 }, + { 235, 111, 7, 1 }, + { 233, 123, 155, 0 }, }, + { { 244, 251, 170, 0 }, + { 102, 171, 111, 1 }, + { 42, 239, 151, 1 }, + { 251, 106, 179, 0 }, }, + { { 252, 198, 47, 0 }, + { 231, 227, 28, 1 }, + { 122, 49, 159, 1 }, + { 156, 99, 243, 1 }, }, + { { 248, 111, 16, 0 }, + { 245, 41, 11, 0 }, + { 4, 123, 15, 1 }, + { 104, 74, 87, 1 }, }, + { { 252, 127, 120, 1 }, + { 253, 173, 79, 1 }, + { 143, 127, 31, 1 }, + { 249, 90, 223, 1 }, }, + { { 241, 171, 217, 0 }, + { 54, 125, 43, 1 }, + { 77, 234, 199, 1 }, + { 234, 95, 54, 0 }, }, + { { 245, 81, 143, 1 }, + { 76, 115, 125, 1 }, + { 248, 197, 87, 1 }, + { 223, 103, 25, 0 }, }, + { { 241, 248, 166, 1 }, + { 78, 187, 122, 0 }, + { 178, 143, 199, 1 }, + { 47, 110, 185, 0 }, }, + { { 241, 86, 24, 0 }, + { 117, 49, 72, 1 }, + { 12, 53, 71, 1 }, + { 137, 70, 87, 0 }, }, + { { 253, 132, 196, 0 }, + { 135, 53, 60, 0 }, + { 17, 144, 223, 1 }, + { 30, 86, 112, 1 }, }, + { { 249, 141, 114, 1 }, + { 159, 191, 9, 0 }, + { 167, 88, 207, 1 }, + { 72, 126, 252, 1 }, }, + { { 253, 15, 85, 1 }, + { 189, 125, 29, 0 }, + { 213, 120, 95, 1 }, + { 92, 95, 94, 1 }, }, + { { 242, 156, 111, 1 }, + { 15, 239, 216, 1 }, + { 251, 28, 167, 1 }, + { 141, 251, 248, 0 }, }, + { { 246, 136, 24, 1 }, + { 30, 41, 140, 1 }, + { 140, 8, 183, 1 }, + { 152, 202, 60, 0 }, }, + { { 246, 7, 197, 0 }, + { 37, 101, 189, 0 }, + { 81, 240, 55, 1 }, + { 94, 211, 82, 0 }, }, + { { 242, 65, 215, 0 }, + { 84, 103, 185, 0 }, + { 117, 193, 39, 1 }, + { 78, 243, 21, 0 }, }, + { { 246, 241, 27, 0 }, + { 86, 99, 207, 1 }, + { 108, 71, 183, 1 }, + { 249, 227, 53, 0 }, }, + { { 242, 230, 203, 1 }, + { 111, 103, 170, 1 }, + { 233, 179, 167, 1 }, + { 170, 243, 123, 0 }, }, + { { 250, 213, 32, 1 }, + { 207, 161, 201, 0 }, + { 130, 85, 175, 1 }, + { 73, 194, 249, 1 }, }, + { { 254, 67, 233, 0 }, + { 228, 229, 173, 1 }, + { 75, 225, 63, 1 }, + { 218, 211, 147, 1 }, }, + { { 243, 251, 142, 0 }, + { 102, 59, 251, 1 }, + { 56, 239, 231, 1 }, + { 239, 238, 51, 0 }, }, + { { 255, 187, 218, 0 }, + { 182, 63, 239, 1 }, + { 45, 238, 255, 1 }, + { 251, 254, 54, 1 }, }, + { { 251, 201, 14, 1 }, + { 206, 59, 153, 1 }, + { 184, 73, 239, 1 }, + { 204, 238, 57, 1 }, }, }; + +static unsigned char DICT_6X6_1000_BYTES[][4][5] = + { { { 30, 61, 216, 42, 6 }, + { 227, 186, 70, 49, 9 }, + { 101, 65, 187, 199, 8 }, + { 152, 198, 37, 220, 7 }, }, + { { 14, 251, 163, 137, 1 }, + { 215, 230, 24, 5, 14 }, + { 137, 28, 93, 247, 0 }, + { 122, 1, 134, 126, 11 }, }, + { { 21, 144, 126, 172, 13 }, + { 236, 105, 87, 80, 6 }, + { 179, 87, 224, 154, 8 }, + { 96, 174, 169, 99, 7 }, }, + { { 201, 27, 48, 105, 14 }, + { 66, 50, 75, 222, 12 }, + { 121, 96, 205, 137, 3 }, + { 55, 189, 36, 196, 2 }, }, + { { 214, 7, 214, 225, 5 }, + { 164, 203, 74, 191, 2 }, + { 168, 118, 190, 6, 11 }, + { 79, 213, 45, 50, 5 }, }, + { { 216, 232, 224, 230, 8 }, + { 43, 140, 19, 138, 15 }, + { 22, 112, 113, 113, 11 }, + { 245, 28, 131, 29, 4 }, }, + { { 66, 104, 180, 31, 5 }, + { 13, 165, 192, 149, 13 }, + { 175, 130, 209, 100, 2 }, + { 186, 144, 58, 91, 0 }, }, + { { 136, 165, 15, 41, 10 }, + { 19, 115, 23, 38, 0 }, + { 89, 79, 10, 81, 1 }, + { 6, 78, 140, 236, 8 }, }, + { { 48, 125, 82, 79, 13 }, + { 109, 110, 97, 60, 9 }, + { 191, 36, 171, 224, 12 }, + { 147, 200, 103, 107, 6 }, }, + { { 60, 47, 52, 179, 12 }, + { 131, 11, 235, 52, 15 }, + { 60, 210, 207, 67, 12 }, + { 242, 205, 125, 12, 1 }, }, + { { 69, 223, 199, 78, 3 }, + { 252, 247, 24, 232, 9 }, + { 199, 46, 63, 186, 2 }, + { 145, 113, 142, 243, 15 }, }, + { { 72, 216, 91, 37, 7 }, + { 126, 84, 86, 148, 8 }, + { 234, 77, 161, 177, 2 }, + { 18, 150, 162, 167, 14 }, }, + { { 113, 5, 88, 252, 6 }, + { 40, 58, 230, 248, 2 }, + { 99, 241, 170, 8, 14 }, + { 65, 246, 117, 193, 4 }, }, + { { 134, 220, 250, 208, 7 }, + { 228, 212, 212, 59, 14 }, + { 224, 181, 243, 182, 1 }, + { 125, 194, 178, 178, 7 }, }, + { { 141, 114, 169, 63, 6 }, + { 219, 180, 206, 70, 5 }, + { 111, 201, 84, 235, 1 }, + { 166, 39, 50, 221, 11 }, }, + { { 162, 184, 157, 205, 14 }, + { 89, 177, 117, 31, 10 }, + { 123, 59, 145, 212, 5 }, + { 95, 138, 232, 217, 10 }, }, + { { 9, 253, 30, 156, 4 }, + { 75, 103, 212, 112, 10 }, + { 35, 151, 139, 249, 0 }, + { 80, 226, 190, 109, 2 }, }, + { { 21, 77, 189, 24, 15 }, + { 148, 191, 197, 112, 12 }, + { 241, 139, 219, 42, 8 }, + { 48, 234, 63, 210, 9 }, }, + { { 48, 10, 49, 14, 2 }, + { 24, 56, 40, 16, 13 }, + { 71, 8, 197, 0, 12 }, + { 176, 129, 65, 193, 8 }, }, + { { 72, 7, 239, 175, 13 }, + { 62, 227, 79, 164, 7 }, + { 191, 95, 126, 1, 2 }, + { 226, 95, 44, 119, 12 }, }, + { { 86, 223, 17, 219, 6 }, + { 208, 62, 216, 189, 11 }, + { 109, 184, 143, 182, 10 }, + { 219, 209, 183, 192, 11 }, }, + { { 102, 136, 50, 116, 12 }, + { 136, 64, 243, 153, 12 }, + { 50, 228, 193, 22, 6 }, + { 57, 156, 240, 33, 1 }, }, + { { 118, 232, 203, 120, 1 }, + { 181, 236, 182, 137, 8 }, + { 129, 237, 49, 118, 14 }, + { 25, 22, 211, 122, 13 }, }, + { { 154, 83, 217, 207, 3 }, + { 126, 190, 12, 31, 3 }, + { 207, 57, 188, 165, 9 }, + { 207, 131, 7, 215, 14 }, }, + { { 169, 203, 132, 2, 4 }, + { 2, 135, 120, 66, 9 }, + { 36, 2, 29, 57, 5 }, + { 148, 33, 238, 20, 0 }, }, + { { 198, 117, 73, 73, 0 }, + { 241, 38, 4, 175, 0 }, + { 9, 41, 42, 230, 3 }, + { 15, 82, 6, 72, 15 }, }, + { { 193, 210, 136, 148, 1 }, + { 76, 132, 156, 194, 2 }, + { 130, 145, 20, 184, 3 }, + { 68, 51, 146, 19, 2 }, }, + { { 231, 72, 8, 82, 11 }, + { 132, 20, 165, 203, 9 }, + { 212, 161, 1, 46, 7 }, + { 157, 58, 82, 130, 1 }, }, + { { 234, 47, 202, 132, 8 }, + { 43, 194, 45, 163, 10 }, + { 18, 21, 63, 69, 7 }, + { 92, 91, 68, 61, 4 }, }, + { { 233, 99, 183, 123, 1 }, + { 23, 231, 170, 222, 5 }, + { 141, 238, 220, 105, 7 }, + { 167, 181, 94, 126, 8 }, }, + { { 250, 54, 101, 42, 15 }, + { 119, 57, 107, 163, 5 }, + { 245, 74, 102, 197, 15 }, + { 172, 93, 105, 206, 14 }, }, + { { 6, 91, 255, 123, 13 }, + { 244, 231, 207, 29, 13 }, + { 189, 239, 253, 166, 0 }, + { 187, 143, 62, 114, 15 }, }, + { { 5, 65, 215, 45, 6 }, + { 184, 247, 66, 84, 0 }, + { 107, 78, 184, 42, 0 }, + { 2, 164, 46, 241, 13 }, }, + { { 12, 247, 36, 106, 2 }, + { 195, 55, 26, 40, 5 }, + { 69, 98, 78, 243, 0 }, + { 161, 69, 142, 204, 3 }, }, + { { 19, 56, 163, 158, 11 }, + { 93, 248, 129, 65, 15 }, + { 215, 156, 81, 204, 8 }, + { 248, 40, 17, 251, 10 }, }, + { 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62, 213, 47, 2 }, }, + { { 255, 135, 146, 120, 1 }, + { 134, 234, 186, 251, 0 }, + { 129, 228, 158, 31, 15 }, + { 13, 245, 213, 118, 1 }, }, + { { 249, 195, 188, 9, 10 }, + { 2, 191, 61, 214, 4 }, + { 89, 3, 220, 57, 15 }, + { 38, 187, 207, 212, 0 }, }, + { { 255, 202, 25, 209, 12 }, + { 146, 12, 253, 223, 10 }, + { 56, 185, 133, 63, 15 }, + { 95, 187, 243, 4, 9 }, }, + { { 255, 239, 23, 165, 10 }, + { 155, 95, 59, 247, 10 }, + { 90, 94, 143, 127, 15 }, + { 94, 253, 207, 173, 9 }, }, + { { 253, 254, 218, 140, 1 }, + { 239, 236, 60, 242, 10 }, + { 131, 21, 183, 251, 15 }, + { 84, 243, 195, 127, 7 }, }, + { { 6, 66, 233, 9, 7 }, + { 180, 180, 76, 5, 4 }, + { 233, 9, 116, 38, 0 }, + { 42, 3, 34, 210, 13 }, }, + { { 3, 36, 36, 70, 13 }, + { 13, 1, 65, 105, 5 }, + { 182, 34, 66, 76, 0 }, + { 169, 104, 40, 11, 0 }, }, + { { 7, 94, 92, 135, 12 }, + { 232, 5, 77, 117, 11 }, + { 62, 19, 167, 174, 0 }, + { 218, 235, 42, 1, 7 }, }, + { { 7, 136, 66, 250, 6 }, + { 160, 112, 210, 73, 11 }, + { 101, 244, 33, 30, 0 }, + { 217, 36, 176, 224, 5 }, }, + { { 10, 7, 178, 27, 11 }, + { 6, 242, 137, 53, 5 }, + { 221, 132, 222, 5, 0 }, + { 170, 201, 20, 246, 0 }, }, + { { 16, 148, 220, 241, 14 }, + { 96, 153, 215, 60, 2 }, + { 120, 243, 178, 144, 8 }, + { 67, 206, 185, 144, 6 }, }, + { { 22, 162, 90, 176, 15 }, + { 165, 88, 223, 17, 2 }, + { 240, 213, 164, 86, 8 }, + { 72, 143, 177, 170, 5 }, }, + { { 16, 253, 203, 109, 14 }, + { 121, 254, 87, 44, 8 }, + { 123, 109, 59, 240, 8 }, + { 19, 78, 167, 249, 14 }, }, + { { 17, 52, 172, 162, 12 }, + { 65, 137, 71, 96, 7 }, + { 52, 83, 82, 200, 8 }, + { 224, 110, 41, 24, 2 }, }, + { { 17, 166, 62, 16, 1 }, + { 5, 73, 156, 112, 4 }, + { 128, 135, 198, 88, 8 }, + { 32, 227, 153, 42, 0 }, }, + { { 30, 88, 44, 226, 2 }, + { 194, 29, 6, 9, 15 }, + { 68, 115, 65, 167, 8 }, + { 249, 6, 11, 132, 3 }, }, + { { 24, 99, 58, 139, 0 }, + { 3, 110, 12, 20, 7 }, + { 13, 21, 204, 97, 8 }, + { 226, 131, 7, 108, 0 }, }, + { { 26, 99, 1, 47, 13 }, + { 31, 46, 75, 5, 1 }, + { 191, 72, 12, 101, 8 }, + { 138, 13, 39, 79, 8 }, }, + { { 26, 241, 71, 206, 15 }, + { 127, 127, 81, 9, 3 }, + { 247, 62, 40, 245, 8 }, + { 201, 8, 175, 239, 14 }, }, + { { 25, 108, 177, 139, 1 }, + { 23, 172, 0, 116, 15 }, + { 141, 24, 211, 105, 8 }, + { 242, 224, 3, 94, 8 }, }, + { { 29, 149, 207, 92, 12 }, + { 250, 235, 213, 104, 0 }, + { 51, 175, 58, 155, 8 }, + { 1, 106, 189, 117, 15 }, }, + { { 25, 158, 56, 146, 2 }, + { 66, 24, 156, 112, 15 }, + { 68, 145, 199, 153, 8 }, + { 240, 227, 145, 132, 2 }, }, + { { 31, 252, 86, 35, 10 }, + { 227, 93, 19, 117, 9 }, + { 92, 70, 163, 255, 8 }, + { 154, 236, 139, 172, 7 }, }, + { { 36, 27, 41, 179, 3 }, + { 212, 18, 174, 4, 15 }, + { 204, 217, 77, 130, 4 }, + { 242, 7, 84, 130, 11 }, }, + { { 38, 231, 136, 133, 0 }, + { 137, 134, 60, 37, 2 }, + { 10, 17, 30, 118, 4 }, + { 74, 67, 198, 25, 1 }, }, + { { 33, 7, 54, 188, 1 }, + { 12, 99, 170, 112, 6 }, + { 131, 214, 206, 8, 4 }, + { 96, 229, 92, 99, 0 }, }, + { { 40, 77, 70, 86, 10 }, + { 42, 87, 161, 40, 9 }, + { 86, 166, 43, 33, 4 }, + { 145, 72, 94, 165, 4 }, }, + { { 46, 236, 227, 69, 8 }, + { 187, 196, 49, 45, 12 }, + { 26, 44, 115, 119, 4 }, + { 59, 72, 194, 61, 13 }, }, + { { 45, 79, 225, 77, 4 }, + { 186, 166, 104, 108, 12 }, + { 43, 40, 127, 43, 4 }, + { 51, 97, 102, 85, 13 }, }, + { { 45, 138, 40, 60, 7 }, + { 142, 48, 254, 64, 12 }, + { 227, 193, 69, 27, 4 }, + { 48, 39, 240, 199, 1 }, }, + { { 52, 248, 62, 55, 1 }, + { 205, 77, 182, 20, 13 }, + { 142, 199, 193, 242, 12 }, + { 178, 134, 219, 43, 3 }, }, + { { 56, 99, 93, 125, 8 }, + { 59, 47, 175, 28, 0 }, + { 27, 235, 172, 97, 12 }, + { 3, 143, 95, 77, 12 }, }, + { { 63, 162, 28, 196, 12 }, + { 139, 9, 125, 89, 2 }, + { 50, 51, 132, 95, 12 }, + { 73, 171, 233, 13, 1 }, }, + { { 66, 221, 151, 174, 14 }, + { 88, 247, 83, 177, 11 }, + { 119, 94, 155, 180, 2 }, + { 216, 220, 174, 241, 10 }, }, + { { 68, 223, 18, 214, 11 }, + { 204, 86, 153, 184, 11 }, + { 214, 180, 143, 178, 2 }, + { 209, 217, 150, 163, 3 }, }, + { { 65, 58, 205, 236, 8 }, + { 121, 161, 15, 200, 10 }, + { 19, 123, 53, 200, 2 }, + { 81, 63, 8, 89, 14 }, }, + { { 65, 192, 219, 73, 4 }, + { 48, 228, 84, 220, 0 }, + { 41, 45, 176, 56, 2 }, + { 3, 178, 162, 112, 12 }, }, + { { 76, 180, 0, 200, 13 }, + { 199, 32, 81, 168, 2 }, + { 177, 48, 2, 211, 2 }, + { 65, 88, 160, 78, 3 }, }, + { { 73, 35, 72, 149, 2 }, + { 43, 18, 140, 196, 2 }, + { 74, 145, 44, 73, 2 }, + { 66, 51, 20, 141, 4 }, }, + { { 82, 55, 185, 92, 6 }, + { 89, 186, 204, 185, 4 }, + { 99, 169, 222, 196, 10 }, + { 41, 211, 53, 217, 10 }, }, + { { 82, 81, 56, 221, 10 }, + { 72, 62, 133, 157, 6 }, + { 91, 177, 200, 164, 10 }, + { 107, 154, 23, 193, 2 }, }, + { { 94, 113, 146, 65, 3 }, + { 199, 222, 0, 157, 0 }, + { 200, 36, 152, 231, 10 }, + { 11, 144, 7, 190, 3 }, }, + { { 92, 178, 113, 235, 13 }, + { 247, 40, 91, 156, 7 }, + { 189, 120, 228, 211, 10 }, + { 227, 157, 161, 78, 15 }, }, + { { 91, 238, 55, 54, 6 }, + { 27, 93, 218, 241, 13 }, + { 102, 206, 199, 125, 10 }, + { 184, 245, 187, 173, 8 }, }, + { { 96, 5, 132, 21, 2 }, + { 8, 147, 160, 164, 0 }, + { 74, 130, 26, 0, 6 }, + { 2, 80, 92, 145, 0 }, }, + { { 100, 8, 128, 51, 8 }, + { 128, 128, 163, 132, 9 }, + { 28, 192, 17, 2, 6 }, + { 146, 28, 80, 16, 1 }, }, + { { 110, 40, 135, 140, 3 }, + { 159, 241, 32, 129, 10 }, + { 195, 30, 17, 71, 6 }, + { 88, 16, 72, 255, 9 }, }, + { { 108, 85, 84, 181, 7 }, + { 238, 23, 226, 180, 2 }, + { 234, 210, 170, 163, 6 }, + { 66, 212, 126, 135, 7 }, }, + { { 104, 186, 254, 70, 1 }, + { 111, 193, 60, 152, 13 }, + { 134, 39, 245, 209, 6 }, + { 177, 147, 200, 63, 6 }, }, + { { 104, 179, 85, 202, 7 }, + { 119, 51, 120, 152, 3 }, + { 229, 58, 172, 209, 6 }, + { 193, 145, 236, 206, 14 }, }, + { { 117, 156, 155, 102, 9 }, + { 220, 200, 55, 248, 9 }, + { 150, 109, 147, 154, 14 }, + { 145, 254, 193, 51, 11 }, }, + { { 124, 11, 200, 10, 0 }, + { 162, 170, 44, 128, 9 }, + { 5, 1, 61, 3, 14 }, + { 144, 19, 69, 84, 5 }, }, + { { 126, 89, 104, 196, 9 }, + { 238, 14, 37, 137, 14 }, + { 146, 49, 105, 167, 14 }, + { 121, 26, 71, 7, 7 }, }, + { { 120, 111, 61, 52, 5 }, + { 31, 15, 238, 176, 12 }, + { 162, 203, 207, 97, 14 }, + { 48, 215, 127, 15, 8 }, }, + { { 120, 193, 191, 255, 10 }, + { 26, 255, 183, 156, 7 }, + { 95, 255, 216, 49, 14 }, + { 227, 158, 223, 245, 8 }, }, + { { 122, 218, 185, 69, 10 }, + { 90, 156, 61, 157, 12 }, + { 90, 41, 213, 181, 14 }, + { 59, 155, 195, 149, 10 }, }, + { { 128, 60, 123, 156, 0 }, + { 121, 96, 132, 50, 14 }, + { 3, 157, 227, 192, 1 }, + { 116, 194, 16, 105, 14 }, }, + { { 135, 20, 88, 249, 7 }, + { 228, 48, 198, 127, 2 }, + { 233, 241, 162, 142, 1 }, + { 79, 230, 48, 194, 7 }, }, + { { 131, 27, 5, 165, 13 }, + { 92, 3, 75, 71, 10 }, + { 186, 90, 13, 140, 1 }, + { 94, 45, 44, 3, 10 }, }, + { { 136, 59, 180, 103, 4 }, + { 75, 131, 74, 30, 13 }, + { 46, 98, 221, 193, 1 }, + { 183, 133, 44, 29, 2 }, }, + { { 140, 169, 136, 156, 0 }, + { 139, 162, 148, 2, 10 }, + { 3, 145, 25, 83, 1 }, + { 84, 2, 148, 93, 1 }, }, + { { 142, 177, 3, 26, 11 }, + { 215, 114, 145, 3, 1 }, + { 213, 140, 8, 215, 1 }, + { 140, 8, 148, 238, 11 }, }, + { { 143, 39, 191, 54, 4 }, + { 155, 195, 206, 115, 5 }, + { 38, 207, 222, 79, 1 }, + { 172, 231, 60, 61, 9 }, }, + { { 143, 22, 179, 202, 0 }, + { 210, 224, 8, 123, 7 }, + { 5, 60, 214, 143, 1 }, + { 237, 225, 0, 116, 11 }, }, + { { 148, 24, 222, 74, 0 }, + { 224, 233, 4, 26, 9 }, + { 5, 39, 177, 130, 9 }, + { 149, 130, 9, 112, 7 }, }, + { { 147, 69, 36, 197, 0 }, + { 8, 15, 0, 111, 6 }, + { 10, 50, 74, 44, 9 }, + { 111, 96, 15, 1, 0 }, }, + { { 156, 253, 156, 216, 5 }, + { 199, 175, 212, 58, 10 }, + { 161, 179, 155, 243, 9 }, + { 85, 194, 191, 94, 3 }, }, + { { 155, 34, 55, 120, 13 }, + { 23, 105, 203, 91, 4 }, + { 177, 238, 196, 77, 9 }, + { 45, 173, 57, 110, 8 }, }, + { { 153, 250, 163, 209, 6 }, + { 83, 220, 216, 78, 14 }, + { 104, 188, 85, 249, 9 }, + { 119, 33, 179, 188, 10 }, }, + { { 162, 159, 28, 84, 3 }, + { 76, 19, 188, 59, 8 }, + { 194, 163, 143, 148, 5 }, + { 29, 195, 220, 131, 2 }, }, + { { 172, 79, 91, 26, 11 }, + { 182, 118, 173, 50, 9 }, + { 213, 141, 175, 35, 5 }, + { 148, 203, 86, 230, 13 }, }, + { { 172, 191, 109, 54, 6 }, + { 251, 19, 254, 34, 13 }, + { 102, 203, 111, 211, 5 }, + { 180, 71, 252, 141, 15 }, }, + { { 169, 185, 76, 64, 8 }, + { 99, 3, 53, 74, 8 }, + { 16, 35, 41, 217, 5 }, + { 21, 42, 204, 12, 6 }, }, + { { 182, 40, 233, 2, 12 }, + { 177, 136, 101, 3, 13 }, + { 52, 9, 113, 70, 13 }, + { 188, 10, 97, 24, 13 }, }, + { { 180, 109, 218, 222, 0 }, + { 169, 238, 164, 58, 11 }, + { 7, 181, 187, 98, 13 }, + { 213, 194, 87, 121, 5 }, }, + { { 178, 110, 246, 10, 1 }, + { 37, 237, 40, 51, 13 }, + { 133, 6, 247, 100, 13 }, + { 188, 193, 75, 122, 4 }, }, + { { 179, 37, 153, 105, 14 }, + { 17, 186, 103, 127, 0 }, + { 121, 105, 154, 76, 13 }, + { 15, 238, 101, 216, 8 }, }, + { { 179, 80, 40, 17, 5 }, + { 68, 12, 228, 71, 4 }, + { 168, 129, 64, 172, 13 }, + { 46, 34, 115, 2, 2 }, }, + { { 190, 28, 27, 59, 6 }, + { 210, 120, 230, 55, 9 }, + { 109, 205, 131, 135, 13 }, + { 158, 198, 113, 228, 11 }, }, + { { 188, 127, 85, 99, 14 }, + { 243, 31, 107, 62, 9 }, + { 124, 106, 175, 227, 13 }, + { 151, 205, 111, 140, 15 }, }, + { { 188, 175, 230, 141, 5 }, + { 175, 235, 120, 38, 14 }, + { 171, 22, 127, 83, 13 }, + { 118, 65, 237, 127, 5 }, }, + { { 189, 37, 146, 140, 4 }, + { 139, 234, 96, 114, 2 }, + { 35, 20, 154, 75, 13 }, + { 68, 224, 101, 125, 1 }, }, + { { 196, 27, 214, 183, 1 }, + { 236, 195, 138, 150, 11 }, + { 142, 214, 189, 130, 3 }, + { 214, 149, 28, 51, 7 }, }, + { { 198, 99, 190, 252, 14 }, + { 137, 247, 207, 155, 6 }, + { 115, 247, 220, 102, 3 }, + { 109, 159, 62, 249, 1 }, }, + { { 198, 86, 130, 19, 13 }, + { 196, 196, 201, 167, 1 }, + { 188, 132, 22, 166, 3 }, + { 142, 89, 50, 50, 3 }, }, + { { 198, 139, 73, 36, 10 }, + { 184, 18, 31, 131, 8 }, + { 82, 73, 45, 22, 3 }, + { 28, 31, 132, 129, 13 }, }, + { { 193, 61, 206, 190, 2 }, + { 105, 243, 134, 226, 11 }, + { 71, 215, 59, 200, 3 }, + { 212, 118, 28, 249, 6 }, }, + { { 197, 25, 109, 109, 1 }, + { 252, 35, 6, 206, 12 }, + { 139, 107, 105, 138, 3 }, + { 55, 54, 12, 67, 15 }, }, + { { 199, 77, 61, 239, 11 }, + { 156, 55, 7, 255, 15 }, + { 223, 123, 203, 46, 3 }, + { 255, 254, 14, 195, 9 }, }, + { { 193, 90, 43, 220, 9 }, + { 92, 100, 141, 202, 14 }, + { 147, 189, 69, 168, 3 }, + { 117, 59, 18, 99, 10 }, }, + { { 202, 35, 114, 33, 12 }, + { 35, 66, 75, 151, 4 }, + { 56, 68, 236, 69, 3 }, + { 46, 157, 36, 44, 4 }, }, + { { 207, 199, 244, 213, 9 }, + { 174, 135, 153, 255, 6 }, + { 154, 178, 254, 63, 3 }, + { 111, 249, 158, 23, 5 }, }, + { { 208, 49, 39, 226, 6 }, + { 81, 91, 66, 138, 7 }, + { 100, 126, 72, 192, 11 }, + { 229, 20, 45, 168, 10 }, }, + { { 212, 119, 84, 14, 0 }, + { 233, 47, 8, 178, 1 }, + { 7, 2, 174, 226, 11 }, + { 132, 209, 15, 73, 7 }, }, + { { 209, 134, 49, 90, 2 }, + { 16, 56, 152, 250, 5 }, + { 69, 168, 198, 24, 11 }, + { 165, 241, 145, 192, 8 }, }, + { { 219, 76, 100, 122, 11 }, + { 38, 61, 131, 235, 13 }, + { 213, 226, 99, 45, 11 }, + { 189, 124, 27, 198, 4 }, }, + { { 219, 132, 135, 144, 8 }, + { 18, 201, 145, 227, 2 }, + { 16, 158, 18, 29, 11 }, + { 76, 120, 153, 52, 8 }, }, + { { 223, 222, 6, 112, 0 }, + { 194, 77, 154, 235, 8 }, + { 0, 230, 7, 191, 11 }, + { 29, 117, 155, 36, 3 }, }, + { { 226, 41, 186, 96, 0 }, + { 1, 194, 38, 155, 12 }, + { 0, 101, 217, 68, 7 }, + { 61, 150, 68, 56, 0 }, }, + { { 225, 64, 224, 141, 6 }, + { 40, 180, 96, 198, 6 }, + { 107, 16, 112, 40, 7 }, + { 102, 48, 98, 209, 4 }, }, + { { 225, 154, 144, 165, 2 }, + { 72, 144, 58, 214, 10 }, + { 74, 80, 149, 152, 7 }, + { 86, 181, 192, 145, 2 }, }, + { { 231, 242, 192, 250, 9 }, + { 229, 164, 187, 203, 3 }, + { 149, 240, 52, 254, 7 }, + { 205, 61, 210, 90, 7 }, }, + { { 238, 173, 190, 131, 8 }, + { 131, 195, 53, 183, 15 }, + { 28, 23, 219, 87, 7 }, + { 254, 218, 204, 60, 1 }, }, + { { 240, 28, 242, 124, 1 }, + { 108, 232, 162, 186, 12 }, + { 131, 228, 243, 128, 15 }, + { 53, 212, 81, 115, 6 }, }, + { { 247, 101, 168, 38, 4 }, + { 137, 142, 102, 227, 5 }, + { 38, 65, 90, 110, 15 }, + { 172, 118, 103, 25, 1 }, }, + { { 247, 236, 195, 164, 13 }, + { 189, 204, 115, 227, 10 }, + { 178, 92, 51, 126, 15 }, + { 92, 124, 227, 59, 13 }, }, + { { 248, 45, 84, 113, 4 }, + { 35, 11, 226, 190, 8 }, + { 40, 226, 171, 65, 15 }, + { 23, 212, 125, 12, 4 }, }, + { { 254, 133, 143, 205, 11 }, + { 158, 251, 53, 175, 2 }, + { 219, 63, 26, 23, 15 }, + { 79, 90, 205, 247, 9 }, }, + { { 248, 227, 91, 11, 6 }, + { 51, 126, 124, 150, 1 }, + { 109, 13, 172, 113, 15 }, + { 134, 147, 231, 236, 12 }, }, + { { 254, 214, 62, 31, 15 }, + { 206, 125, 253, 183, 5 }, + { 255, 135, 198, 183, 15 }, + { 174, 219, 251, 231, 3 }, }, }; + +static unsigned char DICT_7X7_1000_BYTES[][4][7] = + { { { 221, 92, 108, 165, 202, 10, 1 }, + { 99, 179, 173, 228, 49, 180, 0 }, + { 168, 41, 210, 155, 29, 93, 1 }, + { 22, 198, 19, 218, 230, 227, 0 }, }, + { { 228, 27, 241, 62, 64, 171, 0 }, + { 17, 253, 137, 11, 181, 42, 1 }, + { 106, 129, 62, 71, 236, 19, 1 }, + { 170, 86, 232, 72, 223, 196, 0 }, }, + { { 158, 170, 43, 172, 93, 39, 1 }, + { 163, 182, 158, 145, 75, 171, 1 }, + { 242, 93, 26, 234, 42, 188, 1 }, + { 234, 233, 68, 188, 182, 226, 1 }, }, + { { 166, 103, 5, 183, 233, 76, 0 }, + { 221, 48, 50, 221, 165, 172, 0 }, + { 25, 75, 246, 208, 115, 50, 1 }, + { 26, 210, 221, 166, 6, 93, 1 }, }, + { { 198, 188, 123, 19, 50, 86, 0 }, + { 253, 193, 139, 113, 154, 97, 0 }, + { 53, 38, 100, 111, 30, 177, 1 }, + { 67, 44, 199, 104, 193, 223, 1 }, }, + { { 88, 128, 20, 35, 89, 238, 0 }, + { 4, 122, 28, 80, 184, 133, 1 }, + { 59, 205, 98, 20, 0, 141, 0 }, + { 208, 142, 133, 28, 47, 16, 0 }, }, + { { 211, 107, 190, 111, 84, 72, 0 }, + { 164, 240, 198, 70, 247, 63, 0 }, + { 9, 21, 123, 62, 235, 101, 1 }, + { 126, 119, 177, 49, 135, 146, 1 }, }, + { { 60, 161, 109, 136, 139, 219, 0 }, + { 37, 14, 191, 169, 44, 198, 0 }, + { 109, 232, 136, 219, 66, 158, 0 }, + { 49, 154, 74, 254, 184, 82, 0 }, }, + { { 137, 7, 31, 86, 150, 158, 0 }, + { 112, 74, 104, 49, 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}, + { { 246, 117, 82, 145, 217, 185, 1 }, + { 211, 93, 55, 204, 54, 225, 1 }, + { 206, 205, 196, 165, 87, 55, 1 }, + { 195, 182, 25, 246, 93, 101, 1 }, }, + { { 245, 114, 198, 173, 192, 65, 0 }, + { 5, 53, 39, 206, 19, 62, 0 }, + { 65, 1, 218, 177, 167, 87, 1 }, + { 62, 100, 57, 242, 86, 80, 0 }, }, + { { 247, 124, 210, 85, 227, 70, 0 }, + { 221, 209, 127, 126, 19, 48, 0 }, + { 49, 99, 213, 37, 159, 119, 1 }, + { 6, 100, 63, 127, 69, 221, 1 }, }, + { { 246, 132, 78, 31, 171, 28, 0 }, + { 249, 0, 53, 120, 187, 230, 0 }, + { 28, 106, 252, 57, 16, 183, 1 }, + { 51, 238, 143, 86, 0, 79, 1 }, }, + { { 248, 61, 136, 57, 165, 1, 1 }, + { 122, 167, 54, 74, 84, 34, 0 }, + { 192, 82, 206, 8, 222, 15, 1 }, + { 34, 21, 41, 54, 114, 175, 0 }, }, + { { 251, 54, 195, 223, 220, 215, 1 }, + { 214, 31, 111, 219, 211, 251, 0 }, + { 245, 157, 253, 225, 182, 111, 1 }, + { 111, 229, 237, 251, 124, 53, 1 }, }, + { { 248, 76, 172, 3, 76, 20, 1 }, + { 98, 146, 132, 94, 208, 228, 0 }, + { 148, 25, 96, 26, 153, 15, 1 }, + { 19, 133, 189, 16, 164, 163, 0 }, }, + { { 251, 160, 208, 185, 211, 75, 1 }, + { 150, 118, 63, 234, 56, 51, 0 }, + { 233, 101, 206, 133, 130, 239, 1 }, + { 102, 14, 43, 254, 55, 52, 1 }, }, + { { 250, 195, 132, 204, 125, 54, 1 }, + { 138, 18, 92, 158, 93, 239, 1 }, + { 182, 95, 25, 144, 225, 175, 1 }, + { 251, 221, 60, 157, 36, 40, 1 }, }, + { { 249, 231, 61, 60, 30, 97, 1 }, + { 118, 102, 134, 45, 93, 191, 1 }, + { 195, 60, 30, 94, 115, 207, 1 }, + { 254, 221, 90, 48, 179, 55, 0 }, }, + { { 248, 255, 88, 101, 6, 119, 1 }, + { 102, 231, 79, 124, 93, 104, 1 }, + { 247, 48, 83, 13, 127, 143, 1 }, + { 139, 93, 31, 121, 115, 179, 0 }, }, + { { 253, 11, 219, 85, 100, 56, 1 }, + { 59, 210, 69, 75, 119, 120, 1 }, + { 142, 19, 85, 109, 232, 95, 1 }, + { 143, 119, 105, 81, 37, 238, 0 }, }, + { { 253, 22, 174, 228, 229, 62, 1 }, + { 107, 51, 252, 154, 115, 124, 1 }, + { 190, 83, 147, 186, 180, 95, 1 }, + { 159, 103, 44, 159, 230, 107, 0 }, }, + { { 254, 73, 163, 120, 194, 52, 0 }, + { 145, 178, 228, 63, 22, 98, 1 }, + { 22, 33, 143, 98, 201, 63, 1 }, + { 163, 52, 126, 19, 166, 196, 1 }, }, + { { 253, 132, 226, 198, 107, 168, 1 }, + { 75, 26, 213, 170, 187, 176, 1 }, + { 138, 235, 49, 163, 144, 223, 1 }, + { 134, 238, 170, 213, 172, 105, 0 }, }, + { { 252, 149, 79, 148, 230, 207, 0 }, + { 125, 31, 45, 185, 127, 36, 0 }, + { 121, 179, 148, 249, 84, 159, 1 }, + { 18, 127, 78, 218, 124, 95, 0 }, }, + { { 254, 165, 35, 88, 48, 164, 1 }, + { 219, 10, 198, 25, 30, 35, 1 }, + { 146, 134, 13, 98, 82, 191, 1 }, + { 226, 60, 76, 49, 168, 109, 1 }, }, + { { 254, 168, 217, 255, 176, 118, 0 }, + { 189, 226, 111, 219, 153, 99, 1 }, + { 55, 6, 255, 205, 138, 191, 1 }, + { 227, 76, 237, 251, 35, 222, 1 }, }, + { { 255, 195, 135, 255, 162, 252, 1 }, + { 159, 42, 100, 255, 191, 126, 1 }, + { 159, 162, 255, 240, 225, 255, 1 }, + { 191, 126, 255, 147, 42, 124, 1 }, }, + { { 95, 114, 124, 241, 17, 248, 0 }, + { 181, 107, 215, 196, 48, 93, 1 }, + { 15, 196, 71, 159, 39, 125, 0 }, + { 221, 6, 17, 245, 235, 86, 1 }, }, + { { 135, 81, 63, 164, 61, 190, 1 }, + { 171, 105, 152, 149, 103, 245, 1 }, + { 190, 222, 18, 254, 69, 112, 1 }, + { 215, 243, 84, 140, 203, 106, 1 }, }, + { { 198, 147, 77, 53, 31, 189, 0 }, + { 177, 45, 17, 113, 125, 237, 1 }, + { 94, 252, 86, 89, 100, 177, 1 }, + { 219, 223, 71, 68, 90, 70, 1 }, }, + { { 231, 230, 150, 226, 6, 159, 1 }, + { 195, 108, 74, 190, 250, 124, 0 }, + { 252, 176, 35, 180, 179, 243, 1 }, + { 31, 47, 190, 169, 27, 97, 1 }, }, }; +} diff --git a/modules/objdetect/test/test_arucodetection.cpp b/modules/objdetect/test/test_arucodetection.cpp new file mode 100644 index 0000000000..aee147c58f --- /dev/null +++ b/modules/objdetect/test/test_arucodetection.cpp @@ -0,0 +1,704 @@ +// This file is part of OpenCV project. +// It is subject to the license terms in the LICENSE file found in the top-level directory +// of this distribution and at http://opencv.org/license.html. + +#include "test_precomp.hpp" +#include "opencv2/objdetect/aruco_detector.hpp" +#include "opencv2/calib3d.hpp" + +namespace opencv_test { namespace { + +/** + * @brief Draw 2D synthetic markers and detect them + */ +class CV_ArucoDetectionSimple : public cvtest::BaseTest { + public: + CV_ArucoDetectionSimple(); + + protected: + void run(int); +}; + + +CV_ArucoDetectionSimple::CV_ArucoDetectionSimple() {} + + +void CV_ArucoDetectionSimple::run(int) { + aruco::ArucoDetector detector(aruco::getPredefinedDictionary(aruco::DICT_6X6_250)); + + // 20 images + for(int i = 0; i < 20; i++) { + + const int markerSidePixels = 100; + int imageSize = markerSidePixels * 2 + 3 * (markerSidePixels / 2); + + // draw synthetic image and store marker corners and ids + vector > groundTruthCorners; + vector groundTruthIds; + Mat img = Mat(imageSize, imageSize, CV_8UC1, Scalar::all(255)); + for(int y = 0; y < 2; y++) { + for(int x = 0; x < 2; x++) { + Mat marker; + int id = i * 4 + y * 2 + x; + aruco::generateImageMarker(detector.getDictionary(), id, markerSidePixels, marker); + Point2f firstCorner = + Point2f(markerSidePixels / 2.f + x * (1.5f * markerSidePixels), + markerSidePixels / 2.f + y * (1.5f * markerSidePixels)); + Mat aux = img.colRange((int)firstCorner.x, (int)firstCorner.x + markerSidePixels) + .rowRange((int)firstCorner.y, (int)firstCorner.y + markerSidePixels); + marker.copyTo(aux); + groundTruthIds.push_back(id); + groundTruthCorners.push_back(vector()); + groundTruthCorners.back().push_back(firstCorner); + groundTruthCorners.back().push_back(firstCorner + Point2f(markerSidePixels - 1, 0)); + groundTruthCorners.back().push_back( + firstCorner + Point2f(markerSidePixels - 1, markerSidePixels - 1)); + groundTruthCorners.back().push_back(firstCorner + Point2f(0, markerSidePixels - 1)); + } + } + if(i % 2 == 1) img.convertTo(img, CV_8UC3); + + // detect markers + vector > corners; + vector ids; + + detector.detectMarkers(img, corners, ids); + + // check detection results + for(unsigned int m = 0; m < groundTruthIds.size(); m++) { + int idx = -1; + for(unsigned int k = 0; k < ids.size(); k++) { + if(groundTruthIds[m] == ids[k]) { + idx = (int)k; + break; + } + } + if(idx == -1) { + ts->printf(cvtest::TS::LOG, "Marker not detected"); + ts->set_failed_test_info(cvtest::TS::FAIL_MISMATCH); + return; + } + + for(int c = 0; c < 4; c++) { + double dist = cv::norm(groundTruthCorners[m][c] - corners[idx][c]); // TODO cvtest + if(dist > 0.001) { + ts->printf(cvtest::TS::LOG, "Incorrect marker corners position"); + ts->set_failed_test_info(cvtest::TS::FAIL_BAD_ACCURACY); + return; + } + } + } + } +} + + +static double deg2rad(double deg) { return deg * CV_PI / 180.; } + +/** + * @brief Get rvec and tvec from yaw, pitch and distance + */ +static void getSyntheticRT(double yaw, double pitch, double distance, Mat &rvec, Mat &tvec) { + + rvec = Mat(3, 1, CV_64FC1); + tvec = Mat(3, 1, CV_64FC1); + + // Rvec + // first put the Z axis aiming to -X (like the camera axis system) + Mat rotZ(3, 1, CV_64FC1); + rotZ.ptr(0)[0] = 0; + rotZ.ptr(0)[1] = 0; + rotZ.ptr(0)[2] = -0.5 * CV_PI; + + Mat rotX(3, 1, CV_64FC1); + rotX.ptr(0)[0] = 0.5 * CV_PI; + rotX.ptr(0)[1] = 0; + rotX.ptr(0)[2] = 0; + + Mat camRvec, camTvec; + composeRT(rotZ, Mat(3, 1, CV_64FC1, Scalar::all(0)), rotX, Mat(3, 1, CV_64FC1, Scalar::all(0)), + camRvec, camTvec); + + // now pitch and yaw angles + Mat rotPitch(3, 1, CV_64FC1); + rotPitch.ptr(0)[0] = 0; + rotPitch.ptr(0)[1] = pitch; + rotPitch.ptr(0)[2] = 0; + + Mat rotYaw(3, 1, CV_64FC1); + rotYaw.ptr(0)[0] = yaw; + rotYaw.ptr(0)[1] = 0; + rotYaw.ptr(0)[2] = 0; + + composeRT(rotPitch, Mat(3, 1, CV_64FC1, Scalar::all(0)), rotYaw, + Mat(3, 1, CV_64FC1, Scalar::all(0)), rvec, tvec); + + // compose both rotations + composeRT(camRvec, Mat(3, 1, CV_64FC1, Scalar::all(0)), rvec, + Mat(3, 1, CV_64FC1, Scalar::all(0)), rvec, tvec); + + // Tvec, just move in z (camera) direction the specific distance + tvec.ptr(0)[0] = 0.; + tvec.ptr(0)[1] = 0.; + tvec.ptr(0)[2] = distance; +} + +/** + * @brief Create a synthetic image of a marker with perspective + */ +static Mat projectMarker(const aruco::Dictionary &dictionary, int id, Mat cameraMatrix, double yaw, + double pitch, double distance, Size imageSize, int markerBorder, + vector &corners, int encloseMarker=0) { + + // canonical image + Mat marker, markerImg; + const int markerSizePixels = 100; + + aruco::generateImageMarker(dictionary, id, markerSizePixels, marker, markerBorder); + marker.copyTo(markerImg); + + if(encloseMarker){ //to enclose the marker + int enclose = int(marker.rows/4); + markerImg = Mat::zeros(marker.rows+(2*enclose), marker.cols+(enclose*2), CV_8UC1); + + Mat field= markerImg.rowRange(int(enclose), int(markerImg.rows-enclose)) + .colRange(int(0), int(markerImg.cols)); + field.setTo(255); + field= markerImg.rowRange(int(0), int(markerImg.rows)) + .colRange(int(enclose), int(markerImg.cols-enclose)); + field.setTo(255); + + field = markerImg(Rect(enclose,enclose,marker.rows,marker.cols)); + marker.copyTo(field); + } + + // get rvec and tvec for the perspective + Mat rvec, tvec; + getSyntheticRT(yaw, pitch, distance, rvec, tvec); + + const float markerLength = 0.05f; + vector markerObjPoints; + markerObjPoints.push_back(Point3f(-markerLength / 2.f, +markerLength / 2.f, 0)); + markerObjPoints.push_back(markerObjPoints[0] + Point3f(markerLength, 0, 0)); + markerObjPoints.push_back(markerObjPoints[0] + Point3f(markerLength, -markerLength, 0)); + markerObjPoints.push_back(markerObjPoints[0] + Point3f(0, -markerLength, 0)); + + // project markers and draw them + Mat distCoeffs(5, 1, CV_64FC1, Scalar::all(0)); + projectPoints(markerObjPoints, rvec, tvec, cameraMatrix, distCoeffs, corners); + + vector originalCorners; + originalCorners.push_back(Point2f(0+float(encloseMarker*markerSizePixels/4), 0+float(encloseMarker*markerSizePixels/4))); + originalCorners.push_back(originalCorners[0]+Point2f((float)markerSizePixels, 0)); + originalCorners.push_back(originalCorners[0]+Point2f((float)markerSizePixels, (float)markerSizePixels)); + originalCorners.push_back(originalCorners[0]+Point2f(0, (float)markerSizePixels)); + + Mat transformation = getPerspectiveTransform(originalCorners, corners); + + Mat img(imageSize, CV_8UC1, Scalar::all(255)); + Mat aux; + const char borderValue = 127; + warpPerspective(markerImg, aux, transformation, imageSize, INTER_NEAREST, BORDER_CONSTANT, + Scalar::all(borderValue)); + + // copy only not-border pixels + for(int y = 0; y < aux.rows; y++) { + for(int x = 0; x < aux.cols; x++) { + if(aux.at(y, x) == borderValue) continue; + img.at(y, x) = aux.at(y, x); + } + } + + return img; +} + +enum class ArucoAlgParams +{ + USE_DEFAULT = 0, + USE_APRILTAG=1, /// Detect marker candidates :: using AprilTag + DETECT_INVERTED_MARKER, /// Check if there is a white marker + USE_ARUCO3 /// Check if aruco3 should be used +}; + + +/** + * @brief Draws markers in perspective and detect them + */ +class CV_ArucoDetectionPerspective : public cvtest::BaseTest { + public: + CV_ArucoDetectionPerspective(ArucoAlgParams arucoAlgParam) : arucoAlgParams(arucoAlgParam) {} + + protected: + void run(int); + ArucoAlgParams arucoAlgParams; +}; + + +void CV_ArucoDetectionPerspective::run(int) { + + int iter = 0; + int szEnclosed = 0; + Mat cameraMatrix = Mat::eye(3, 3, CV_64FC1); + Size imgSize(500, 500); + cameraMatrix.at(0, 0) = cameraMatrix.at(1, 1) = 650; + cameraMatrix.at(0, 2) = imgSize.width / 2; + cameraMatrix.at(1, 2) = imgSize.height / 2; + aruco::DetectorParameters params; + params.minDistanceToBorder = 1; + aruco::ArucoDetector detector(aruco::getPredefinedDictionary(aruco::DICT_6X6_250), params); + + // detect from different positions + for(double distance = 0.1; distance < 0.7; distance += 0.2) { + for(int pitch = 0; pitch < 360; pitch += (distance == 0.1? 60:180)) { + for(int yaw = 70; yaw <= 120; yaw += 40){ + int currentId = iter % 250; + int markerBorder = iter % 2 + 1; + iter++; + vector groundTruthCorners; + aruco::DetectorParameters detectorParameters = params; + detectorParameters.markerBorderBits = markerBorder; + + /// create synthetic image + Mat img= + projectMarker(detector.getDictionary(), currentId, cameraMatrix, deg2rad(yaw), deg2rad(pitch), + distance, imgSize, markerBorder, groundTruthCorners, szEnclosed); + // marker :: Inverted + if(ArucoAlgParams::DETECT_INVERTED_MARKER == arucoAlgParams){ + img = ~img; + detectorParameters.detectInvertedMarker = true; + } + + if(ArucoAlgParams::USE_APRILTAG == arucoAlgParams){ + detectorParameters.cornerRefinementMethod = aruco::CORNER_REFINE_APRILTAG; + } + + if (ArucoAlgParams::USE_ARUCO3 == arucoAlgParams) { + detectorParameters.useAruco3Detection = true; + detectorParameters.cornerRefinementMethod = aruco::CORNER_REFINE_SUBPIX; + } + detector.setDetectorParameters(detectorParameters); + + // detect markers + vector > corners; + vector ids; + detector.detectMarkers(img, corners, ids); + + // check results + if(ids.size() != 1 || (ids.size() == 1 && ids[0] != currentId)) { + if(ids.size() != 1) + ts->printf(cvtest::TS::LOG, "Incorrect number of detected markers"); + else + ts->printf(cvtest::TS::LOG, "Incorrect marker id"); + ts->set_failed_test_info(cvtest::TS::FAIL_MISMATCH); + return; + } + for(int c = 0; c < 4; c++) { + double dist = cv::norm(groundTruthCorners[c] - corners[0][c]); // TODO cvtest + if(dist > 5) { + ts->printf(cvtest::TS::LOG, "Incorrect marker corners position"); + ts->set_failed_test_info(cvtest::TS::FAIL_BAD_ACCURACY); + return; + } + } + } + } + // change the state :: to detect an enclosed inverted marker + if(ArucoAlgParams::DETECT_INVERTED_MARKER == arucoAlgParams && distance == 0.1){ + distance -= 0.1; + szEnclosed++; + } + } +} + + +/** + * @brief Check max and min size in marker detection parameters + */ +class CV_ArucoDetectionMarkerSize : public cvtest::BaseTest { + public: + CV_ArucoDetectionMarkerSize(); + + protected: + void run(int); +}; + + +CV_ArucoDetectionMarkerSize::CV_ArucoDetectionMarkerSize() {} + + +void CV_ArucoDetectionMarkerSize::run(int) { + aruco::DetectorParameters params; + aruco::ArucoDetector detector(aruco::getPredefinedDictionary(aruco::DICT_6X6_250), params); + int markerSide = 20; + int imageSize = 200; + + // 10 cases + for(int i = 0; i < 10; i++) { + Mat marker; + int id = 10 + i * 20; + + // create synthetic image + Mat img = Mat(imageSize, imageSize, CV_8UC1, Scalar::all(255)); + aruco::generateImageMarker(detector.getDictionary(), id, markerSide, marker); + Mat aux = img.colRange(30, 30 + markerSide).rowRange(50, 50 + markerSide); + marker.copyTo(aux); + + vector > corners; + vector ids; + + // set a invalid minMarkerPerimeterRate + aruco::DetectorParameters detectorParameters = params; + detectorParameters.minMarkerPerimeterRate = min(4., (4. * markerSide) / float(imageSize) + 0.1); + detector.setDetectorParameters(detectorParameters); + detector.detectMarkers(img, corners, ids); + if(corners.size() != 0) { + ts->printf(cvtest::TS::LOG, "Error in DetectorParameters::minMarkerPerimeterRate"); + ts->set_failed_test_info(cvtest::TS::FAIL_BAD_ACCURACY); + return; + } + + // set an valid minMarkerPerimeterRate + detectorParameters = params; + detectorParameters.minMarkerPerimeterRate = max(0., (4. * markerSide) / float(imageSize) - 0.1); + detector.setDetectorParameters(detectorParameters); + detector.detectMarkers(img, corners, ids); + if(corners.size() != 1 || (corners.size() == 1 && ids[0] != id)) { + ts->printf(cvtest::TS::LOG, "Error in DetectorParameters::minMarkerPerimeterRate"); + ts->set_failed_test_info(cvtest::TS::FAIL_BAD_ACCURACY); + return; + } + + // set a invalid maxMarkerPerimeterRate + detectorParameters = params; + detectorParameters.maxMarkerPerimeterRate = min(4., (4. * markerSide) / float(imageSize) - 0.1); + detector.setDetectorParameters(detectorParameters); + detector.detectMarkers(img, corners, ids); + if(corners.size() != 0) { + ts->printf(cvtest::TS::LOG, "Error in DetectorParameters::maxMarkerPerimeterRate"); + ts->set_failed_test_info(cvtest::TS::FAIL_BAD_ACCURACY); + return; + } + + // set an valid maxMarkerPerimeterRate + detectorParameters = params; + detectorParameters.maxMarkerPerimeterRate = max(0., (4. * markerSide) / float(imageSize) + 0.1); + detector.setDetectorParameters(detectorParameters); + detector.detectMarkers(img, corners, ids); + if(corners.size() != 1 || (corners.size() == 1 && ids[0] != id)) { + ts->printf(cvtest::TS::LOG, "Error in DetectorParameters::maxMarkerPerimeterRate"); + ts->set_failed_test_info(cvtest::TS::FAIL_BAD_ACCURACY); + return; + } + } +} + + +/** + * @brief Check error correction in marker bits + */ +class CV_ArucoBitCorrection : public cvtest::BaseTest { + public: + CV_ArucoBitCorrection(); + + protected: + void run(int); +}; + + +CV_ArucoBitCorrection::CV_ArucoBitCorrection() {} + + +void CV_ArucoBitCorrection::run(int) { + + aruco::Dictionary dictionary1 = aruco::getPredefinedDictionary(aruco::DICT_6X6_250); + aruco::Dictionary dictionary2 = aruco::getPredefinedDictionary(aruco::DICT_6X6_250); + aruco::DetectorParameters params; + aruco::ArucoDetector detector1(dictionary1, params); + int markerSide = 50; + int imageSize = 150; + + // 10 markers + for(int l = 0; l < 10; l++) { + Mat marker; + int id = 10 + l * 20; + + Mat currentCodeBytes = dictionary1.bytesList.rowRange(id, id + 1); + aruco::DetectorParameters detectorParameters = detector1.getDetectorParameters(); + // 5 valid cases + for(int i = 0; i < 5; i++) { + // how many bit errors (the error is low enough so it can be corrected) + detectorParameters.errorCorrectionRate = 0.2 + i * 0.1; + detector1.setDetectorParameters(detectorParameters); + int errors = + (int)std::floor(dictionary1.maxCorrectionBits * detector1.getDetectorParameters().errorCorrectionRate - 1.); + + // create erroneous marker in currentCodeBits + Mat currentCodeBits = + aruco::Dictionary::getBitsFromByteList(currentCodeBytes, dictionary1.markerSize); + for(int e = 0; e < errors; e++) { + currentCodeBits.ptr()[2 * e] = + !currentCodeBits.ptr()[2 * e]; + } + + // add erroneous marker to dictionary2 in order to create the erroneous marker image + Mat currentCodeBytesError = aruco::Dictionary::getByteListFromBits(currentCodeBits); + currentCodeBytesError.copyTo(dictionary2.bytesList.rowRange(id, id + 1)); + Mat img = Mat(imageSize, imageSize, CV_8UC1, Scalar::all(255)); + dictionary2.generateImageMarker(id, markerSide, marker); + Mat aux = img.colRange(30, 30 + markerSide).rowRange(50, 50 + markerSide); + marker.copyTo(aux); + + // try to detect using original dictionary + vector > corners; + vector ids; + detector1.detectMarkers(img, corners, ids); + if(corners.size() != 1 || (corners.size() == 1 && ids[0] != id)) { + ts->printf(cvtest::TS::LOG, "Error in bit correction"); + ts->set_failed_test_info(cvtest::TS::FAIL_BAD_ACCURACY); + return; + } + } + + // 5 invalid cases + for(int i = 0; i < 5; i++) { + // how many bit errors (the error is too high to be corrected) + detectorParameters.errorCorrectionRate = 0.2 + i * 0.1; + detector1.setDetectorParameters(detectorParameters); + int errors = + (int)std::floor(dictionary1.maxCorrectionBits * detector1.getDetectorParameters().errorCorrectionRate + 1.); + + // create erroneous marker in currentCodeBits + Mat currentCodeBits = + aruco::Dictionary::getBitsFromByteList(currentCodeBytes, dictionary1.markerSize); + for(int e = 0; e < errors; e++) { + currentCodeBits.ptr()[2 * e] = + !currentCodeBits.ptr()[2 * e]; + } + + // dictionary3 is only composed by the modified marker (in its original form) + aruco::Dictionary _dictionary3 = aruco::Dictionary( + dictionary2.bytesList.rowRange(id, id + 1).clone(), + dictionary1.markerSize, + dictionary1.maxCorrectionBits); + aruco::ArucoDetector detector3(_dictionary3, detector1.getDetectorParameters()); + // add erroneous marker to dictionary2 in order to create the erroneous marker image + Mat currentCodeBytesError = aruco::Dictionary::getByteListFromBits(currentCodeBits); + currentCodeBytesError.copyTo(dictionary2.bytesList.rowRange(id, id + 1)); + Mat img = Mat(imageSize, imageSize, CV_8UC1, Scalar::all(255)); + dictionary2.generateImageMarker(id, markerSide, marker); + Mat aux = img.colRange(30, 30 + markerSide).rowRange(50, 50 + markerSide); + marker.copyTo(aux); + + // try to detect using dictionary3, it should fail + vector > corners; + vector ids; + detector3.detectMarkers(img, corners, ids); + if(corners.size() != 0) { + ts->printf(cvtest::TS::LOG, "Error in DetectorParameters::errorCorrectionRate"); + ts->set_failed_test_info(cvtest::TS::FAIL_BAD_ACCURACY); + return; + } + } + } +} + +typedef CV_ArucoDetectionPerspective CV_AprilTagDetectionPerspective; +typedef CV_ArucoDetectionPerspective CV_InvertedArucoDetectionPerspective; +typedef CV_ArucoDetectionPerspective CV_Aruco3DetectionPerspective; + +TEST(CV_InvertedArucoDetectionPerspective, algorithmic) { + CV_InvertedArucoDetectionPerspective test(ArucoAlgParams::DETECT_INVERTED_MARKER); + test.safe_run(); +} + +TEST(CV_AprilTagDetectionPerspective, algorithmic) { + CV_AprilTagDetectionPerspective test(ArucoAlgParams::USE_APRILTAG); + test.safe_run(); +} + +TEST(CV_Aruco3DetectionPerspective, algorithmic) { + CV_Aruco3DetectionPerspective test(ArucoAlgParams::USE_ARUCO3); + test.safe_run(); +} + +TEST(CV_ArucoDetectionSimple, algorithmic) { + CV_ArucoDetectionSimple test; + test.safe_run(); +} + +TEST(CV_ArucoDetectionPerspective, algorithmic) { + CV_ArucoDetectionPerspective test(ArucoAlgParams::USE_DEFAULT); + test.safe_run(); +} + +TEST(CV_ArucoDetectionMarkerSize, algorithmic) { + CV_ArucoDetectionMarkerSize test; + test.safe_run(); +} + +TEST(CV_ArucoBitCorrection, algorithmic) { + CV_ArucoBitCorrection test; + test.safe_run(); +} + +TEST(CV_ArucoDetectMarkers, regression_3192) +{ + aruco::ArucoDetector detector(aruco::getPredefinedDictionary(aruco::DICT_4X4_50)); + vector markerIds; + vector > markerCorners; + string imgPath = cvtest::findDataFile("aruco/regression_3192.png"); + Mat image = imread(imgPath); + const size_t N = 2ull; + const int goldCorners[N][8] = { {345,120, 520,120, 520,295, 345,295}, {101,114, 270,112, 276,287, 101,287} }; + const int goldCornersIds[N] = { 6, 4 }; + map mapGoldCorners; + for (size_t i = 0; i < N; i++) + mapGoldCorners[goldCornersIds[i]] = goldCorners[i]; + + detector.detectMarkers(image, markerCorners, markerIds); + + ASSERT_EQ(N, markerIds.size()); + for (size_t i = 0; i < N; i++) + { + int arucoId = markerIds[i]; + ASSERT_EQ(4ull, markerCorners[i].size()); + ASSERT_TRUE(mapGoldCorners.find(arucoId) != mapGoldCorners.end()); + for (int j = 0; j < 4; j++) + { + EXPECT_NEAR(static_cast(mapGoldCorners[arucoId][j * 2]), markerCorners[i][j].x, 1.f); + EXPECT_NEAR(static_cast(mapGoldCorners[arucoId][j * 2 + 1]), markerCorners[i][j].y, 1.f); + } + } +} + +TEST(CV_ArucoDetectMarkers, regression_2492) +{ + aruco::ArucoDetector detector(aruco::getPredefinedDictionary(aruco::DICT_5X5_50)); + aruco::DetectorParameters detectorParameters = detector.getDetectorParameters(); + detectorParameters.minMarkerDistanceRate = 0.026; + detector.setDetectorParameters(detectorParameters); + vector markerIds; + vector > markerCorners; + string imgPath = cvtest::findDataFile("aruco/regression_2492.png"); + Mat image = imread(imgPath); + const size_t N = 8ull; + const int goldCorners[N][8] = { {179,139, 179,95, 223,95, 223,139}, {99,139, 99,95, 143,95, 143,139}, + {19,139, 19,95, 63,95, 63,139}, {256,140, 256,93, 303,93, 303,140}, + {256,62, 259,21, 300,23, 297,64}, {99,21, 143,17, 147,60, 103,64}, + {69,61, 28,61, 14,21, 58,17}, {174,62, 182,13, 230,19, 223,68} }; + const int goldCornersIds[N] = {13, 13, 13, 13, 1, 15, 14, 4}; + map > mapGoldCorners; + for (size_t i = 0; i < N; i++) + mapGoldCorners[goldCornersIds[i]].push_back(goldCorners[i]); + + detector.detectMarkers(image, markerCorners, markerIds); + + ASSERT_EQ(N, markerIds.size()); + for (size_t i = 0; i < N; i++) + { + int arucoId = markerIds[i]; + ASSERT_EQ(4ull, markerCorners[i].size()); + ASSERT_TRUE(mapGoldCorners.find(arucoId) != mapGoldCorners.end()); + float totalDist = 8.f; + for (size_t k = 0ull; k < mapGoldCorners[arucoId].size(); k++) + { + float dist = 0.f; + for (int j = 0; j < 4; j++) // total distance up to 4 points + { + dist += abs(mapGoldCorners[arucoId][k][j * 2] - markerCorners[i][j].x); + dist += abs(mapGoldCorners[arucoId][k][j * 2 + 1] - markerCorners[i][j].y); + } + totalDist = min(totalDist, dist); + } + EXPECT_LT(totalDist, 8.f); + } +} + +struct ArucoThreading: public testing::TestWithParam +{ + struct NumThreadsSetter { + NumThreadsSetter(const int num_threads) + : original_num_threads_(getNumThreads()) { + setNumThreads(num_threads); + } + + ~NumThreadsSetter() { + setNumThreads(original_num_threads_); + } + private: + int original_num_threads_; + }; +}; + +TEST_P(ArucoThreading, number_of_threads_does_not_change_results) +{ + // We are not testing against different dictionaries + // As we are interested mostly in small images, smaller + // markers is better -> 4x4 + aruco::ArucoDetector detector(aruco::getPredefinedDictionary(aruco::DICT_4X4_50)); + + // Height of the test image can be chosen quite freely + // We aim to test against small images as in those the + // number of threads has most effect + const int height_img = 20; + // Just to get nice white boarder + const int shift = height_img > 10 ? 5 : 1; + const int height_marker = height_img-2*shift; + + // Create a test image + Mat img_marker; + aruco::generateImageMarker(detector.getDictionary(), 23, height_marker, img_marker, 1); + + // Copy to bigger image to get a white border + Mat img(height_img, height_img, CV_8UC1, Scalar(255)); + img_marker.copyTo(img(Rect(shift, shift, height_marker, height_marker))); + + aruco::DetectorParameters detectorParameters = detector.getDetectorParameters(); + detectorParameters.cornerRefinementMethod = GetParam(); + detector.setDetectorParameters(detectorParameters); + + vector > original_corners; + vector original_ids; + { + NumThreadsSetter thread_num_setter(1); + detector.detectMarkers(img, original_corners, original_ids); + } + + ASSERT_EQ(original_ids.size(), 1ull); + ASSERT_EQ(original_corners.size(), 1ull); + + int num_threads_to_test[] = { 2, 8, 16, 32, height_img-1, height_img, height_img+1}; + + for (size_t i_num_threads = 0; i_num_threads < sizeof(num_threads_to_test)/sizeof(int); ++i_num_threads) { + NumThreadsSetter thread_num_setter(num_threads_to_test[i_num_threads]); + + vector > corners; + vector ids; + detector.detectMarkers(img, corners, ids); + + // If we don't find any markers, the test is broken + ASSERT_EQ(ids.size(), 1ull); + + // Make sure we got the same result as the first time + ASSERT_EQ(corners.size(), original_corners.size()); + ASSERT_EQ(ids.size(), original_ids.size()); + ASSERT_EQ(ids.size(), corners.size()); + for (size_t i = 0; i < corners.size(); ++i) { + EXPECT_EQ(ids[i], original_ids[i]); + for (size_t j = 0; j < corners[i].size(); ++j) { + EXPECT_NEAR(corners[i][j].x, original_corners[i][j].x, 0.1f); + EXPECT_NEAR(corners[i][j].y, original_corners[i][j].y, 0.1f); + } + } + } +} + +INSTANTIATE_TEST_CASE_P( + CV_ArucoDetectMarkers, ArucoThreading, + ::testing::Values( + aruco::CORNER_REFINE_NONE, + aruco::CORNER_REFINE_SUBPIX, + aruco::CORNER_REFINE_CONTOUR, + aruco::CORNER_REFINE_APRILTAG + )); + +}} // namespace diff --git a/modules/objdetect/tutorials/images/singlemarkersaxes.jpg b/modules/objdetect/tutorials/images/singlemarkersaxes.jpg new file mode 100644 index 0000000000..c7a1db44d2 Binary files /dev/null and b/modules/objdetect/tutorials/images/singlemarkersaxes.jpg differ diff --git a/modules/objdetect/tutorials/images/singlemarkersaxes2.jpg b/modules/objdetect/tutorials/images/singlemarkersaxes2.jpg new file mode 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