Miscellaneous Image Transformations
===================================

.. highlight:: cpp

.. index:: adaptiveThreshold

adaptiveThreshold
---------------------
.. c:function:: void adaptiveThreshold( const Mat& src, Mat& dst, double maxValue,                        int adaptiveMethod, int thresholdType,                        int blockSize, double C )

    Applies an adaptive threshold to an array.

    :param src: Source 8-bit single-channel image

    :param dst: Destination image; will have the same size and the same type as  ``src``
    
    :param maxValue: The non-zero value assigned to the pixels for which the condition is satisfied. See the discussion

    :param adaptiveMethod: Adaptive thresholding algorithm to use, ``ADAPTIVE_THRESH_MEAN_C``  or  ``ADAPTIVE_THRESH_GAUSSIAN_C``  (see the discussion)

    :param thresholdType: Thresholding type; must be one of  ``THRESH_BINARY``  or  ``THRESH_BINARY_INV``
    :param blockSize: The size of a pixel neighborhood that is used to calculate a threshold value for the pixel: 3, 5, 7, and so on

    :param C: The constant subtracted from the mean or weighted mean (see the discussion); normally, it's positive, but may be zero or negative as well

The function transforms a grayscale image to a binary image according to the formulas:

    * **THRESH_BINARY**

        .. math::

             dst(x,y) =  \fork{\texttt{maxValue}}{if $src(x,y) > T(x,y)$}{0}{otherwise}

    * **THRESH_BINARY_INV**

        .. math::

             dst(x,y) =  \fork{0}{if $src(x,y) > T(x,y)$}{\texttt{maxValue}}{otherwise}

where
:math:`T(x,y)` is a threshold calculated individually for each pixel.

#.
    For the method ``ADAPTIVE_THRESH_MEAN_C``     the threshold value
    :math:`T(x,y)`     is the mean of a
    :math:`\texttt{blockSize} \times \texttt{blockSize}`     neighborhood of
    :math:`(x, y)`     , minus ``C``     .

#.
    For the method ``ADAPTIVE_THRESH_GAUSSIAN_C``     the threshold value
    :math:`T(x, y)`     is the weighted sum (i.e. cross-correlation with a Gaussian window) of a
    :math:`\texttt{blockSize} \times \texttt{blockSize}`     neighborhood of
    :math:`(x, y)`     , minus ``C``     . The default sigma (standard deviation) is used for the specified ``blockSize``     , see
    :func:`getGaussianKernel`     .

The function can process the image in-place.

See also:
:func:`threshold`,:func:`blur`,:func:`GaussianBlur`
.. index:: cvtColor

cvtColor
------------
.. c:function:: void cvtColor( const Mat& src, Mat& dst, int code, int dstCn=0 )

    Converts image from one color space to another

    :param src: The source image, 8-bit unsigned, 16-bit unsigned ( ``CV_16UC...`` ) or single-precision floating-point

    :param dst: The destination image; will have the same size and the same depth as  ``src``
    :param code: The color space conversion code; see the discussion

    :param dstCn: The number of channels in the destination image; if the parameter is 0, the number of the channels will be derived automatically from  ``src``  and the  ``code``

The function converts the input image from one color
space to another. In the case of transformation to-from RGB color space the ordering of the channels should be specified explicitly (RGB or BGR).

The conventional ranges for R, G and B channel values are:

*
    0 to 255 for ``CV_8U``     images

*
    0 to 65535 for ``CV_16U``     images and

*
    0 to 1 for ``CV_32F``     images.

Of course, in the case of linear transformations the range does not matter,
but in the non-linear cases the input RGB image should be normalized to the proper value range in order to get the correct results, e.g. for RGB
:math:`\rightarrow` L*u*v* transformation. For example, if you have a 32-bit floating-point image directly converted from 8-bit image without any scaling, then it will have 0..255 value range, instead of the assumed by the function 0..1. So, before calling ``cvtColor`` , you need first to scale the image down: ::

    img *= 1./255;
    cvtColor(img, img, CV_BGR2Luv);

The function can do the following transformations:

*
    Transformations within RGB space like adding/removing the alpha channel, reversing the channel order, conversion to/from 16-bit RGB color (R5:G6:B5 or R5:G5:B5), as well as conversion to/from grayscale using:

    .. math::

        \text{RGB[A] to Gray:} \quad Y  \leftarrow 0.299  \cdot R + 0.587  \cdot G + 0.114  \cdot B

    and

    .. math::

        \text{Gray to RGB[A]:} \quad R  \leftarrow Y, G  \leftarrow Y, B  \leftarrow Y, A  \leftarrow 0

    The conversion from a RGB image to gray is done with:

    ::

        cvtColor(src, bwsrc, CV_RGB2GRAY);

    ..

    Some more advanced channel reordering can also be done with
    :func:`mixChannels`     .

*
    RGB
    :math:`\leftrightarrow`     CIE XYZ.Rec 709 with D65 white point ( ``CV_BGR2XYZ, CV_RGB2XYZ, CV_XYZ2BGR, CV_XYZ2RGB``     ):

    .. math::

        \begin{bmatrix} X  \\ Y  \\ Z
          \end{bmatrix} \leftarrow \begin{bmatrix} 0.412453 & 0.357580 & 0.180423 \\ 0.212671 & 0.715160 & 0.072169 \\ 0.019334 & 0.119193 & 0.950227
          \end{bmatrix} \cdot \begin{bmatrix} R  \\ G  \\ B
          \end{bmatrix}

    .. math::

        \begin{bmatrix} R  \\ G  \\ B
          \end{bmatrix} \leftarrow \begin{bmatrix} 3.240479 & -1.53715 & -0.498535 \\ -0.969256 &  1.875991 & 0.041556 \\ 0.055648 & -0.204043 & 1.057311
          \end{bmatrix} \cdot \begin{bmatrix} X  \\ Y  \\ Z
          \end{bmatrix}

    :math:`X`,    :math:`Y`     and
    :math:`Z`     cover the whole value range (in the case of floating-point images
    :math:`Z`     may exceed 1).

*
    RGB
    :math:`\leftrightarrow`     YCrCb JPEG (a.k.a. YCC) ( ``CV_BGR2YCrCb, CV_RGB2YCrCb, CV_YCrCb2BGR, CV_YCrCb2RGB``     )

    .. math::

        Y  \leftarrow 0.299  \cdot R + 0.587  \cdot G + 0.114  \cdot B

    .. math::

        Cr  \leftarrow (R-Y)  \cdot 0.713 + delta

    .. math::

        Cb  \leftarrow (B-Y)  \cdot 0.564 + delta

    .. math::

        R  \leftarrow Y + 1.403  \cdot (Cr - delta)

    .. math::

        G  \leftarrow Y - 0.344  \cdot (Cr - delta) - 0.714  \cdot (Cb - delta)

    .. math::

        B  \leftarrow Y + 1.773  \cdot (Cb - delta)

    where

    .. math::

        delta =  \left \{ \begin{array}{l l} 128 &  \mbox{for 8-bit images} \\ 32768 &  \mbox{for 16-bit images} \\ 0.5 &  \mbox{for floating-point images} \end{array} \right .

    Y, Cr and Cb cover the whole value range.

*
    RGB :math:`\leftrightarrow` HSV ( ``CV_BGR2HSV, CV_RGB2HSV, CV_HSV2BGR, CV_HSV2RGB``     )
      in the case of 8-bit and 16-bit images
      R, G and B are converted to floating-point format and scaled to fit the 0 to 1 range

    .. math::

        V  \leftarrow max(R,G,B)

    .. math::

        S  \leftarrow \fork{\frac{V-min(R,G,B)}{V}}{if $V \neq 0$}{0}{otherwise}

    .. math::

        H  \leftarrow \forkthree{{60(G - B)}/{S}}{if $V=R$}{{120+60(B - R)}/{S}}{if $V=G$}{{240+60(R - G)}/{S}}{if $V=B$}

    if
    :math:`H<0`     then
    :math:`H \leftarrow H+360`     On output
    :math:`0 \leq V \leq 1`,    :math:`0 \leq S \leq 1`,    :math:`0 \leq H \leq 360`     .

    The values are then converted to the destination data type:

    * 8-bit images

        .. math::

            V  \leftarrow 255 V, S  \leftarrow 255 S, H  \leftarrow H/2  \text{(to fit to 0 to 255)}

    * 16-bit images (currently not supported)

        .. math::

            V <- 65535 V, S <- 65535 S, H <- H

    * 32-bit images
        H, S, V are left as is

*
    RGB :math:`\leftrightarrow` HLS ( ``CV_BGR2HLS, CV_RGB2HLS, CV_HLS2BGR, CV_HLS2RGB`` ).
      in the case of 8-bit and 16-bit images
      R, G and B are converted to floating-point format and scaled to fit the 0 to 1 range.

    .. math::

        V_{max}  \leftarrow {max}(R,G,B)

    .. math::

        V_{min}  \leftarrow {min}(R,G,B)

    .. math::

        L  \leftarrow \frac{V_{max} + V_{min}}{2}

    .. math::

        S  \leftarrow \fork { \frac{V_{max} - V_{min}}{V_{max} + V_{min}} }{if  $L < 0.5$ }
            { \frac{V_{max} - V_{min}}{2 - (V_{max} + V_{min})} }{if  $L \ge 0.5$ }

    .. math::

        H  \leftarrow \forkthree {{60(G - B)}/{S}}{if  $V_{max}=R$ }
          {{120+60(B - R)}/{S}}{if  $V_{max}=G$ }
          {{240+60(R - G)}/{S}}{if  $V_{max}=B$ }

    if
    :math:`H<0`     then
    :math:`H \leftarrow H+360`     On output
    :math:`0 \leq L \leq 1`,    :math:`0 \leq S \leq 1`,    :math:`0 \leq H \leq 360`     .

    The values are then converted to the destination data type:

    * 8-bit images

        .. math::

            V  \leftarrow 255 \cdot V, S  \leftarrow 255 \cdot S, H  \leftarrow H/2 \; \text{(to fit to 0 to 255)}

    * 16-bit images (currently not supported)

        .. math::

            V <- 65535 \cdot V, S <- 65535 \cdot S, H <- H

    * 32-bit images
        H, S, V are left as is

*
    RGB :math:`\leftrightarrow` CIE L*a*b* ( ``CV_BGR2Lab, CV_RGB2Lab, CV_Lab2BGR, CV_Lab2RGB`` )
      in the case of 8-bit and 16-bit images
      R, G and B are converted to floating-point format and scaled to fit the 0 to 1 range

    .. math::

        \vecthree{X}{Y}{Z} \leftarrow \vecthreethree{0.412453}{0.357580}{0.180423}{0.212671}{0.715160}{0.072169}{0.019334}{0.119193}{0.950227} \cdot \vecthree{R}{G}{B}

    .. math::

        X  \leftarrow X/X_n,  \text{where} X_n = 0.950456

    .. math::

        Z  \leftarrow Z/Z_n,  \text{where} Z_n = 1.088754

    .. math::

        L  \leftarrow \fork{116*Y^{1/3}-16}{for $Y>0.008856$}{903.3*Y}{for $Y \le 0.008856$}

    .. math::

        a  \leftarrow 500 (f(X)-f(Y)) + delta

    .. math::

        b  \leftarrow 200 (f(Y)-f(Z)) + delta

    where

    .. math::

        f(t)= \fork{t^{1/3}}{for $t>0.008856$}{7.787 t+16/116}{for $t\leq 0.008856$}

    and

    .. math::

        delta =  \fork{128}{for 8-bit images}{0}{for floating-point images}

    On output
    :math:`0 \leq L \leq 100`,    :math:`-127 \leq a \leq 127`,    :math:`-127 \leq b \leq 127`     The values are then converted to the destination data type:

    * 8-bit images

        .. math::

            L  \leftarrow L*255/100, \; a  \leftarrow a + 128, \; b  \leftarrow b + 128

    * 16-bit images
        currently not supported

    * 32-bit images
        L, a, b are left as is

*
    RGB :math:`\leftrightarrow` CIE L*u*v* ( ``CV_BGR2Luv, CV_RGB2Luv, CV_Luv2BGR, CV_Luv2RGB`` )
      in the case of 8-bit and 16-bit images
      R, G and B are converted to floating-point format and scaled to fit 0 to 1 range

    .. math::

        \vecthree{X}{Y}{Z} \leftarrow \vecthreethree{0.412453}{0.357580}{0.180423}{0.212671}{0.715160}{0.072169}{0.019334}{0.119193}{0.950227} \cdot \vecthree{R}{G}{B}

    .. math::

        L  \leftarrow \fork{116 Y^{1/3}}{for $Y>0.008856$}{903.3 Y}{for $Y\leq 0.008856$}

    .. math::

        u'  \leftarrow 4*X/(X + 15*Y + 3 Z)

    .. math::

        v'  \leftarrow 9*Y/(X + 15*Y + 3 Z)

    .. math::

        u  \leftarrow 13*L*(u' - u_n)  \quad \text{where} \quad u_n=0.19793943

    .. math::

        v  \leftarrow 13*L*(v' - v_n)  \quad \text{where} \quad v_n=0.46831096

    On output
    :math:`0 \leq L \leq 100`,    :math:`-134 \leq u \leq 220`,    :math:`-140 \leq v \leq 122`     .

    The values are then converted to the destination data type:

    * 8-bit images

        .. math::

            L  \leftarrow 255/100 L, \; u  \leftarrow 255/354 (u + 134), \; v  \leftarrow 255/256 (v + 140)

    * 16-bit images
        currently not supported

    * 32-bit images
        L, u, v are left as is

    The above formulas for converting RGB to/from various color spaces have been taken from multiple sources on Web, primarily from the Charles Poynton site
    http://www.poynton.com/ColorFAQ.html

*
    Bayer :math:`\rightarrow`     RGB ( ``CV_BayerBG2BGR, CV_BayerGB2BGR, CV_BayerRG2BGR, CV_BayerGR2BGR, CV_BayerBG2RGB, CV_BayerGB2RGB, CV_BayerRG2RGB, CV_BayerGR2RGB``     ) The Bayer pattern is widely used in CCD and CMOS cameras. It allows one to get color pictures from a single plane where R,G and B pixels (sensors of a particular component) are interleaved like this:

    .. math::

        \newcommand{\Rcell}{\color{red}R} \newcommand{\Gcell}{\color{green}G} \newcommand{\Bcell}{\color{blue}B} \definecolor{BackGray}{rgb}{0.8,0.8,0.8} \begin{array}{ c c c c c } \Rcell & \Gcell & \Rcell & \Gcell & \Rcell \\ \Gcell & \colorbox{BackGray}{\Bcell} & \colorbox{BackGray}{\Gcell} & \Bcell & \Gcell \\ \Rcell & \Gcell & \Rcell & \Gcell & \Rcell \\ \Gcell & \Bcell & \Gcell & \Bcell & \Gcell \\ \Rcell & \Gcell & \Rcell & \Gcell & \Rcell \end{array}

    The output RGB components of a pixel are interpolated from 1, 2 or
    4 neighbors of the pixel having the same color. There are several
    modifications of the above pattern that can be achieved by shifting
    the pattern one pixel left and/or one pixel up. The two letters
    :math:`C_1`     and
    :math:`C_2`     in the conversion constants ``CV_Bayer``     :math:`C_1 C_2`     ``2BGR``     and ``CV_Bayer``     :math:`C_1 C_2`     ``2RGB``     indicate the particular pattern
    type - these are components from the second row, second and third
    columns, respectively. For example, the above pattern has very
    popular "BG" type.

.. index:: distanceTransform

distanceTransform
---------------------
.. c:function:: void distanceTransform( const Mat& src, Mat& dst, int distanceType, int maskSize )

.. c:function:: void distanceTransform( const Mat& src, Mat& dst, Mat& labels, int distanceType, int maskSize )

    Calculates the distance to the closest zero pixel for each pixel of the source image.

    :param src: 8-bit, single-channel (binary) source image

    :param dst: Output image with calculated distances; will be 32-bit floating-point, single-channel image of the same size as  ``src``
    :param distanceType: Type of distance; can be  ``CV_DIST_L1, CV_DIST_L2``  or  ``CV_DIST_C``
    :param maskSize: Size of the distance transform mask; can be 3, 5 or  ``CV_DIST_MASK_PRECISE``  (the latter option is only supported by the first of the functions). In the case of  ``CV_DIST_L1``  or  ``CV_DIST_C``  distance type the parameter is forced to 3, because a  :math:`3\times 3`  mask gives the same result as a  :math:`5\times 5`  or any larger aperture.

    :param labels: The optional output 2d array of labels - the discrete Voronoi diagram; will have type  ``CV_32SC1``  and the same size as  ``src`` . See the discussion

The functions ``distanceTransform`` calculate the approximate or precise
distance from every binary image pixel to the nearest zero pixel.
(for zero image pixels the distance will obviously be zero).

When ``maskSize == CV_DIST_MASK_PRECISE`` and ``distanceType == CV_DIST_L2`` , the function runs the algorithm described in
Felzenszwalb04
.

In other cases the algorithm
Borgefors86
is used, that is,
for pixel the function finds the shortest path to the nearest zero pixel
consisting of basic shifts: horizontal,
vertical, diagonal or knight's move (the latest is available for a
:math:`5\times 5` mask). The overall distance is calculated as a sum of these
basic distances. Because the distance function should be symmetric,
all of the horizontal and vertical shifts must have the same cost (that
is denoted as ``a`` ), all the diagonal shifts must have the
same cost (denoted ``b`` ), and all knight's moves must have
the same cost (denoted ``c`` ). For ``CV_DIST_C`` and ``CV_DIST_L1`` types the distance is calculated precisely,
whereas for ``CV_DIST_L2`` (Euclidian distance) the distance
can be calculated only with some relative error (a
:math:`5\times 5` mask
gives more accurate results). For ``a``,``b`` and ``c`` OpenCV uses the values suggested in the original paper:

.. table::

    ==============  ===================  ======================
    ``CV_DIST_C``   :math:`(3\times 3)`  a = 1, b = 1 \
    ==============  ===================  ======================
    ``CV_DIST_L1``  :math:`(3\times 3)`  a = 1, b = 2 \
    ``CV_DIST_L2``  :math:`(3\times 3)`  a=0.955, b=1.3693 \
    ``CV_DIST_L2``  :math:`(5\times 5)`  a=1, b=1.4, c=2.1969 \
    ==============  ===================  ======================

Typically, for a fast, coarse distance estimation ``CV_DIST_L2``,a
:math:`3\times 3` mask is used, and for a more accurate distance estimation ``CV_DIST_L2`` , a
:math:`5\times 5` mask or the precise algorithm is used.
Note that both the precise and the approximate algorithms are linear on the number of pixels.

The second variant of the function does not only compute the minimum distance for each pixel
:math:`(x, y)`,but it also identifies the nearest the nearest connected
component consisting of zero pixels. Index of the component is stored in
:math:`\texttt{labels}(x, y)` .
The connected components of zero pixels are also found and marked by the function.

In this mode the complexity is still linear.
That is, the function provides a very fast way to compute Voronoi diagram for the binary image.
Currently, this second variant can only use the approximate distance transform algorithm.

.. index:: floodFill

floodFill
-------------
.. c:function:: int floodFill( Mat& image, Point seed, Scalar newVal, Rect* rect=0, Scalar loDiff=Scalar(), Scalar upDiff=Scalar(),               int flags=4 )

.. c:function:: int floodFill( Mat& image, Mat& mask, Point seed, Scalar newVal, Rect* rect=0, Scalar loDiff=Scalar(), Scalar upDiff=Scalar(), int flags=4 )

    Fills a connected component with the given color.

    :param image: Input/output 1- or 3-channel, 8-bit or floating-point image. It is modified by the function unless the  ``FLOODFILL_MASK_ONLY``  flag is set (in the second variant of the function; see below)

    :param mask: (For the second function only) Operation mask, should be a single-channel 8-bit image, 2 pixels wider and 2 pixels taller. The function uses and updates the mask, so the user takes responsibility of initializing the  ``mask``  content. Flood-filling can't go across non-zero pixels in the mask, for example, an edge detector output can be used as a mask to stop filling at edges. It is possible to use the same mask in multiple calls to the function to make sure the filled area do not overlap.  **Note** : because the mask is larger than the filled image, a pixel  :math:`(x, y)`  in  ``image``  will correspond to the pixel  :math:`(x+1, y+1)`  in the  ``mask``
    :param seed: The starting point

    :param newVal: New value of the repainted domain pixels

    :param loDiff: Maximal lower brightness/color difference between the currently observed pixel and one of its neighbors belonging to the component, or a seed pixel being added to the component

    :param upDiff: Maximal upper brightness/color difference between the currently observed pixel and one of its neighbors belonging to the component, or a seed pixel being added to the component

    :param rect: The optional output parameter that the function sets to the minimum bounding rectangle of the repainted domain

    :param flags: The operation flags. Lower bits contain connectivity value, 4 (by default) or 8, used within the function. Connectivity determines which neighbors of a pixel are considered. Upper bits can be 0 or a combination of the following flags:

            * **FLOODFILL_FIXED_RANGE** if set, the difference between the current pixel and seed pixel is considered, otherwise the difference between neighbor pixels is considered (i.e. the range is floating)

            * **FLOODFILL_MASK_ONLY** (for the second variant only) if set, the function does not change the image ( ``newVal``  is ignored), but fills the mask

The functions ``floodFill`` fill a connected component starting from the seed point with the specified color. The connectivity is determined by the color/brightness closeness of the neighbor pixels. The pixel at
:math:`(x,y)` is considered to belong to the repainted domain if:

* grayscale image, floating range

    .. math::

        \texttt{src} (x',y')- \texttt{loDiff} \leq \texttt{src} (x,y)  \leq \texttt{src} (x',y')+ \texttt{upDiff}

* grayscale image, fixed range

    .. math::

        \texttt{src} ( \texttt{seed} .x, \texttt{seed} .y)- \texttt{loDiff} \leq \texttt{src} (x,y)  \leq \texttt{src} ( \texttt{seed} .x, \texttt{seed} .y)+ \texttt{upDiff}

* color image, floating range

    .. math::

        \texttt{src} (x',y')_r- \texttt{loDiff} _r \leq \texttt{src} (x,y)_r \leq \texttt{src} (x',y')_r+ \texttt{upDiff} _r

    .. math::

        \texttt{src} (x',y')_g- \texttt{loDiff} _g \leq \texttt{src} (x,y)_g \leq \texttt{src} (x',y')_g+ \texttt{upDiff} _g

    .. math::

        \texttt{src} (x',y')_b- \texttt{loDiff} _b \leq \texttt{src} (x,y)_b \leq \texttt{src} (x',y')_b+ \texttt{upDiff} _b

* color image, fixed range

    .. math::

        \texttt{src} ( \texttt{seed} .x, \texttt{seed} .y)_r- \texttt{loDiff} _r \leq \texttt{src} (x,y)_r \leq \texttt{src} ( \texttt{seed} .x, \texttt{seed} .y)_r+ \texttt{upDiff} _r

    .. math::

        \texttt{src} ( \texttt{seed} .x, \texttt{seed} .y)_g- \texttt{loDiff} _g \leq \texttt{src} (x,y)_g \leq \texttt{src} ( \texttt{seed} .x, \texttt{seed} .y)_g+ \texttt{upDiff} _g

    .. math::

        \texttt{src} ( \texttt{seed} .x, \texttt{seed} .y)_b- \texttt{loDiff} _b \leq \texttt{src} (x,y)_b \leq \texttt{src} ( \texttt{seed} .x, \texttt{seed} .y)_b+ \texttt{upDiff} _b

where
:math:`src(x',y')` is the value of one of pixel neighbors that is already known to belong to the component. That is, to be added to the connected component, a pixel's color/brightness should be close enough to the:

*
    color/brightness of one of its neighbors that are already referred to the connected component in the case of floating range

*
    color/brightness of the seed point in the case of fixed range.

By using these functions you can either mark a connected component with the specified color in-place, or build a mask and then extract the contour or copy the region to another image etc. Various modes of the function are demonstrated in ``floodfill.c`` sample.

See also:
:func:`findContours`
.. index:: inpaint

inpaint
-----------
.. c:function:: void inpaint( const Mat& src, const Mat& inpaintMask,              Mat& dst, double inpaintRadius, int flags )

    Inpaints the selected region in the image.

    :param src: The input 8-bit 1-channel or 3-channel image.

    :param inpaintMask: The inpainting mask, 8-bit 1-channel image. Non-zero pixels indicate the area that needs to be inpainted.

    :param dst: The output image; will have the same size and the same type as  ``src``
    
    :param inpaintRadius: The radius of a circlular neighborhood of each point inpainted that is considered by the algorithm.

    :param flags: The inpainting method, one of the following:

            * **INPAINT_NS** Navier-Stokes based method.

            * **INPAINT_TELEA** The method by Alexandru Telea  Telea04

The function reconstructs the selected image area from the pixel near the area boundary. The function may be used to remove dust and scratches from a scanned photo, or to remove undesirable objects from still images or video. See
http://en.wikipedia.org/wiki/Inpainting
for more details.

.. index:: integral

integral
------------
.. c:function:: void integral( const Mat& image, Mat& sum, int sdepth=-1 )

.. c:function:: void integral( const Mat& image, Mat& sum, Mat& sqsum, int sdepth=-1 )

.. c:function:: void integral( const Mat& image, Mat& sum,  Mat& sqsum, Mat& tilted, int sdepth=-1 )

    Calculates the integral of an image.

    :param image: The source image,  :math:`W \times H` , 8-bit or floating-point (32f or 64f)

    :param sum: The integral image,  :math:`(W+1)\times (H+1)` , 32-bit integer or floating-point (32f or 64f)

    :param sqsum: The integral image for squared pixel values,  :math:`(W+1)\times (H+1)` , double precision floating-point (64f)

    :param tilted: The integral for the image rotated by 45 degrees,  :math:`(W+1)\times (H+1)` , the same data type as  ``sum``
    
    :param sdepth: The desired depth of the integral and the tilted integral images,  ``CV_32S`` ,   ``CV_32F``  or  ``CV_64F``

The functions calculate one or more integral images for the source image as following:

.. math::

    \texttt{sum} (X,Y) =  \sum _{x<X,y<Y}  \texttt{image} (x,y)

.. math::

    \texttt{sqsum} (X,Y) =  \sum _{x<X,y<Y}  \texttt{image} (x,y)^2

.. math::

    \texttt{tilted} (X,Y) =  \sum _{y<Y,abs(x-X+1) \leq Y-y-1}  \texttt{image} (x,y)

Using these integral images, one may calculate sum, mean and standard deviation over a specific up-right or rotated rectangular region of the image in a constant time, for example:

.. math::

    \sum _{x_1 \leq x < x_2,  \, y_1  \leq y < y_2}  \texttt{image} (x,y) =  \texttt{sum} (x_2,y_2)- \texttt{sum} (x_1,y_2)- \texttt{sum} (x_2,y_1)+ \texttt{sum} (x_1,x_1)

It makes possible to do a fast blurring or fast block correlation with variable window size, for example. In the case of multi-channel images, sums for each channel are accumulated independently.

As a practical example, the next figure shows the calculation of the integral of a straight rectangle ``Rect(3,3,3,2)`` and of a tilted rectangle ``Rect(5,1,2,3)`` . The selected pixels in the original ``image`` are shown, as well as the relative pixels in the integral images ``sum`` and ``tilted`` .

\begin{center}

.. image:: ../../pics/integral.png

\end{center}

.. index:: threshold

threshold
-------------
.. c:function:: double threshold( const Mat& src, Mat& dst, double thresh,                  double maxVal, int thresholdType )

    Applies a fixed-level threshold to each array element

    :param src: Source array (single-channel, 8-bit of 32-bit floating point)

    :param dst: Destination array; will have the same size and the same type as  ``src``
    
    :param thresh: Threshold value

    :param maxVal: Maximum value to use with  ``THRESH_BINARY``  and  ``THRESH_BINARY_INV``  thresholding types

    :param thresholdType: Thresholding type (see the discussion)

The function applies fixed-level thresholding
to a single-channel array. The function is typically used to get a
bi-level (binary) image out of a grayscale image (
:func:`compare` could
be also used for this purpose) or for removing a noise, i.e. filtering
out pixels with too small or too large values. There are several
types of thresholding that the function supports that are determined by ``thresholdType`` :

    * **THRESH_BINARY**

        .. math::

              \texttt{dst} (x,y) =  \fork{\texttt{maxVal}}{if $\texttt{src}(x,y) > \texttt{thresh}$}{0}{otherwise}

    * **THRESH_BINARY_INV**

        .. math::

              \texttt{dst} (x,y) =  \fork{0}{if $\texttt{src}(x,y) > \texttt{thresh}$}{\texttt{maxVal}}{otherwise}

    * **THRESH_TRUNC**

        .. math::

              \texttt{dst} (x,y) =  \fork{\texttt{threshold}}{if $\texttt{src}(x,y) > \texttt{thresh}$}{\texttt{src}(x,y)}{otherwise}

    * **THRESH_TOZERO**

        .. math::

              \texttt{dst} (x,y) =  \fork{\texttt{src}(x,y)}{if $\texttt{src}(x,y) > \texttt{thresh}$}{0}{otherwise}

    * **THRESH_TOZERO_INV**

        .. math::

              \texttt{dst} (x,y) =  \fork{0}{if $\texttt{src}(x,y) > \texttt{thresh}$}{\texttt{src}(x,y)}{otherwise}

Also, the special value ``THRESH_OTSU`` may be combined with
one of the above values. In this case the function determines the optimal threshold
value using Otsu's algorithm and uses it instead of the specified ``thresh`` .
The function returns the computed threshold value.
Currently, Otsu's method is implemented only for 8-bit images.

.. image:: ../../pics/threshold.png

See also:
:func:`adaptiveThreshold`,:func:`findContours`,:func:`compare`,:func:`min`,:func:`max`
.. index:: watershed

watershed
-------------
.. c:function:: void watershed( const Mat& image, Mat& markers )

    Does marker-based image segmentation using watershed algrorithm

    :param image: The input 8-bit 3-channel image.

    :param markers: The input/output 32-bit single-channel image (map) of markers. It should have the same size as  ``image``

The function implements one of the variants
of watershed, non-parametric marker-based segmentation algorithm,
described in
Meyer92
. Before passing the image to the
function, user has to outline roughly the desired regions in the image ``markers`` with positive (
:math:`>0` ) indices, i.e. every region is
represented as one or more connected components with the pixel values
1, 2, 3 etc (such markers can be retrieved from a binary mask
using
:func:`findContours` and
:func:`drawContours` , see ``watershed.cpp`` demo).
The markers will be "seeds" of the future image
regions. All the other pixels in ``markers`` , which relation to the
outlined regions is not known and should be defined by the algorithm,
should be set to 0's. On the output of the function, each pixel in
markers is set to one of values of the "seed" components, or to -1 at
boundaries between the regions.

Note, that it is not necessary that every two neighbor connected
components are separated by a watershed boundary (-1's pixels), for
example, in case when such tangent components exist in the initial
marker image. Visual demonstration and usage example of the function
can be found in OpenCV samples directory; see ``watershed.cpp`` demo.

See also:
:func:`findContours`
.. index:: grabCut

grabCut
-----------
.. c:function:: void grabCut(const Mat& image, Mat& mask, Rect rect, Mat& bgdModel, Mat& fgdModel, int iterCount, int mode )

    Runs GrabCut algorithm

    :param image: The input 8-bit 3-channel image.

    :param mask: The input/output 8-bit single-channel mask. Its elements may have one of four values. The mask is initialize when  ``mode==GC_INIT_WITH_RECT``
        * **GC_BGD** Certainly a background pixel

        * **GC_FGD** Certainly a foreground (object) pixel

        * **GC_PR_BGD** Likely a background pixel

        * **GC_PR_BGD** Likely a foreground pixel

    :param rect: The ROI containing the segmented object. The pixels outside of the ROI are marked as "certainly a background". The parameter is only used when  ``mode==GC_INIT_WITH_RECT``
    
    :param bgdModel, fgdModel: Temporary arrays used for segmentation. Do not modify them while you are processing the same image

    :param iterCount: The number of iterations the algorithm should do before returning the result. Note that the result can be refined with further calls with the  ``mode==GC_INIT_WITH_MASK``  or  ``mode==GC_EVAL``
    
    :param mode: The operation mode

        * **GC_INIT_WITH_RECT** The function initializes the state and the mask using the provided rectangle. After that it runs  ``iterCount``  iterations of the algorithm

        * **GC_INIT_WITH_MASK** The function initializes the state using the provided mask. Note that  ``GC_INIT_WITH_RECT``  and  ``GC_INIT_WITH_MASK``  can be combined, then all the pixels outside of the ROI are automatically initialized with  ``GC_BGD``.

        * **GC_EVAL** The value means that algorithm should just resume.

The function implements the `GrabCut <http://en.wikipedia.org/wiki/GrabCut>`_
image segmentation algorithm.
See the sample grabcut.cpp on how to use the function.