.. _Pyramids: Image Pyramids *************** Goal ===== In this tutorial you will learn how to: * Use the OpenCV functions :pyr_up:`pyrUp <>` and :pyr_down:`pyrDown <>` to downsample or upsample a given image. Theory ======= .. note:: The explanation below belongs to the book **Learning OpenCV** by Bradski and Kaehler. * Usually we need to convert an image to a size different than its original. For this, there are two possible options: * *Upsize* the image (zoom in) or * *Downsize* it (zoom out). * Although there is a *geometric transformation* function in OpenCV that -literally- resize an image (:resize:`resize <>`, which we will show in a future tutorial), in this section we analyze first the use of **Image Pyramids**, which are widely applied in a huge range of vision applications. Image Pyramid -------------- * An image pyramid is a collection of images - all arising from a single original image - that are successively downsampled until some desired stopping point is reached. * There are two common kinds of image pyramids: * **Gaussian pyramid:** Used to downsample images * **Laplacian pyramid:** Used to reconstruct an upsampled image from an image lower in the pyramid (with less resolution) * In this tutorial we'll use the *Gaussian pyramid*. Gaussian Pyramid ^^^^^^^^^^^^^^^^^ * Imagine the pyramid as a set of layers in which the higher the layer, the smaller the size. .. image:: images/Pyramids_Tutorial_Pyramid_Theory.png :alt: Pyramid figure :align: center * Every layer is numbered from bottom to top, so layer :math:`(i+1)` (denoted as :math:`G_{i+1}` is smaller than layer :math:`i` (:math:`G_{i}`). * To produce layer :math:`(i+1)` in the Gaussian pyramid, we do the following: * Convolve :math:`G_{i}` with a Gaussian kernel: .. math:: \frac{1}{16} \begin{bmatrix} 1 & 4 & 6 & 4 & 1 \\ 4 & 16 & 24 & 16 & 4 \\ 6 & 24 & 36 & 24 & 6 \\ 4 & 16 & 24 & 16 & 4 \\ 1 & 4 & 6 & 4 & 1 \end{bmatrix} * Remove every even-numbered row and column. * You can easily notice that the resulting image will be exactly one-quarter the area of its predecessor. Iterating this process on the input image :math:`G_{0}` (original image) produces the entire pyramid. * The procedure above was useful to downsample an image. What if we want to make it bigger?: * First, upsize the image to twice the original in each dimension, wit the new even rows and columns filled with zeros (:math:`0`) * Perform a convolution with the same kernel shown above (multiplied by 4) to approximate the values of the "missing pixels" * These two procedures (downsampling and upsampling as explained above) are implemented by the OpenCV functions :pyr_up:`pyrUp <>` and :pyr_down:`pyrDown <>`, as we will see in an example with the code below: .. note:: When we reduce the size of an image, we are actually *losing* information of the image. Code ====== This tutorial code's is shown lines below. You can also download it from `here `_ .. code-block:: cpp #include "opencv2/imgproc/imgproc.hpp" #include "opencv2/highgui/highgui.hpp" #include #include #include using namespace cv; /// Global variables Mat src, dst, tmp; char* window_name = "Pyramids Demo"; /** * @function main */ int main( int argc, char** argv ) { /// General instructions printf( "\n Zoom In-Out demo \n " ); printf( "------------------ \n" ); printf( " * [u] -> Zoom in \n" ); printf( " * [d] -> Zoom out \n" ); printf( " * [ESC] -> Close program \n \n" ); /// Test image - Make sure it s divisible by 2^{n} src = imread( "../images/chicky_512.jpg" ); if( !src.data ) { printf(" No data! -- Exiting the program \n"); return -1; } tmp = src; dst = tmp; /// Create window namedWindow( window_name, CV_WINDOW_AUTOSIZE ); imshow( window_name, dst ); /// Loop while( true ) { int c; c = waitKey(10); if( (char)c == 27 ) { break; } if( (char)c == 'u' ) { pyrUp( tmp, dst, Size( tmp.cols*2, tmp.rows*2 ) ); printf( "** Zoom In: Image x 2 \n" ); } else if( (char)c == 'd' ) { pyrDown( tmp, dst, Size( tmp.cols/2, tmp.rows/2 ) ); printf( "** Zoom Out: Image / 2 \n" ); } imshow( window_name, dst ); tmp = dst; } return 0; } Explanation ============= #. Let's check the general structure of the program: * Load an image (in this case it is defined in the program, the user does not have to enter it as an argument) .. code-block:: cpp /// Test image - Make sure it s divisible by 2^{n} src = imread( "../images/chicky_512.jpg" ); if( !src.data ) { printf(" No data! -- Exiting the program \n"); return -1; } * Create a Mat object to store the result of the operations (*dst*) and one to save temporal results (*tmp*). .. code-block:: cpp Mat src, dst, tmp; /* ... */ tmp = src; dst = tmp; * Create a window to display the result .. code-block:: cpp namedWindow( window_name, CV_WINDOW_AUTOSIZE ); imshow( window_name, dst ); * Perform an infinite loop waiting for user input. .. code-block:: cpp while( true ) { int c; c = waitKey(10); if( (char)c == 27 ) { break; } if( (char)c == 'u' ) { pyrUp( tmp, dst, Size( tmp.cols*2, tmp.rows*2 ) ); printf( "** Zoom In: Image x 2 \n" ); } else if( (char)c == 'd' ) { pyrDown( tmp, dst, Size( tmp.cols/2, tmp.rows/2 ) ); printf( "** Zoom Out: Image / 2 \n" ); } imshow( window_name, dst ); tmp = dst; } Our program exits if the user presses *ESC*. Besides, it has two options: * **Perform upsampling (after pressing 'u')** .. code-block:: cpp pyrUp( tmp, dst, Size( tmp.cols*2, tmp.rows*2 ) We use the function :pyr_up:`pyrUp <>` with 03 arguments: * *tmp*: The current image, it is initialized with the *src* original image. * *dst*: The destination image (to be shown on screen, supposedly the double of the input image) * *Size( tmp.cols*2, tmp.rows*2 )* : The destination size. Since we are upsampling, :pyr_up:`pyrUp <>` expects a size double than the input image (in this case *tmp*). * **Perform downsampling (after pressing 'd')** .. code-block:: cpp pyrDown( tmp, dst, Size( tmp.cols/2, tmp.rows/2 ) Similarly as with :pyr_up:`pyrUp <>`, we use the function :pyr_down:`pyrDown <>` with 03 arguments: * *tmp*: The current image, it is initialized with the *src* original image. * *dst*: The destination image (to be shown on screen, supposedly half the input image) * *Size( tmp.cols/2, tmp.rows/2 )* : The destination size. Since we are upsampling, :pyr_down:`pyrDown <>` expects half the size the input image (in this case *tmp*). * Notice that it is important that the input image can be divided by a factor of two (in both dimensions). Otherwise, an error will be shown. * Finally, we update the input image **tmp** with the current image displayed, so the subsequent operations are performed on it. .. code-block:: cpp tmp = dst; Results ======== * After compiling the code above we can test it. The program calls an image **chicky_512.jpg** that comes in the *tutorial_code/image* folder. Notice that this image is :math:`512 \times 512`, hence a downsample won't generate any error (:math:`512 = 2^{9}`). The original image is shown below: .. image:: images/Pyramids_Tutorial_Original_Image.jpg :alt: Pyramids: Original image :align: center * First we apply two successive :pyr_down:`pyrDown <>` operations by pressing 'd'. Our output is: .. image:: images/Pyramids_Tutorial_PyrDown_Result.jpg :alt: Pyramids: PyrDown Result :align: center * Note that we should have lost some resolution due to the fact that we are diminishing the size of the image. This is evident after we apply :pyr_up:`pyrUp <>` twice (by pressing 'u'). Our output is now: .. image:: images/Pyramids_Tutorial_PyrUp_Result.jpg :alt: Pyramids: PyrUp Result :align: center