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diff --git a/thirdparty1/linux/include/opencv2/core.hpp b/thirdparty1/linux/include/opencv2/core.hpp new file mode 100644 index 0000000..6b89c42 --- /dev/null +++ b/thirdparty1/linux/include/opencv2/core.hpp @@ -0,0 +1,3220 @@ +/*M/////////////////////////////////////////////////////////////////////////////////////// +// +// IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING. +// +// By downloading, copying, installing or using the software you agree to this license. +// If you do not agree to this license, do not download, install, +// copy or use the software. +// +// +// License Agreement +// For Open Source Computer Vision Library +// +// Copyright (C) 2000-2015, Intel Corporation, all rights reserved. +// Copyright (C) 2009-2011, Willow Garage Inc., all rights reserved. +// Copyright (C) 2015, OpenCV Foundation, all rights reserved. +// Copyright (C) 2015, Itseez Inc., all rights reserved. +// Third party copyrights are property of their respective owners. +// +// Redistribution and use in source and binary forms, with or without modification, +// are permitted provided that the following conditions are met: +// +// * Redistribution's of source code must retain the above copyright notice, +// this list of conditions and the following disclaimer. +// +// * Redistribution's in binary form must reproduce the above copyright notice, +// this list of conditions and the following disclaimer in the documentation +// and/or other materials provided with the distribution. +// +// * The name of the copyright holders may not be used to endorse or promote products +// derived from this software without specific prior written permission. +// +// This software is provided by the copyright holders and contributors "as is" and +// any express or implied warranties, including, but not limited to, the implied +// warranties of merchantability and fitness for a particular purpose are disclaimed. +// In no event shall the Intel Corporation or contributors be liable for any direct, +// indirect, incidental, special, exemplary, or consequential damages +// (including, but not limited to, procurement of substitute goods or services; +// loss of use, data, or profits; or business interruption) however caused +// and on any theory of liability, whether in contract, strict liability, +// or tort (including negligence or otherwise) arising in any way out of +// the use of this software, even if advised of the possibility of such damage. +// +//M*/ + +#ifndef OPENCV_CORE_HPP +#define OPENCV_CORE_HPP + +#ifndef __cplusplus +# error core.hpp header must be compiled as C++ +#endif + +#include "opencv2/core/cvdef.h" +#include "opencv2/core/version.hpp" +#include "opencv2/core/base.hpp" +#include "opencv2/core/cvstd.hpp" +#include "opencv2/core/traits.hpp" +#include "opencv2/core/matx.hpp" +#include "opencv2/core/types.hpp" +#include "opencv2/core/mat.hpp" +#include "opencv2/core/persistence.hpp" + +/** +@defgroup core Core functionality +@{ + @defgroup core_basic Basic structures + @defgroup core_c C structures and operations + @{ + @defgroup core_c_glue Connections with C++ + @} + @defgroup core_array Operations on arrays + @defgroup core_xml XML/YAML Persistence + @defgroup core_cluster Clustering + @defgroup core_utils Utility and system functions and macros + @{ + @defgroup core_utils_sse SSE utilities + @defgroup core_utils_neon NEON utilities + @} + @defgroup core_opengl OpenGL interoperability + @defgroup core_ipp Intel IPP Asynchronous C/C++ Converters + @defgroup core_optim Optimization Algorithms + @defgroup core_directx DirectX interoperability + @defgroup core_eigen Eigen support + @defgroup core_opencl OpenCL support + @defgroup core_va_intel Intel VA-API/OpenCL (CL-VA) interoperability + @defgroup core_hal Hardware Acceleration Layer + @{ + @defgroup core_hal_functions Functions + @defgroup core_hal_interface Interface + @defgroup core_hal_intrin Universal intrinsics + @{ + @defgroup core_hal_intrin_impl Private implementation helpers + @} + @} +@} + */ + +namespace cv { + +//! @addtogroup core_utils +//! @{ + +/*! @brief Class passed to an error. + +This class encapsulates all or almost all necessary +information about the error happened in the program. The exception is +usually constructed and thrown implicitly via CV_Error and CV_Error_ macros. +@see error + */ +class CV_EXPORTS Exception : public std::exception +{ +public: + /*! + Default constructor + */ + Exception(); + /*! + Full constructor. Normally the constuctor is not called explicitly. + Instead, the macros CV_Error(), CV_Error_() and CV_Assert() are used. + */ + Exception(int _code, const String& _err, const String& _func, const String& _file, int _line); + virtual ~Exception() throw(); + + /*! + \return the error description and the context as a text string. + */ + virtual const char *what() const throw(); + void formatMessage(); + + String msg; ///< the formatted error message + + int code; ///< error code @see CVStatus + String err; ///< error description + String func; ///< function name. Available only when the compiler supports getting it + String file; ///< source file name where the error has occured + int line; ///< line number in the source file where the error has occured +}; + +/*! @brief Signals an error and raises the exception. + +By default the function prints information about the error to stderr, +then it either stops if cv::setBreakOnError() had been called before or raises the exception. +It is possible to alternate error processing by using cv::redirectError(). +@param exc the exception raisen. +@deprecated drop this version + */ +CV_EXPORTS void error( const Exception& exc ); + +enum SortFlags { SORT_EVERY_ROW = 0, //!< each matrix row is sorted independently + SORT_EVERY_COLUMN = 1, //!< each matrix column is sorted + //!< independently; this flag and the previous one are + //!< mutually exclusive. + SORT_ASCENDING = 0, //!< each matrix row is sorted in the ascending + //!< order. + SORT_DESCENDING = 16 //!< each matrix row is sorted in the + //!< descending order; this flag and the previous one are also + //!< mutually exclusive. + }; + +//! @} core_utils + +//! @addtogroup core +//! @{ + +//! Covariation flags +enum CovarFlags { + /** The output covariance matrix is calculated as: + \f[\texttt{scale} \cdot [ \texttt{vects} [0]- \texttt{mean} , \texttt{vects} [1]- \texttt{mean} ,...]^T \cdot [ \texttt{vects} [0]- \texttt{mean} , \texttt{vects} [1]- \texttt{mean} ,...],\f] + The covariance matrix will be nsamples x nsamples. Such an unusual covariance matrix is used + for fast PCA of a set of very large vectors (see, for example, the EigenFaces technique for + face recognition). Eigenvalues of this "scrambled" matrix match the eigenvalues of the true + covariance matrix. The "true" eigenvectors can be easily calculated from the eigenvectors of + the "scrambled" covariance matrix. */ + COVAR_SCRAMBLED = 0, + /**The output covariance matrix is calculated as: + \f[\texttt{scale} \cdot [ \texttt{vects} [0]- \texttt{mean} , \texttt{vects} [1]- \texttt{mean} ,...] \cdot [ \texttt{vects} [0]- \texttt{mean} , \texttt{vects} [1]- \texttt{mean} ,...]^T,\f] + covar will be a square matrix of the same size as the total number of elements in each input + vector. One and only one of COVAR_SCRAMBLED and COVAR_NORMAL must be specified.*/ + COVAR_NORMAL = 1, + /** If the flag is specified, the function does not calculate mean from + the input vectors but, instead, uses the passed mean vector. This is useful if mean has been + pre-calculated or known in advance, or if the covariance matrix is calculated by parts. In + this case, mean is not a mean vector of the input sub-set of vectors but rather the mean + vector of the whole set.*/ + COVAR_USE_AVG = 2, + /** If the flag is specified, the covariance matrix is scaled. In the + "normal" mode, scale is 1./nsamples . In the "scrambled" mode, scale is the reciprocal of the + total number of elements in each input vector. By default (if the flag is not specified), the + covariance matrix is not scaled ( scale=1 ).*/ + COVAR_SCALE = 4, + /** If the flag is + specified, all the input vectors are stored as rows of the samples matrix. mean should be a + single-row vector in this case.*/ + COVAR_ROWS = 8, + /** If the flag is + specified, all the input vectors are stored as columns of the samples matrix. mean should be a + single-column vector in this case.*/ + COVAR_COLS = 16 +}; + +//! k-Means flags +enum KmeansFlags { + /** Select random initial centers in each attempt.*/ + KMEANS_RANDOM_CENTERS = 0, + /** Use kmeans++ center initialization by Arthur and Vassilvitskii [Arthur2007].*/ + KMEANS_PP_CENTERS = 2, + /** During the first (and possibly the only) attempt, use the + user-supplied labels instead of computing them from the initial centers. For the second and + further attempts, use the random or semi-random centers. Use one of KMEANS_\*_CENTERS flag + to specify the exact method.*/ + KMEANS_USE_INITIAL_LABELS = 1 +}; + +//! type of line +enum LineTypes { + FILLED = -1, + LINE_4 = 4, //!< 4-connected line + LINE_8 = 8, //!< 8-connected line + LINE_AA = 16 //!< antialiased line +}; + +//! Only a subset of Hershey fonts +//! <http://sources.isc.org/utils/misc/hershey-font.txt> are supported +enum HersheyFonts { + FONT_HERSHEY_SIMPLEX = 0, //!< normal size sans-serif font + FONT_HERSHEY_PLAIN = 1, //!< small size sans-serif font + FONT_HERSHEY_DUPLEX = 2, //!< normal size sans-serif font (more complex than FONT_HERSHEY_SIMPLEX) + FONT_HERSHEY_COMPLEX = 3, //!< normal size serif font + FONT_HERSHEY_TRIPLEX = 4, //!< normal size serif font (more complex than FONT_HERSHEY_COMPLEX) + FONT_HERSHEY_COMPLEX_SMALL = 5, //!< smaller version of FONT_HERSHEY_COMPLEX + FONT_HERSHEY_SCRIPT_SIMPLEX = 6, //!< hand-writing style font + FONT_HERSHEY_SCRIPT_COMPLEX = 7, //!< more complex variant of FONT_HERSHEY_SCRIPT_SIMPLEX + FONT_ITALIC = 16 //!< flag for italic font +}; + +enum ReduceTypes { REDUCE_SUM = 0, //!< the output is the sum of all rows/columns of the matrix. + REDUCE_AVG = 1, //!< the output is the mean vector of all rows/columns of the matrix. + REDUCE_MAX = 2, //!< the output is the maximum (column/row-wise) of all rows/columns of the matrix. + REDUCE_MIN = 3 //!< the output is the minimum (column/row-wise) of all rows/columns of the matrix. + }; + + +/** @brief Swaps two matrices +*/ +CV_EXPORTS void swap(Mat& a, Mat& b); +/** @overload */ +CV_EXPORTS void swap( UMat& a, UMat& b ); + +//! @} core + +//! @addtogroup core_array +//! @{ + +/** @brief Computes the source location of an extrapolated pixel. + +The function computes and returns the coordinate of a donor pixel corresponding to the specified +extrapolated pixel when using the specified extrapolation border mode. For example, if you use +cv::BORDER_WRAP mode in the horizontal direction, cv::BORDER_REFLECT_101 in the vertical direction and +want to compute value of the "virtual" pixel Point(-5, 100) in a floating-point image img , it +looks like: +@code{.cpp} + float val = img.at<float>(borderInterpolate(100, img.rows, cv::BORDER_REFLECT_101), + borderInterpolate(-5, img.cols, cv::BORDER_WRAP)); +@endcode +Normally, the function is not called directly. It is used inside filtering functions and also in +copyMakeBorder. +@param p 0-based coordinate of the extrapolated pixel along one of the axes, likely \<0 or \>= len +@param len Length of the array along the corresponding axis. +@param borderType Border type, one of the cv::BorderTypes, except for cv::BORDER_TRANSPARENT and +cv::BORDER_ISOLATED . When borderType==cv::BORDER_CONSTANT , the function always returns -1, regardless +of p and len. + +@sa copyMakeBorder +*/ +CV_EXPORTS_W int borderInterpolate(int p, int len, int borderType); + +/** @brief Forms a border around an image. + +The function copies the source image into the middle of the destination image. The areas to the +left, to the right, above and below the copied source image will be filled with extrapolated +pixels. This is not what filtering functions based on it do (they extrapolate pixels on-fly), but +what other more complex functions, including your own, may do to simplify image boundary handling. + +The function supports the mode when src is already in the middle of dst . In this case, the +function does not copy src itself but simply constructs the border, for example: + +@code{.cpp} + // let border be the same in all directions + int border=2; + // constructs a larger image to fit both the image and the border + Mat gray_buf(rgb.rows + border*2, rgb.cols + border*2, rgb.depth()); + // select the middle part of it w/o copying data + Mat gray(gray_canvas, Rect(border, border, rgb.cols, rgb.rows)); + // convert image from RGB to grayscale + cvtColor(rgb, gray, COLOR_RGB2GRAY); + // form a border in-place + copyMakeBorder(gray, gray_buf, border, border, + border, border, BORDER_REPLICATE); + // now do some custom filtering ... + ... +@endcode +@note When the source image is a part (ROI) of a bigger image, the function will try to use the +pixels outside of the ROI to form a border. To disable this feature and always do extrapolation, as +if src was not a ROI, use borderType | BORDER_ISOLATED. + +@param src Source image. +@param dst Destination image of the same type as src and the size Size(src.cols+left+right, +src.rows+top+bottom) . +@param top +@param bottom +@param left +@param right Parameter specifying how many pixels in each direction from the source image rectangle +to extrapolate. For example, top=1, bottom=1, left=1, right=1 mean that 1 pixel-wide border needs +to be built. +@param borderType Border type. See borderInterpolate for details. +@param value Border value if borderType==BORDER_CONSTANT . + +@sa borderInterpolate +*/ +CV_EXPORTS_W void copyMakeBorder(InputArray src, OutputArray dst, + int top, int bottom, int left, int right, + int borderType, const Scalar& value = Scalar() ); + +/** @brief Calculates the per-element sum of two arrays or an array and a scalar. + +The function add calculates: +- Sum of two arrays when both input arrays have the same size and the same number of channels: +\f[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src1}(I) + \texttt{src2}(I)) \quad \texttt{if mask}(I) \ne0\f] +- Sum of an array and a scalar when src2 is constructed from Scalar or has the same number of +elements as `src1.channels()`: +\f[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src1}(I) + \texttt{src2} ) \quad \texttt{if mask}(I) \ne0\f] +- Sum of a scalar and an array when src1 is constructed from Scalar or has the same number of +elements as `src2.channels()`: +\f[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src1} + \texttt{src2}(I) ) \quad \texttt{if mask}(I) \ne0\f] +where `I` is a multi-dimensional index of array elements. In case of multi-channel arrays, each +channel is processed independently. + +The first function in the list above can be replaced with matrix expressions: +@code{.cpp} + dst = src1 + src2; + dst += src1; // equivalent to add(dst, src1, dst); +@endcode +The input arrays and the output array can all have the same or different depths. For example, you +can add a 16-bit unsigned array to a 8-bit signed array and store the sum as a 32-bit +floating-point array. Depth of the output array is determined by the dtype parameter. In the second +and third cases above, as well as in the first case, when src1.depth() == src2.depth(), dtype can +be set to the default -1. In this case, the output array will have the same depth as the input +array, be it src1, src2 or both. +@note Saturation is not applied when the output array has the depth CV_32S. You may even get +result of an incorrect sign in the case of overflow. +@param src1 first input array or a scalar. +@param src2 second input array or a scalar. +@param dst output array that has the same size and number of channels as the input array(s); the +depth is defined by dtype or src1/src2. +@param mask optional operation mask - 8-bit single channel array, that specifies elements of the +output array to be changed. +@param dtype optional depth of the output array (see the discussion below). +@sa subtract, addWeighted, scaleAdd, Mat::convertTo +*/ +CV_EXPORTS_W void add(InputArray src1, InputArray src2, OutputArray dst, + InputArray mask = noArray(), int dtype = -1); + +/** @brief Calculates the per-element difference between two arrays or array and a scalar. + +The function subtract calculates: +- Difference between two arrays, when both input arrays have the same size and the same number of +channels: + \f[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src1}(I) - \texttt{src2}(I)) \quad \texttt{if mask}(I) \ne0\f] +- Difference between an array and a scalar, when src2 is constructed from Scalar or has the same +number of elements as `src1.channels()`: + \f[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src1}(I) - \texttt{src2} ) \quad \texttt{if mask}(I) \ne0\f] +- Difference between a scalar and an array, when src1 is constructed from Scalar or has the same +number of elements as `src2.channels()`: + \f[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src1} - \texttt{src2}(I) ) \quad \texttt{if mask}(I) \ne0\f] +- The reverse difference between a scalar and an array in the case of `SubRS`: + \f[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src2} - \texttt{src1}(I) ) \quad \texttt{if mask}(I) \ne0\f] +where I is a multi-dimensional index of array elements. In case of multi-channel arrays, each +channel is processed independently. + +The first function in the list above can be replaced with matrix expressions: +@code{.cpp} + dst = src1 - src2; + dst -= src1; // equivalent to subtract(dst, src1, dst); +@endcode +The input arrays and the output array can all have the same or different depths. For example, you +can subtract to 8-bit unsigned arrays and store the difference in a 16-bit signed array. Depth of +the output array is determined by dtype parameter. In the second and third cases above, as well as +in the first case, when src1.depth() == src2.depth(), dtype can be set to the default -1. In this +case the output array will have the same depth as the input array, be it src1, src2 or both. +@note Saturation is not applied when the output array has the depth CV_32S. You may even get +result of an incorrect sign in the case of overflow. +@param src1 first input array or a scalar. +@param src2 second input array or a scalar. +@param dst output array of the same size and the same number of channels as the input array. +@param mask optional operation mask; this is an 8-bit single channel array that specifies elements +of the output array to be changed. +@param dtype optional depth of the output array +@sa add, addWeighted, scaleAdd, Mat::convertTo + */ +CV_EXPORTS_W void subtract(InputArray src1, InputArray src2, OutputArray dst, + InputArray mask = noArray(), int dtype = -1); + + +/** @brief Calculates the per-element scaled product of two arrays. + +The function multiply calculates the per-element product of two arrays: + +\f[\texttt{dst} (I)= \texttt{saturate} ( \texttt{scale} \cdot \texttt{src1} (I) \cdot \texttt{src2} (I))\f] + +There is also a @ref MatrixExpressions -friendly variant of the first function. See Mat::mul . + +For a not-per-element matrix product, see gemm . + +@note Saturation is not applied when the output array has the depth +CV_32S. You may even get result of an incorrect sign in the case of +overflow. +@param src1 first input array. +@param src2 second input array of the same size and the same type as src1. +@param dst output array of the same size and type as src1. +@param scale optional scale factor. +@param dtype optional depth of the output array +@sa add, subtract, divide, scaleAdd, addWeighted, accumulate, accumulateProduct, accumulateSquare, +Mat::convertTo +*/ +CV_EXPORTS_W void multiply(InputArray src1, InputArray src2, + OutputArray dst, double scale = 1, int dtype = -1); + +/** @brief Performs per-element division of two arrays or a scalar by an array. + +The function cv::divide divides one array by another: +\f[\texttt{dst(I) = saturate(src1(I)*scale/src2(I))}\f] +or a scalar by an array when there is no src1 : +\f[\texttt{dst(I) = saturate(scale/src2(I))}\f] + +When src2(I) is zero, dst(I) will also be zero. Different channels of +multi-channel arrays are processed independently. + +@note Saturation is not applied when the output array has the depth CV_32S. You may even get +result of an incorrect sign in the case of overflow. +@param src1 first input array. +@param src2 second input array of the same size and type as src1. +@param scale scalar factor. +@param dst output array of the same size and type as src2. +@param dtype optional depth of the output array; if -1, dst will have depth src2.depth(), but in +case of an array-by-array division, you can only pass -1 when src1.depth()==src2.depth(). +@sa multiply, add, subtract +*/ +CV_EXPORTS_W void divide(InputArray src1, InputArray src2, OutputArray dst, + double scale = 1, int dtype = -1); + +/** @overload */ +CV_EXPORTS_W void divide(double scale, InputArray src2, + OutputArray dst, int dtype = -1); + +/** @brief Calculates the sum of a scaled array and another array. + +The function scaleAdd is one of the classical primitive linear algebra operations, known as DAXPY +or SAXPY in [BLAS](http://en.wikipedia.org/wiki/Basic_Linear_Algebra_Subprograms). It calculates +the sum of a scaled array and another array: +\f[\texttt{dst} (I)= \texttt{scale} \cdot \texttt{src1} (I) + \texttt{src2} (I)\f] +The function can also be emulated with a matrix expression, for example: +@code{.cpp} + Mat A(3, 3, CV_64F); + ... + A.row(0) = A.row(1)*2 + A.row(2); +@endcode +@param src1 first input array. +@param alpha scale factor for the first array. +@param src2 second input array of the same size and type as src1. +@param dst output array of the same size and type as src1. +@sa add, addWeighted, subtract, Mat::dot, Mat::convertTo +*/ +CV_EXPORTS_W void scaleAdd(InputArray src1, double alpha, InputArray src2, OutputArray dst); + +/** @brief Calculates the weighted sum of two arrays. + +The function addWeighted calculates the weighted sum of two arrays as follows: +\f[\texttt{dst} (I)= \texttt{saturate} ( \texttt{src1} (I)* \texttt{alpha} + \texttt{src2} (I)* \texttt{beta} + \texttt{gamma} )\f] +where I is a multi-dimensional index of array elements. In case of multi-channel arrays, each +channel is processed independently. +The function can be replaced with a matrix expression: +@code{.cpp} + dst = src1*alpha + src2*beta + gamma; +@endcode +@note Saturation is not applied when the output array has the depth CV_32S. You may even get +result of an incorrect sign in the case of overflow. +@param src1 first input array. +@param alpha weight of the first array elements. +@param src2 second input array of the same size and channel number as src1. +@param beta weight of the second array elements. +@param gamma scalar added to each sum. +@param dst output array that has the same size and number of channels as the input arrays. +@param dtype optional depth of the output array; when both input arrays have the same depth, dtype +can be set to -1, which will be equivalent to src1.depth(). +@sa add, subtract, scaleAdd, Mat::convertTo +*/ +CV_EXPORTS_W void addWeighted(InputArray src1, double alpha, InputArray src2, + double beta, double gamma, OutputArray dst, int dtype = -1); + +/** @brief Scales, calculates absolute values, and converts the result to 8-bit. + +On each element of the input array, the function convertScaleAbs +performs three operations sequentially: scaling, taking an absolute +value, conversion to an unsigned 8-bit type: +\f[\texttt{dst} (I)= \texttt{saturate\_cast<uchar>} (| \texttt{src} (I)* \texttt{alpha} + \texttt{beta} |)\f] +In case of multi-channel arrays, the function processes each channel +independently. When the output is not 8-bit, the operation can be +emulated by calling the Mat::convertTo method (or by using matrix +expressions) and then by calculating an absolute value of the result. +For example: +@code{.cpp} + Mat_<float> A(30,30); + randu(A, Scalar(-100), Scalar(100)); + Mat_<float> B = A*5 + 3; + B = abs(B); + // Mat_<float> B = abs(A*5+3) will also do the job, + // but it will allocate a temporary matrix +@endcode +@param src input array. +@param dst output array. +@param alpha optional scale factor. +@param beta optional delta added to the scaled values. +@sa Mat::convertTo, cv::abs(const Mat&) +*/ +CV_EXPORTS_W void convertScaleAbs(InputArray src, OutputArray dst, + double alpha = 1, double beta = 0); + +/** @brief Converts an array to half precision floating number. + +This function converts FP32 (single precision floating point) from/to FP16 (half precision floating point). The input array has to have type of CV_32F or +CV_16S to represent the bit depth. If the input array is neither of them, the function will raise an error. +The format of half precision floating point is defined in IEEE 754-2008. + +@param src input array. +@param dst output array. +*/ +CV_EXPORTS_W void convertFp16(InputArray src, OutputArray dst); + +/** @brief Performs a look-up table transform of an array. + +The function LUT fills the output array with values from the look-up table. Indices of the entries +are taken from the input array. That is, the function processes each element of src as follows: +\f[\texttt{dst} (I) \leftarrow \texttt{lut(src(I) + d)}\f] +where +\f[d = \fork{0}{if \(\texttt{src}\) has depth \(\texttt{CV_8U}\)}{128}{if \(\texttt{src}\) has depth \(\texttt{CV_8S}\)}\f] +@param src input array of 8-bit elements. +@param lut look-up table of 256 elements; in case of multi-channel input array, the table should +either have a single channel (in this case the same table is used for all channels) or the same +number of channels as in the input array. +@param dst output array of the same size and number of channels as src, and the same depth as lut. +@sa convertScaleAbs, Mat::convertTo +*/ +CV_EXPORTS_W void LUT(InputArray src, InputArray lut, OutputArray dst); + +/** @brief Calculates the sum of array elements. + +The function cv::sum calculates and returns the sum of array elements, +independently for each channel. +@param src input array that must have from 1 to 4 channels. +@sa countNonZero, mean, meanStdDev, norm, minMaxLoc, reduce +*/ +CV_EXPORTS_AS(sumElems) Scalar sum(InputArray src); + +/** @brief Counts non-zero array elements. + +The function returns the number of non-zero elements in src : +\f[\sum _{I: \; \texttt{src} (I) \ne0 } 1\f] +@param src single-channel array. +@sa mean, meanStdDev, norm, minMaxLoc, calcCovarMatrix +*/ +CV_EXPORTS_W int countNonZero( InputArray src ); + +/** @brief Returns the list of locations of non-zero pixels + +Given a binary matrix (likely returned from an operation such +as threshold(), compare(), >, ==, etc, return all of +the non-zero indices as a cv::Mat or std::vector<cv::Point> (x,y) +For example: +@code{.cpp} + cv::Mat binaryImage; // input, binary image + cv::Mat locations; // output, locations of non-zero pixels + cv::findNonZero(binaryImage, locations); + + // access pixel coordinates + Point pnt = locations.at<Point>(i); +@endcode +or +@code{.cpp} + cv::Mat binaryImage; // input, binary image + vector<Point> locations; // output, locations of non-zero pixels + cv::findNonZero(binaryImage, locations); + + // access pixel coordinates + Point pnt = locations[i]; +@endcode +@param src single-channel array (type CV_8UC1) +@param idx the output array, type of cv::Mat or std::vector<Point>, corresponding to non-zero indices in the input +*/ +CV_EXPORTS_W void findNonZero( InputArray src, OutputArray idx ); + +/** @brief Calculates an average (mean) of array elements. + +The function cv::mean calculates the mean value M of array elements, +independently for each channel, and return it: +\f[\begin{array}{l} N = \sum _{I: \; \texttt{mask} (I) \ne 0} 1 \\ M_c = \left ( \sum _{I: \; \texttt{mask} (I) \ne 0}{ \texttt{mtx} (I)_c} \right )/N \end{array}\f] +When all the mask elements are 0's, the function returns Scalar::all(0) +@param src input array that should have from 1 to 4 channels so that the result can be stored in +Scalar_ . +@param mask optional operation mask. +@sa countNonZero, meanStdDev, norm, minMaxLoc +*/ +CV_EXPORTS_W Scalar mean(InputArray src, InputArray mask = noArray()); + +/** Calculates a mean and standard deviation of array elements. + +The function cv::meanStdDev calculates the mean and the standard deviation M +of array elements independently for each channel and returns it via the +output parameters: +\f[\begin{array}{l} N = \sum _{I, \texttt{mask} (I) \ne 0} 1 \\ \texttt{mean} _c = \frac{\sum_{ I: \; \texttt{mask}(I) \ne 0} \texttt{src} (I)_c}{N} \\ \texttt{stddev} _c = \sqrt{\frac{\sum_{ I: \; \texttt{mask}(I) \ne 0} \left ( \texttt{src} (I)_c - \texttt{mean} _c \right )^2}{N}} \end{array}\f] +When all the mask elements are 0's, the function returns +mean=stddev=Scalar::all(0). +@note The calculated standard deviation is only the diagonal of the +complete normalized covariance matrix. If the full matrix is needed, you +can reshape the multi-channel array M x N to the single-channel array +M\*N x mtx.channels() (only possible when the matrix is continuous) and +then pass the matrix to calcCovarMatrix . +@param src input array that should have from 1 to 4 channels so that the results can be stored in +Scalar_ 's. +@param mean output parameter: calculated mean value. +@param stddev output parameter: calculateded standard deviation. +@param mask optional operation mask. +@sa countNonZero, mean, norm, minMaxLoc, calcCovarMatrix +*/ +CV_EXPORTS_W void meanStdDev(InputArray src, OutputArray mean, OutputArray stddev, + InputArray mask=noArray()); + +/** @brief Calculates an absolute array norm, an absolute difference norm, or a +relative difference norm. + +The function cv::norm calculates an absolute norm of src1 (when there is no +src2 ): + +\f[norm = \forkthree{\|\texttt{src1}\|_{L_{\infty}} = \max _I | \texttt{src1} (I)|}{if \(\texttt{normType} = \texttt{NORM_INF}\) } +{ \| \texttt{src1} \| _{L_1} = \sum _I | \texttt{src1} (I)|}{if \(\texttt{normType} = \texttt{NORM_L1}\) } +{ \| \texttt{src1} \| _{L_2} = \sqrt{\sum_I \texttt{src1}(I)^2} }{if \(\texttt{normType} = \texttt{NORM_L2}\) }\f] + +or an absolute or relative difference norm if src2 is there: + +\f[norm = \forkthree{\|\texttt{src1}-\texttt{src2}\|_{L_{\infty}} = \max _I | \texttt{src1} (I) - \texttt{src2} (I)|}{if \(\texttt{normType} = \texttt{NORM_INF}\) } +{ \| \texttt{src1} - \texttt{src2} \| _{L_1} = \sum _I | \texttt{src1} (I) - \texttt{src2} (I)|}{if \(\texttt{normType} = \texttt{NORM_L1}\) } +{ \| \texttt{src1} - \texttt{src2} \| _{L_2} = \sqrt{\sum_I (\texttt{src1}(I) - \texttt{src2}(I))^2} }{if \(\texttt{normType} = \texttt{NORM_L2}\) }\f] + +or + +\f[norm = \forkthree{\frac{\|\texttt{src1}-\texttt{src2}\|_{L_{\infty}} }{\|\texttt{src2}\|_{L_{\infty}} }}{if \(\texttt{normType} = \texttt{NORM_RELATIVE_INF}\) } +{ \frac{\|\texttt{src1}-\texttt{src2}\|_{L_1} }{\|\texttt{src2}\|_{L_1}} }{if \(\texttt{normType} = \texttt{NORM_RELATIVE_L1}\) } +{ \frac{\|\texttt{src1}-\texttt{src2}\|_{L_2} }{\|\texttt{src2}\|_{L_2}} }{if \(\texttt{normType} = \texttt{NORM_RELATIVE_L2}\) }\f] + +The function cv::norm returns the calculated norm. + +When the mask parameter is specified and it is not empty, the norm is +calculated only over the region specified by the mask. + +A multi-channel input arrays are treated as a single-channel, that is, +the results for all channels are combined. + +@param src1 first input array. +@param normType type of the norm (see cv::NormTypes). +@param mask optional operation mask; it must have the same size as src1 and CV_8UC1 type. +*/ +CV_EXPORTS_W double norm(InputArray src1, int normType = NORM_L2, InputArray mask = noArray()); + +/** @overload +@param src1 first input array. +@param src2 second input array of the same size and the same type as src1. +@param normType type of the norm (cv::NormTypes). +@param mask optional operation mask; it must have the same size as src1 and CV_8UC1 type. +*/ +CV_EXPORTS_W double norm(InputArray src1, InputArray src2, + int normType = NORM_L2, InputArray mask = noArray()); +/** @overload +@param src first input array. +@param normType type of the norm (see cv::NormTypes). +*/ +CV_EXPORTS double norm( const SparseMat& src, int normType ); + +/** @brief computes PSNR image/video quality metric + +see http://en.wikipedia.org/wiki/Peak_signal-to-noise_ratio for details +@todo document + */ +CV_EXPORTS_W double PSNR(InputArray src1, InputArray src2); + +/** @brief naive nearest neighbor finder + +see http://en.wikipedia.org/wiki/Nearest_neighbor_search +@todo document + */ +CV_EXPORTS_W void batchDistance(InputArray src1, InputArray src2, + OutputArray dist, int dtype, OutputArray nidx, + int normType = NORM_L2, int K = 0, + InputArray mask = noArray(), int update = 0, + bool crosscheck = false); + +/** @brief Normalizes the norm or value range of an array. + +The function cv::normalize normalizes scale and shift the input array elements so that +\f[\| \texttt{dst} \| _{L_p}= \texttt{alpha}\f] +(where p=Inf, 1 or 2) when normType=NORM_INF, NORM_L1, or NORM_L2, respectively; or so that +\f[\min _I \texttt{dst} (I)= \texttt{alpha} , \, \, \max _I \texttt{dst} (I)= \texttt{beta}\f] + +when normType=NORM_MINMAX (for dense arrays only). The optional mask specifies a sub-array to be +normalized. This means that the norm or min-n-max are calculated over the sub-array, and then this +sub-array is modified to be normalized. If you want to only use the mask to calculate the norm or +min-max but modify the whole array, you can use norm and Mat::convertTo. + +In case of sparse matrices, only the non-zero values are analyzed and transformed. Because of this, +the range transformation for sparse matrices is not allowed since it can shift the zero level. + +Possible usage with some positive example data: +@code{.cpp} + vector<double> positiveData = { 2.0, 8.0, 10.0 }; + vector<double> normalizedData_l1, normalizedData_l2, normalizedData_inf, normalizedData_minmax; + + // Norm to probability (total count) + // sum(numbers) = 20.0 + // 2.0 0.1 (2.0/20.0) + // 8.0 0.4 (8.0/20.0) + // 10.0 0.5 (10.0/20.0) + normalize(positiveData, normalizedData_l1, 1.0, 0.0, NORM_L1); + + // Norm to unit vector: ||positiveData|| = 1.0 + // 2.0 0.15 + // 8.0 0.62 + // 10.0 0.77 + normalize(positiveData, normalizedData_l2, 1.0, 0.0, NORM_L2); + + // Norm to max element + // 2.0 0.2 (2.0/10.0) + // 8.0 0.8 (8.0/10.0) + // 10.0 1.0 (10.0/10.0) + normalize(positiveData, normalizedData_inf, 1.0, 0.0, NORM_INF); + + // Norm to range [0.0;1.0] + // 2.0 0.0 (shift to left border) + // 8.0 0.75 (6.0/8.0) + // 10.0 1.0 (shift to right border) + normalize(positiveData, normalizedData_minmax, 1.0, 0.0, NORM_MINMAX); +@endcode + +@param src input array. +@param dst output array of the same size as src . +@param alpha norm value to normalize to or the lower range boundary in case of the range +normalization. +@param beta upper range boundary in case of the range normalization; it is not used for the norm +normalization. +@param norm_type normalization type (see cv::NormTypes). +@param dtype when negative, the output array has the same type as src; otherwise, it has the same +number of channels as src and the depth =CV_MAT_DEPTH(dtype). +@param mask optional operation mask. +@sa norm, Mat::convertTo, SparseMat::convertTo +*/ +CV_EXPORTS_W void normalize( InputArray src, InputOutputArray dst, double alpha = 1, double beta = 0, + int norm_type = NORM_L2, int dtype = -1, InputArray mask = noArray()); + +/** @overload +@param src input array. +@param dst output array of the same size as src . +@param alpha norm value to normalize to or the lower range boundary in case of the range +normalization. +@param normType normalization type (see cv::NormTypes). +*/ +CV_EXPORTS void normalize( const SparseMat& src, SparseMat& dst, double alpha, int normType ); + +/** @brief Finds the global minimum and maximum in an array. + +The function cv::minMaxLoc finds the minimum and maximum element values and their positions. The +extremums are searched across the whole array or, if mask is not an empty array, in the specified +array region. + +The function do not work with multi-channel arrays. If you need to find minimum or maximum +elements across all the channels, use Mat::reshape first to reinterpret the array as +single-channel. Or you may extract the particular channel using either extractImageCOI , or +mixChannels , or split . +@param src input single-channel array. +@param minVal pointer to the returned minimum value; NULL is used if not required. +@param maxVal pointer to the returned maximum value; NULL is used if not required. +@param minLoc pointer to the returned minimum location (in 2D case); NULL is used if not required. +@param maxLoc pointer to the returned maximum location (in 2D case); NULL is used if not required. +@param mask optional mask used to select a sub-array. +@sa max, min, compare, inRange, extractImageCOI, mixChannels, split, Mat::reshape +*/ +CV_EXPORTS_W void minMaxLoc(InputArray src, CV_OUT double* minVal, + CV_OUT double* maxVal = 0, CV_OUT Point* minLoc = 0, + CV_OUT Point* maxLoc = 0, InputArray mask = noArray()); + + +/** @brief Finds the global minimum and maximum in an array + +The function cv::minMaxIdx finds the minimum and maximum element values and their positions. The +extremums are searched across the whole array or, if mask is not an empty array, in the specified +array region. The function does not work with multi-channel arrays. If you need to find minimum or +maximum elements across all the channels, use Mat::reshape first to reinterpret the array as +single-channel. Or you may extract the particular channel using either extractImageCOI , or +mixChannels , or split . In case of a sparse matrix, the minimum is found among non-zero elements +only. +@note When minIdx is not NULL, it must have at least 2 elements (as well as maxIdx), even if src is +a single-row or single-column matrix. In OpenCV (following MATLAB) each array has at least 2 +dimensions, i.e. single-column matrix is Mx1 matrix (and therefore minIdx/maxIdx will be +(i1,0)/(i2,0)) and single-row matrix is 1xN matrix (and therefore minIdx/maxIdx will be +(0,j1)/(0,j2)). +@param src input single-channel array. +@param minVal pointer to the returned minimum value; NULL is used if not required. +@param maxVal pointer to the returned maximum value; NULL is used if not required. +@param minIdx pointer to the returned minimum location (in nD case); NULL is used if not required; +Otherwise, it must point to an array of src.dims elements, the coordinates of the minimum element +in each dimension are stored there sequentially. +@param maxIdx pointer to the returned maximum location (in nD case). NULL is used if not required. +@param mask specified array region +*/ +CV_EXPORTS void minMaxIdx(InputArray src, double* minVal, double* maxVal = 0, + int* minIdx = 0, int* maxIdx = 0, InputArray mask = noArray()); + +/** @overload +@param a input single-channel array. +@param minVal pointer to the returned minimum value; NULL is used if not required. +@param maxVal pointer to the returned maximum value; NULL is used if not required. +@param minIdx pointer to the returned minimum location (in nD case); NULL is used if not required; +Otherwise, it must point to an array of src.dims elements, the coordinates of the minimum element +in each dimension are stored there sequentially. +@param maxIdx pointer to the returned maximum location (in nD case). NULL is used if not required. +*/ +CV_EXPORTS void minMaxLoc(const SparseMat& a, double* minVal, + double* maxVal, int* minIdx = 0, int* maxIdx = 0); + +/** @brief Reduces a matrix to a vector. + +The function cv::reduce reduces the matrix to a vector by treating the matrix rows/columns as a set of +1D vectors and performing the specified operation on the vectors until a single row/column is +obtained. For example, the function can be used to compute horizontal and vertical projections of a +raster image. In case of REDUCE_MAX and REDUCE_MIN , the output image should have the same type as the source one. +In case of REDUCE_SUM and REDUCE_AVG , the output may have a larger element bit-depth to preserve accuracy. +And multi-channel arrays are also supported in these two reduction modes. +@param src input 2D matrix. +@param dst output vector. Its size and type is defined by dim and dtype parameters. +@param dim dimension index along which the matrix is reduced. 0 means that the matrix is reduced to +a single row. 1 means that the matrix is reduced to a single column. +@param rtype reduction operation that could be one of cv::ReduceTypes +@param dtype when negative, the output vector will have the same type as the input matrix, +otherwise, its type will be CV_MAKE_TYPE(CV_MAT_DEPTH(dtype), src.channels()). +@sa repeat +*/ +CV_EXPORTS_W void reduce(InputArray src, OutputArray dst, int dim, int rtype, int dtype = -1); + +/** @brief Creates one multi-channel array out of several single-channel ones. + +The function cv::merge merges several arrays to make a single multi-channel array. That is, each +element of the output array will be a concatenation of the elements of the input arrays, where +elements of i-th input array are treated as mv[i].channels()-element vectors. + +The function cv::split does the reverse operation. If you need to shuffle channels in some other +advanced way, use cv::mixChannels. +@param mv input array of matrices to be merged; all the matrices in mv must have the same +size and the same depth. +@param count number of input matrices when mv is a plain C array; it must be greater than zero. +@param dst output array of the same size and the same depth as mv[0]; The number of channels will +be equal to the parameter count. +@sa mixChannels, split, Mat::reshape +*/ +CV_EXPORTS void merge(const Mat* mv, size_t count, OutputArray dst); + +/** @overload +@param mv input vector of matrices to be merged; all the matrices in mv must have the same +size and the same depth. +@param dst output array of the same size and the same depth as mv[0]; The number of channels will +be the total number of channels in the matrix array. + */ +CV_EXPORTS_W void merge(InputArrayOfArrays mv, OutputArray dst); + +/** @brief Divides a multi-channel array into several single-channel arrays. + +The function cv::split splits a multi-channel array into separate single-channel arrays: +\f[\texttt{mv} [c](I) = \texttt{src} (I)_c\f] +If you need to extract a single channel or do some other sophisticated channel permutation, use +mixChannels . +@param src input multi-channel array. +@param mvbegin output array; the number of arrays must match src.channels(); the arrays themselves are +reallocated, if needed. +@sa merge, mixChannels, cvtColor +*/ +CV_EXPORTS void split(const Mat& src, Mat* mvbegin); + +/** @overload +@param m input multi-channel array. +@param mv output vector of arrays; the arrays themselves are reallocated, if needed. +*/ +CV_EXPORTS_W void split(InputArray m, OutputArrayOfArrays mv); + +/** @brief Copies specified channels from input arrays to the specified channels of +output arrays. + +The function cv::mixChannels provides an advanced mechanism for shuffling image channels. + +cv::split,cv::merge,cv::extractChannel,cv::insertChannel and some forms of cv::cvtColor are partial cases of cv::mixChannels. + +In the example below, the code splits a 4-channel BGRA image into a 3-channel BGR (with B and R +channels swapped) and a separate alpha-channel image: +@code{.cpp} + Mat bgra( 100, 100, CV_8UC4, Scalar(255,0,0,255) ); + Mat bgr( bgra.rows, bgra.cols, CV_8UC3 ); + Mat alpha( bgra.rows, bgra.cols, CV_8UC1 ); + + // forming an array of matrices is a quite efficient operation, + // because the matrix data is not copied, only the headers + Mat out[] = { bgr, alpha }; + // bgra[0] -> bgr[2], bgra[1] -> bgr[1], + // bgra[2] -> bgr[0], bgra[3] -> alpha[0] + int from_to[] = { 0,2, 1,1, 2,0, 3,3 }; + mixChannels( &bgra, 1, out, 2, from_to, 4 ); +@endcode +@note Unlike many other new-style C++ functions in OpenCV (see the introduction section and +Mat::create ), cv::mixChannels requires the output arrays to be pre-allocated before calling the +function. +@param src input array or vector of matrices; all of the matrices must have the same size and the +same depth. +@param nsrcs number of matrices in `src`. +@param dst output array or vector of matrices; all the matrices **must be allocated**; their size and +depth must be the same as in `src[0]`. +@param ndsts number of matrices in `dst`. +@param fromTo array of index pairs specifying which channels are copied and where; fromTo[k\*2] is +a 0-based index of the input channel in src, fromTo[k\*2+1] is an index of the output channel in +dst; the continuous channel numbering is used: the first input image channels are indexed from 0 to +src[0].channels()-1, the second input image channels are indexed from src[0].channels() to +src[0].channels() + src[1].channels()-1, and so on, the same scheme is used for the output image +channels; as a special case, when fromTo[k\*2] is negative, the corresponding output channel is +filled with zero . +@param npairs number of index pairs in `fromTo`. +@sa split, merge, extractChannel, insertChannel, cvtColor +*/ +CV_EXPORTS void mixChannels(const Mat* src, size_t nsrcs, Mat* dst, size_t ndsts, + const int* fromTo, size_t npairs); + +/** @overload +@param src input array or vector of matrices; all of the matrices must have the same size and the +same depth. +@param dst output array or vector of matrices; all the matrices **must be allocated**; their size and +depth must be the same as in src[0]. +@param fromTo array of index pairs specifying which channels are copied and where; fromTo[k\*2] is +a 0-based index of the input channel in src, fromTo[k\*2+1] is an index of the output channel in +dst; the continuous channel numbering is used: the first input image channels are indexed from 0 to +src[0].channels()-1, the second input image channels are indexed from src[0].channels() to +src[0].channels() + src[1].channels()-1, and so on, the same scheme is used for the output image +channels; as a special case, when fromTo[k\*2] is negative, the corresponding output channel is +filled with zero . +@param npairs number of index pairs in fromTo. +*/ +CV_EXPORTS void mixChannels(InputArrayOfArrays src, InputOutputArrayOfArrays dst, + const int* fromTo, size_t npairs); + +/** @overload +@param src input array or vector of matrices; all of the matrices must have the same size and the +same depth. +@param dst output array or vector of matrices; all the matrices **must be allocated**; their size and +depth must be the same as in src[0]. +@param fromTo array of index pairs specifying which channels are copied and where; fromTo[k\*2] is +a 0-based index of the input channel in src, fromTo[k\*2+1] is an index of the output channel in +dst; the continuous channel numbering is used: the first input image channels are indexed from 0 to +src[0].channels()-1, the second input image channels are indexed from src[0].channels() to +src[0].channels() + src[1].channels()-1, and so on, the same scheme is used for the output image +channels; as a special case, when fromTo[k\*2] is negative, the corresponding output channel is +filled with zero . +*/ +CV_EXPORTS_W void mixChannels(InputArrayOfArrays src, InputOutputArrayOfArrays dst, + const std::vector<int>& fromTo); + +/** @brief Extracts a single channel from src (coi is 0-based index) +@param src input array +@param dst output array +@param coi index of channel to extract +@sa mixChannels, split +*/ +CV_EXPORTS_W void extractChannel(InputArray src, OutputArray dst, int coi); + +/** @brief Inserts a single channel to dst (coi is 0-based index) +@param src input array +@param dst output array +@param coi index of channel for insertion +@sa mixChannels, merge +*/ +CV_EXPORTS_W void insertChannel(InputArray src, InputOutputArray dst, int coi); + +/** @brief Flips a 2D array around vertical, horizontal, or both axes. + +The function cv::flip flips the array in one of three different ways (row +and column indices are 0-based): +\f[\texttt{dst} _{ij} = +\left\{ +\begin{array}{l l} +\texttt{src} _{\texttt{src.rows}-i-1,j} & if\; \texttt{flipCode} = 0 \\ +\texttt{src} _{i, \texttt{src.cols} -j-1} & if\; \texttt{flipCode} > 0 \\ +\texttt{src} _{ \texttt{src.rows} -i-1, \texttt{src.cols} -j-1} & if\; \texttt{flipCode} < 0 \\ +\end{array} +\right.\f] +The example scenarios of using the function are the following: +* Vertical flipping of the image (flipCode == 0) to switch between + top-left and bottom-left image origin. This is a typical operation + in video processing on Microsoft Windows\* OS. +* Horizontal flipping of the image with the subsequent horizontal + shift and absolute difference calculation to check for a + vertical-axis symmetry (flipCode \> 0). +* Simultaneous horizontal and vertical flipping of the image with + the subsequent shift and absolute difference calculation to check + for a central symmetry (flipCode \< 0). +* Reversing the order of point arrays (flipCode \> 0 or + flipCode == 0). +@param src input array. +@param dst output array of the same size and type as src. +@param flipCode a flag to specify how to flip the array; 0 means +flipping around the x-axis and positive value (for example, 1) means +flipping around y-axis. Negative value (for example, -1) means flipping +around both axes. +@sa transpose , repeat , completeSymm +*/ +CV_EXPORTS_W void flip(InputArray src, OutputArray dst, int flipCode); + +enum RotateFlags { + ROTATE_90_CLOCKWISE = 0, //Rotate 90 degrees clockwise + ROTATE_180 = 1, //Rotate 180 degrees clockwise + ROTATE_90_COUNTERCLOCKWISE = 2, //Rotate 270 degrees clockwise +}; +/** @brief Rotates a 2D array in multiples of 90 degrees. +The function rotate rotates the array in one of three different ways: +* Rotate by 90 degrees clockwise (rotateCode = ROTATE_90). +* Rotate by 180 degrees clockwise (rotateCode = ROTATE_180). +* Rotate by 270 degrees clockwise (rotateCode = ROTATE_270). +@param src input array. +@param dst output array of the same type as src. The size is the same with ROTATE_180, +and the rows and cols are switched for ROTATE_90 and ROTATE_270. +@param rotateCode an enum to specify how to rotate the array; see the enum RotateFlags +@sa transpose , repeat , completeSymm, flip, RotateFlags +*/ +CV_EXPORTS_W void rotate(InputArray src, OutputArray dst, int rotateCode); + +/** @brief Fills the output array with repeated copies of the input array. + +The function cv::repeat duplicates the input array one or more times along each of the two axes: +\f[\texttt{dst} _{ij}= \texttt{src} _{i\mod src.rows, \; j\mod src.cols }\f] +The second variant of the function is more convenient to use with @ref MatrixExpressions. +@param src input array to replicate. +@param ny Flag to specify how many times the `src` is repeated along the +vertical axis. +@param nx Flag to specify how many times the `src` is repeated along the +horizontal axis. +@param dst output array of the same type as `src`. +@sa cv::reduce +*/ +CV_EXPORTS_W void repeat(InputArray src, int ny, int nx, OutputArray dst); + +/** @overload +@param src input array to replicate. +@param ny Flag to specify how many times the `src` is repeated along the +vertical axis. +@param nx Flag to specify how many times the `src` is repeated along the +horizontal axis. + */ +CV_EXPORTS Mat repeat(const Mat& src, int ny, int nx); + +/** @brief Applies horizontal concatenation to given matrices. + +The function horizontally concatenates two or more cv::Mat matrices (with the same number of rows). +@code{.cpp} + cv::Mat matArray[] = { cv::Mat(4, 1, CV_8UC1, cv::Scalar(1)), + cv::Mat(4, 1, CV_8UC1, cv::Scalar(2)), + cv::Mat(4, 1, CV_8UC1, cv::Scalar(3)),}; + + cv::Mat out; + cv::hconcat( matArray, 3, out ); + //out: + //[1, 2, 3; + // 1, 2, 3; + // 1, 2, 3; + // 1, 2, 3] +@endcode +@param src input array or vector of matrices. all of the matrices must have the same number of rows and the same depth. +@param nsrc number of matrices in src. +@param dst output array. It has the same number of rows and depth as the src, and the sum of cols of the src. +@sa cv::vconcat(const Mat*, size_t, OutputArray), @sa cv::vconcat(InputArrayOfArrays, OutputArray) and @sa cv::vconcat(InputArray, InputArray, OutputArray) +*/ +CV_EXPORTS void hconcat(const Mat* src, size_t nsrc, OutputArray dst); +/** @overload + @code{.cpp} + cv::Mat_<float> A = (cv::Mat_<float>(3, 2) << 1, 4, + 2, 5, + 3, 6); + cv::Mat_<float> B = (cv::Mat_<float>(3, 2) << 7, 10, + 8, 11, + 9, 12); + + cv::Mat C; + cv::hconcat(A, B, C); + //C: + //[1, 4, 7, 10; + // 2, 5, 8, 11; + // 3, 6, 9, 12] + @endcode + @param src1 first input array to be considered for horizontal concatenation. + @param src2 second input array to be considered for horizontal concatenation. + @param dst output array. It has the same number of rows and depth as the src1 and src2, and the sum of cols of the src1 and src2. + */ +CV_EXPORTS void hconcat(InputArray src1, InputArray src2, OutputArray dst); +/** @overload + @code{.cpp} + std::vector<cv::Mat> matrices = { cv::Mat(4, 1, CV_8UC1, cv::Scalar(1)), + cv::Mat(4, 1, CV_8UC1, cv::Scalar(2)), + cv::Mat(4, 1, CV_8UC1, cv::Scalar(3)),}; + + cv::Mat out; + cv::hconcat( matrices, out ); + //out: + //[1, 2, 3; + // 1, 2, 3; + // 1, 2, 3; + // 1, 2, 3] + @endcode + @param src input array or vector of matrices. all of the matrices must have the same number of rows and the same depth. + @param dst output array. It has the same number of rows and depth as the src, and the sum of cols of the src. +same depth. + */ +CV_EXPORTS_W void hconcat(InputArrayOfArrays src, OutputArray dst); + +/** @brief Applies vertical concatenation to given matrices. + +The function vertically concatenates two or more cv::Mat matrices (with the same number of cols). +@code{.cpp} + cv::Mat matArray[] = { cv::Mat(1, 4, CV_8UC1, cv::Scalar(1)), + cv::Mat(1, 4, CV_8UC1, cv::Scalar(2)), + cv::Mat(1, 4, CV_8UC1, cv::Scalar(3)),}; + + cv::Mat out; + cv::vconcat( matArray, 3, out ); + //out: + //[1, 1, 1, 1; + // 2, 2, 2, 2; + // 3, 3, 3, 3] +@endcode +@param src input array or vector of matrices. all of the matrices must have the same number of cols and the same depth. +@param nsrc number of matrices in src. +@param dst output array. It has the same number of cols and depth as the src, and the sum of rows of the src. +@sa cv::hconcat(const Mat*, size_t, OutputArray), @sa cv::hconcat(InputArrayOfArrays, OutputArray) and @sa cv::hconcat(InputArray, InputArray, OutputArray) +*/ +CV_EXPORTS void vconcat(const Mat* src, size_t nsrc, OutputArray dst); +/** @overload + @code{.cpp} + cv::Mat_<float> A = (cv::Mat_<float>(3, 2) << 1, 7, + 2, 8, + 3, 9); + cv::Mat_<float> B = (cv::Mat_<float>(3, 2) << 4, 10, + 5, 11, + 6, 12); + + cv::Mat C; + cv::vconcat(A, B, C); + //C: + //[1, 7; + // 2, 8; + // 3, 9; + // 4, 10; + // 5, 11; + // 6, 12] + @endcode + @param src1 first input array to be considered for vertical concatenation. + @param src2 second input array to be considered for vertical concatenation. + @param dst output array. It has the same number of cols and depth as the src1 and src2, and the sum of rows of the src1 and src2. + */ +CV_EXPORTS void vconcat(InputArray src1, InputArray src2, OutputArray dst); +/** @overload + @code{.cpp} + std::vector<cv::Mat> matrices = { cv::Mat(1, 4, CV_8UC1, cv::Scalar(1)), + cv::Mat(1, 4, CV_8UC1, cv::Scalar(2)), + cv::Mat(1, 4, CV_8UC1, cv::Scalar(3)),}; + + cv::Mat out; + cv::vconcat( matrices, out ); + //out: + //[1, 1, 1, 1; + // 2, 2, 2, 2; + // 3, 3, 3, 3] + @endcode + @param src input array or vector of matrices. all of the matrices must have the same number of cols and the same depth + @param dst output array. It has the same number of cols and depth as the src, and the sum of rows of the src. +same depth. + */ +CV_EXPORTS_W void vconcat(InputArrayOfArrays src, OutputArray dst); + +/** @brief computes bitwise conjunction of the two arrays (dst = src1 & src2) +Calculates the per-element bit-wise conjunction of two arrays or an +array and a scalar. + +The function cv::bitwise_and calculates the per-element bit-wise logical conjunction for: +* Two arrays when src1 and src2 have the same size: + \f[\texttt{dst} (I) = \texttt{src1} (I) \wedge \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0\f] +* An array and a scalar when src2 is constructed from Scalar or has + the same number of elements as `src1.channels()`: + \f[\texttt{dst} (I) = \texttt{src1} (I) \wedge \texttt{src2} \quad \texttt{if mask} (I) \ne0\f] +* A scalar and an array when src1 is constructed from Scalar or has + the same number of elements as `src2.channels()`: + \f[\texttt{dst} (I) = \texttt{src1} \wedge \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0\f] +In case of floating-point arrays, their machine-specific bit +representations (usually IEEE754-compliant) are used for the operation. +In case of multi-channel arrays, each channel is processed +independently. In the second and third cases above, the scalar is first +converted to the array type. +@param src1 first input array or a scalar. +@param src2 second input array or a scalar. +@param dst output array that has the same size and type as the input +arrays. +@param mask optional operation mask, 8-bit single channel array, that +specifies elements of the output array to be changed. +*/ +CV_EXPORTS_W void bitwise_and(InputArray src1, InputArray src2, + OutputArray dst, InputArray mask = noArray()); + +/** @brief Calculates the per-element bit-wise disjunction of two arrays or an +array and a scalar. + +The function cv::bitwise_or calculates the per-element bit-wise logical disjunction for: +* Two arrays when src1 and src2 have the same size: + \f[\texttt{dst} (I) = \texttt{src1} (I) \vee \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0\f] +* An array and a scalar when src2 is constructed from Scalar or has + the same number of elements as `src1.channels()`: + \f[\texttt{dst} (I) = \texttt{src1} (I) \vee \texttt{src2} \quad \texttt{if mask} (I) \ne0\f] +* A scalar and an array when src1 is constructed from Scalar or has + the same number of elements as `src2.channels()`: + \f[\texttt{dst} (I) = \texttt{src1} \vee \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0\f] +In case of floating-point arrays, their machine-specific bit +representations (usually IEEE754-compliant) are used for the operation. +In case of multi-channel arrays, each channel is processed +independently. In the second and third cases above, the scalar is first +converted to the array type. +@param src1 first input array or a scalar. +@param src2 second input array or a scalar. +@param dst output array that has the same size and type as the input +arrays. +@param mask optional operation mask, 8-bit single channel array, that +specifies elements of the output array to be changed. +*/ +CV_EXPORTS_W void bitwise_or(InputArray src1, InputArray src2, + OutputArray dst, InputArray mask = noArray()); + +/** @brief Calculates the per-element bit-wise "exclusive or" operation on two +arrays or an array and a scalar. + +The function cv::bitwise_xor calculates the per-element bit-wise logical "exclusive-or" +operation for: +* Two arrays when src1 and src2 have the same size: + \f[\texttt{dst} (I) = \texttt{src1} (I) \oplus \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0\f] +* An array and a scalar when src2 is constructed from Scalar or has + the same number of elements as `src1.channels()`: + \f[\texttt{dst} (I) = \texttt{src1} (I) \oplus \texttt{src2} \quad \texttt{if mask} (I) \ne0\f] +* A scalar and an array when src1 is constructed from Scalar or has + the same number of elements as `src2.channels()`: + \f[\texttt{dst} (I) = \texttt{src1} \oplus \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0\f] +In case of floating-point arrays, their machine-specific bit +representations (usually IEEE754-compliant) are used for the operation. +In case of multi-channel arrays, each channel is processed +independently. In the 2nd and 3rd cases above, the scalar is first +converted to the array type. +@param src1 first input array or a scalar. +@param src2 second input array or a scalar. +@param dst output array that has the same size and type as the input +arrays. +@param mask optional operation mask, 8-bit single channel array, that +specifies elements of the output array to be changed. +*/ +CV_EXPORTS_W void bitwise_xor(InputArray src1, InputArray src2, + OutputArray dst, InputArray mask = noArray()); + +/** @brief Inverts every bit of an array. + +The function cv::bitwise_not calculates per-element bit-wise inversion of the input +array: +\f[\texttt{dst} (I) = \neg \texttt{src} (I)\f] +In case of a floating-point input array, its machine-specific bit +representation (usually IEEE754-compliant) is used for the operation. In +case of multi-channel arrays, each channel is processed independently. +@param src input array. +@param dst output array that has the same size and type as the input +array. +@param mask optional operation mask, 8-bit single channel array, that +specifies elements of the output array to be changed. +*/ +CV_EXPORTS_W void bitwise_not(InputArray src, OutputArray dst, + InputArray mask = noArray()); + +/** @brief Calculates the per-element absolute difference between two arrays or between an array and a scalar. + +The function cv::absdiff calculates: +* Absolute difference between two arrays when they have the same + size and type: + \f[\texttt{dst}(I) = \texttt{saturate} (| \texttt{src1}(I) - \texttt{src2}(I)|)\f] +* Absolute difference between an array and a scalar when the second + array is constructed from Scalar or has as many elements as the + number of channels in `src1`: + \f[\texttt{dst}(I) = \texttt{saturate} (| \texttt{src1}(I) - \texttt{src2} |)\f] +* Absolute difference between a scalar and an array when the first + array is constructed from Scalar or has as many elements as the + number of channels in `src2`: + \f[\texttt{dst}(I) = \texttt{saturate} (| \texttt{src1} - \texttt{src2}(I) |)\f] + where I is a multi-dimensional index of array elements. In case of + multi-channel arrays, each channel is processed independently. +@note Saturation is not applied when the arrays have the depth CV_32S. +You may even get a negative value in the case of overflow. +@param src1 first input array or a scalar. +@param src2 second input array or a scalar. +@param dst output array that has the same size and type as input arrays. +@sa cv::abs(const Mat&) +*/ +CV_EXPORTS_W void absdiff(InputArray src1, InputArray src2, OutputArray dst); + +/** @brief Checks if array elements lie between the elements of two other arrays. + +The function checks the range as follows: +- For every element of a single-channel input array: + \f[\texttt{dst} (I)= \texttt{lowerb} (I)_0 \leq \texttt{src} (I)_0 \leq \texttt{upperb} (I)_0\f] +- For two-channel arrays: + \f[\texttt{dst} (I)= \texttt{lowerb} (I)_0 \leq \texttt{src} (I)_0 \leq \texttt{upperb} (I)_0 \land \texttt{lowerb} (I)_1 \leq \texttt{src} (I)_1 \leq \texttt{upperb} (I)_1\f] +- and so forth. + +That is, dst (I) is set to 255 (all 1 -bits) if src (I) is within the +specified 1D, 2D, 3D, ... box and 0 otherwise. + +When the lower and/or upper boundary parameters are scalars, the indexes +(I) at lowerb and upperb in the above formulas should be omitted. +@param src first input array. +@param lowerb inclusive lower boundary array or a scalar. +@param upperb inclusive upper boundary array or a scalar. +@param dst output array of the same size as src and CV_8U type. +*/ +CV_EXPORTS_W void inRange(InputArray src, InputArray lowerb, + InputArray upperb, OutputArray dst); + +/** @brief Performs the per-element comparison of two arrays or an array and scalar value. + +The function compares: +* Elements of two arrays when src1 and src2 have the same size: + \f[\texttt{dst} (I) = \texttt{src1} (I) \,\texttt{cmpop}\, \texttt{src2} (I)\f] +* Elements of src1 with a scalar src2 when src2 is constructed from + Scalar or has a single element: + \f[\texttt{dst} (I) = \texttt{src1}(I) \,\texttt{cmpop}\, \texttt{src2}\f] +* src1 with elements of src2 when src1 is constructed from Scalar or + has a single element: + \f[\texttt{dst} (I) = \texttt{src1} \,\texttt{cmpop}\, \texttt{src2} (I)\f] +When the comparison result is true, the corresponding element of output +array is set to 255. The comparison operations can be replaced with the +equivalent matrix expressions: +@code{.cpp} + Mat dst1 = src1 >= src2; + Mat dst2 = src1 < 8; + ... +@endcode +@param src1 first input array or a scalar; when it is an array, it must have a single channel. +@param src2 second input array or a scalar; when it is an array, it must have a single channel. +@param dst output array of type ref CV_8U that has the same size and the same number of channels as + the input arrays. +@param cmpop a flag, that specifies correspondence between the arrays (cv::CmpTypes) +@sa checkRange, min, max, threshold +*/ +CV_EXPORTS_W void compare(InputArray src1, InputArray src2, OutputArray dst, int cmpop); + +/** @brief Calculates per-element minimum of two arrays or an array and a scalar. + +The function cv::min calculates the per-element minimum of two arrays: +\f[\texttt{dst} (I)= \min ( \texttt{src1} (I), \texttt{src2} (I))\f] +or array and a scalar: +\f[\texttt{dst} (I)= \min ( \texttt{src1} (I), \texttt{value} )\f] +@param src1 first input array. +@param src2 second input array of the same size and type as src1. +@param dst output array of the same size and type as src1. +@sa max, compare, inRange, minMaxLoc +*/ +CV_EXPORTS_W void min(InputArray src1, InputArray src2, OutputArray dst); +/** @overload +needed to avoid conflicts with const _Tp& std::min(const _Tp&, const _Tp&, _Compare) +*/ +CV_EXPORTS void min(const Mat& src1, const Mat& src2, Mat& dst); +/** @overload +needed to avoid conflicts with const _Tp& std::min(const _Tp&, const _Tp&, _Compare) +*/ +CV_EXPORTS void min(const UMat& src1, const UMat& src2, UMat& dst); + +/** @brief Calculates per-element maximum of two arrays or an array and a scalar. + +The function cv::max calculates the per-element maximum of two arrays: +\f[\texttt{dst} (I)= \max ( \texttt{src1} (I), \texttt{src2} (I))\f] +or array and a scalar: +\f[\texttt{dst} (I)= \max ( \texttt{src1} (I), \texttt{value} )\f] +@param src1 first input array. +@param src2 second input array of the same size and type as src1 . +@param dst output array of the same size and type as src1. +@sa min, compare, inRange, minMaxLoc, @ref MatrixExpressions +*/ +CV_EXPORTS_W void max(InputArray src1, InputArray src2, OutputArray dst); +/** @overload +needed to avoid conflicts with const _Tp& std::min(const _Tp&, const _Tp&, _Compare) +*/ +CV_EXPORTS void max(const Mat& src1, const Mat& src2, Mat& dst); +/** @overload +needed to avoid conflicts with const _Tp& std::min(const _Tp&, const _Tp&, _Compare) +*/ +CV_EXPORTS void max(const UMat& src1, const UMat& src2, UMat& dst); + +/** @brief Calculates a square root of array elements. + +The function cv::sqrt calculates a square root of each input array element. +In case of multi-channel arrays, each channel is processed +independently. The accuracy is approximately the same as of the built-in +std::sqrt . +@param src input floating-point array. +@param dst output array of the same size and type as src. +*/ +CV_EXPORTS_W void sqrt(InputArray src, OutputArray dst); + +/** @brief Raises every array element to a power. + +The function cv::pow raises every element of the input array to power : +\f[\texttt{dst} (I) = \fork{\texttt{src}(I)^{power}}{if \(\texttt{power}\) is integer}{|\texttt{src}(I)|^{power}}{otherwise}\f] + +So, for a non-integer power exponent, the absolute values of input array +elements are used. However, it is possible to get true values for +negative values using some extra operations. In the example below, +computing the 5th root of array src shows: +@code{.cpp} + Mat mask = src < 0; + pow(src, 1./5, dst); + subtract(Scalar::all(0), dst, dst, mask); +@endcode +For some values of power, such as integer values, 0.5 and -0.5, +specialized faster algorithms are used. + +Special values (NaN, Inf) are not handled. +@param src input array. +@param power exponent of power. +@param dst output array of the same size and type as src. +@sa sqrt, exp, log, cartToPolar, polarToCart +*/ +CV_EXPORTS_W void pow(InputArray src, double power, OutputArray dst); + +/** @brief Calculates the exponent of every array element. + +The function cv::exp calculates the exponent of every element of the input +array: +\f[\texttt{dst} [I] = e^{ src(I) }\f] + +The maximum relative error is about 7e-6 for single-precision input and +less than 1e-10 for double-precision input. Currently, the function +converts denormalized values to zeros on output. Special values (NaN, +Inf) are not handled. +@param src input array. +@param dst output array of the same size and type as src. +@sa log , cartToPolar , polarToCart , phase , pow , sqrt , magnitude +*/ +CV_EXPORTS_W void exp(InputArray src, OutputArray dst); + +/** @brief Calculates the natural logarithm of every array element. + +The function cv::log calculates the natural logarithm of every element of the input array: +\f[\texttt{dst} (I) = \log (\texttt{src}(I)) \f] + +Output on zero, negative and special (NaN, Inf) values is undefined. + +@param src input array. +@param dst output array of the same size and type as src . +@sa exp, cartToPolar, polarToCart, phase, pow, sqrt, magnitude +*/ +CV_EXPORTS_W void log(InputArray src, OutputArray dst); + +/** @brief Calculates x and y coordinates of 2D vectors from their magnitude and angle. + +The function cv::polarToCart calculates the Cartesian coordinates of each 2D +vector represented by the corresponding elements of magnitude and angle: +\f[\begin{array}{l} \texttt{x} (I) = \texttt{magnitude} (I) \cos ( \texttt{angle} (I)) \\ \texttt{y} (I) = \texttt{magnitude} (I) \sin ( \texttt{angle} (I)) \\ \end{array}\f] + +The relative accuracy of the estimated coordinates is about 1e-6. +@param magnitude input floating-point array of magnitudes of 2D vectors; +it can be an empty matrix (=Mat()), in this case, the function assumes +that all the magnitudes are =1; if it is not empty, it must have the +same size and type as angle. +@param angle input floating-point array of angles of 2D vectors. +@param x output array of x-coordinates of 2D vectors; it has the same +size and type as angle. +@param y output array of y-coordinates of 2D vectors; it has the same +size and type as angle. +@param angleInDegrees when true, the input angles are measured in +degrees, otherwise, they are measured in radians. +@sa cartToPolar, magnitude, phase, exp, log, pow, sqrt +*/ +CV_EXPORTS_W void polarToCart(InputArray magnitude, InputArray angle, + OutputArray x, OutputArray y, bool angleInDegrees = false); + +/** @brief Calculates the magnitude and angle of 2D vectors. + +The function cv::cartToPolar calculates either the magnitude, angle, or both +for every 2D vector (x(I),y(I)): +\f[\begin{array}{l} \texttt{magnitude} (I)= \sqrt{\texttt{x}(I)^2+\texttt{y}(I)^2} , \\ \texttt{angle} (I)= \texttt{atan2} ( \texttt{y} (I), \texttt{x} (I))[ \cdot180 / \pi ] \end{array}\f] + +The angles are calculated with accuracy about 0.3 degrees. For the point +(0,0), the angle is set to 0. +@param x array of x-coordinates; this must be a single-precision or +double-precision floating-point array. +@param y array of y-coordinates, that must have the same size and same type as x. +@param magnitude output array of magnitudes of the same size and type as x. +@param angle output array of angles that has the same size and type as +x; the angles are measured in radians (from 0 to 2\*Pi) or in degrees (0 to 360 degrees). +@param angleInDegrees a flag, indicating whether the angles are measured +in radians (which is by default), or in degrees. +@sa Sobel, Scharr +*/ +CV_EXPORTS_W void cartToPolar(InputArray x, InputArray y, + OutputArray magnitude, OutputArray angle, + bool angleInDegrees = false); + +/** @brief Calculates the rotation angle of 2D vectors. + +The function cv::phase calculates the rotation angle of each 2D vector that +is formed from the corresponding elements of x and y : +\f[\texttt{angle} (I) = \texttt{atan2} ( \texttt{y} (I), \texttt{x} (I))\f] + +The angle estimation accuracy is about 0.3 degrees. When x(I)=y(I)=0 , +the corresponding angle(I) is set to 0. +@param x input floating-point array of x-coordinates of 2D vectors. +@param y input array of y-coordinates of 2D vectors; it must have the +same size and the same type as x. +@param angle output array of vector angles; it has the same size and +same type as x . +@param angleInDegrees when true, the function calculates the angle in +degrees, otherwise, they are measured in radians. +*/ +CV_EXPORTS_W void phase(InputArray x, InputArray y, OutputArray angle, + bool angleInDegrees = false); + +/** @brief Calculates the magnitude of 2D vectors. + +The function cv::magnitude calculates the magnitude of 2D vectors formed +from the corresponding elements of x and y arrays: +\f[\texttt{dst} (I) = \sqrt{\texttt{x}(I)^2 + \texttt{y}(I)^2}\f] +@param x floating-point array of x-coordinates of the vectors. +@param y floating-point array of y-coordinates of the vectors; it must +have the same size as x. +@param magnitude output array of the same size and type as x. +@sa cartToPolar, polarToCart, phase, sqrt +*/ +CV_EXPORTS_W void magnitude(InputArray x, InputArray y, OutputArray magnitude); + +/** @brief Checks every element of an input array for invalid values. + +The function cv::checkRange checks that every array element is neither NaN nor infinite. When minVal \> +-DBL_MAX and maxVal \< DBL_MAX, the function also checks that each value is between minVal and +maxVal. In case of multi-channel arrays, each channel is processed independently. If some values +are out of range, position of the first outlier is stored in pos (when pos != NULL). Then, the +function either returns false (when quiet=true) or throws an exception. +@param a input array. +@param quiet a flag, indicating whether the functions quietly return false when the array elements +are out of range or they throw an exception. +@param pos optional output parameter, when not NULL, must be a pointer to array of src.dims +elements. +@param minVal inclusive lower boundary of valid values range. +@param maxVal exclusive upper boundary of valid values range. +*/ +CV_EXPORTS_W bool checkRange(InputArray a, bool quiet = true, CV_OUT Point* pos = 0, + double minVal = -DBL_MAX, double maxVal = DBL_MAX); + +/** @brief converts NaN's to the given number +*/ +CV_EXPORTS_W void patchNaNs(InputOutputArray a, double val = 0); + +/** @brief Performs generalized matrix multiplication. + +The function cv::gemm performs generalized matrix multiplication similar to the +gemm functions in BLAS level 3. For example, +`gemm(src1, src2, alpha, src3, beta, dst, GEMM_1_T + GEMM_3_T)` +corresponds to +\f[\texttt{dst} = \texttt{alpha} \cdot \texttt{src1} ^T \cdot \texttt{src2} + \texttt{beta} \cdot \texttt{src3} ^T\f] + +In case of complex (two-channel) data, performed a complex matrix +multiplication. + +The function can be replaced with a matrix expression. For example, the +above call can be replaced with: +@code{.cpp} + dst = alpha*src1.t()*src2 + beta*src3.t(); +@endcode +@param src1 first multiplied input matrix that could be real(CV_32FC1, +CV_64FC1) or complex(CV_32FC2, CV_64FC2). +@param src2 second multiplied input matrix of the same type as src1. +@param alpha weight of the matrix product. +@param src3 third optional delta matrix added to the matrix product; it +should have the same type as src1 and src2. +@param beta weight of src3. +@param dst output matrix; it has the proper size and the same type as +input matrices. +@param flags operation flags (cv::GemmFlags) +@sa mulTransposed , transform +*/ +CV_EXPORTS_W void gemm(InputArray src1, InputArray src2, double alpha, + InputArray src3, double beta, OutputArray dst, int flags = 0); + +/** @brief Calculates the product of a matrix and its transposition. + +The function cv::mulTransposed calculates the product of src and its +transposition: +\f[\texttt{dst} = \texttt{scale} ( \texttt{src} - \texttt{delta} )^T ( \texttt{src} - \texttt{delta} )\f] +if aTa=true , and +\f[\texttt{dst} = \texttt{scale} ( \texttt{src} - \texttt{delta} ) ( \texttt{src} - \texttt{delta} )^T\f] +otherwise. The function is used to calculate the covariance matrix. With +zero delta, it can be used as a faster substitute for general matrix +product A\*B when B=A' +@param src input single-channel matrix. Note that unlike gemm, the +function can multiply not only floating-point matrices. +@param dst output square matrix. +@param aTa Flag specifying the multiplication ordering. See the +description below. +@param delta Optional delta matrix subtracted from src before the +multiplication. When the matrix is empty ( delta=noArray() ), it is +assumed to be zero, that is, nothing is subtracted. If it has the same +size as src , it is simply subtracted. Otherwise, it is "repeated" (see +repeat ) to cover the full src and then subtracted. Type of the delta +matrix, when it is not empty, must be the same as the type of created +output matrix. See the dtype parameter description below. +@param scale Optional scale factor for the matrix product. +@param dtype Optional type of the output matrix. When it is negative, +the output matrix will have the same type as src . Otherwise, it will be +type=CV_MAT_DEPTH(dtype) that should be either CV_32F or CV_64F . +@sa calcCovarMatrix, gemm, repeat, reduce +*/ +CV_EXPORTS_W void mulTransposed( InputArray src, OutputArray dst, bool aTa, + InputArray delta = noArray(), + double scale = 1, int dtype = -1 ); + +/** @brief Transposes a matrix. + +The function cv::transpose transposes the matrix src : +\f[\texttt{dst} (i,j) = \texttt{src} (j,i)\f] +@note No complex conjugation is done in case of a complex matrix. It it +should be done separately if needed. +@param src input array. +@param dst output array of the same type as src. +*/ +CV_EXPORTS_W void transpose(InputArray src, OutputArray dst); + +/** @brief Performs the matrix transformation of every array element. + +The function cv::transform performs the matrix transformation of every +element of the array src and stores the results in dst : +\f[\texttt{dst} (I) = \texttt{m} \cdot \texttt{src} (I)\f] +(when m.cols=src.channels() ), or +\f[\texttt{dst} (I) = \texttt{m} \cdot [ \texttt{src} (I); 1]\f] +(when m.cols=src.channels()+1 ) + +Every element of the N -channel array src is interpreted as N -element +vector that is transformed using the M x N or M x (N+1) matrix m to +M-element vector - the corresponding element of the output array dst . + +The function may be used for geometrical transformation of +N -dimensional points, arbitrary linear color space transformation (such +as various kinds of RGB to YUV transforms), shuffling the image +channels, and so forth. +@param src input array that must have as many channels (1 to 4) as +m.cols or m.cols-1. +@param dst output array of the same size and depth as src; it has as +many channels as m.rows. +@param m transformation 2x2 or 2x3 floating-point matrix. +@sa perspectiveTransform, getAffineTransform, estimateAffine2D, warpAffine, warpPerspective +*/ +CV_EXPORTS_W void transform(InputArray src, OutputArray dst, InputArray m ); + +/** @brief Performs the perspective matrix transformation of vectors. + +The function cv::perspectiveTransform transforms every element of src by +treating it as a 2D or 3D vector, in the following way: +\f[(x, y, z) \rightarrow (x'/w, y'/w, z'/w)\f] +where +\f[(x', y', z', w') = \texttt{mat} \cdot \begin{bmatrix} x & y & z & 1 \end{bmatrix}\f] +and +\f[w = \fork{w'}{if \(w' \ne 0\)}{\infty}{otherwise}\f] + +Here a 3D vector transformation is shown. In case of a 2D vector +transformation, the z component is omitted. + +@note The function transforms a sparse set of 2D or 3D vectors. If you +want to transform an image using perspective transformation, use +warpPerspective . If you have an inverse problem, that is, you want to +compute the most probable perspective transformation out of several +pairs of corresponding points, you can use getPerspectiveTransform or +findHomography . +@param src input two-channel or three-channel floating-point array; each +element is a 2D/3D vector to be transformed. +@param dst output array of the same size and type as src. +@param m 3x3 or 4x4 floating-point transformation matrix. +@sa transform, warpPerspective, getPerspectiveTransform, findHomography +*/ +CV_EXPORTS_W void perspectiveTransform(InputArray src, OutputArray dst, InputArray m ); + +/** @brief Copies the lower or the upper half of a square matrix to another half. + +The function cv::completeSymm copies the lower half of a square matrix to +its another half. The matrix diagonal remains unchanged: +* \f$\texttt{mtx}_{ij}=\texttt{mtx}_{ji}\f$ for \f$i > j\f$ if + lowerToUpper=false +* \f$\texttt{mtx}_{ij}=\texttt{mtx}_{ji}\f$ for \f$i < j\f$ if + lowerToUpper=true +@param mtx input-output floating-point square matrix. +@param lowerToUpper operation flag; if true, the lower half is copied to +the upper half. Otherwise, the upper half is copied to the lower half. +@sa flip, transpose +*/ +CV_EXPORTS_W void completeSymm(InputOutputArray mtx, bool lowerToUpper = false); + +/** @brief Initializes a scaled identity matrix. + +The function cv::setIdentity initializes a scaled identity matrix: +\f[\texttt{mtx} (i,j)= \fork{\texttt{value}}{ if \(i=j\)}{0}{otherwise}\f] + +The function can also be emulated using the matrix initializers and the +matrix expressions: +@code + Mat A = Mat::eye(4, 3, CV_32F)*5; + // A will be set to [[5, 0, 0], [0, 5, 0], [0, 0, 5], [0, 0, 0]] +@endcode +@param mtx matrix to initialize (not necessarily square). +@param s value to assign to diagonal elements. +@sa Mat::zeros, Mat::ones, Mat::setTo, Mat::operator= +*/ +CV_EXPORTS_W void setIdentity(InputOutputArray mtx, const Scalar& s = Scalar(1)); + +/** @brief Returns the determinant of a square floating-point matrix. + +The function cv::determinant calculates and returns the determinant of the +specified matrix. For small matrices ( mtx.cols=mtx.rows\<=3 ), the +direct method is used. For larger matrices, the function uses LU +factorization with partial pivoting. + +For symmetric positively-determined matrices, it is also possible to use +eigen decomposition to calculate the determinant. +@param mtx input matrix that must have CV_32FC1 or CV_64FC1 type and +square size. +@sa trace, invert, solve, eigen, @ref MatrixExpressions +*/ +CV_EXPORTS_W double determinant(InputArray mtx); + +/** @brief Returns the trace of a matrix. + +The function cv::trace returns the sum of the diagonal elements of the +matrix mtx . +\f[\mathrm{tr} ( \texttt{mtx} ) = \sum _i \texttt{mtx} (i,i)\f] +@param mtx input matrix. +*/ +CV_EXPORTS_W Scalar trace(InputArray mtx); + +/** @brief Finds the inverse or pseudo-inverse of a matrix. + +The function cv::invert inverts the matrix src and stores the result in dst +. When the matrix src is singular or non-square, the function calculates +the pseudo-inverse matrix (the dst matrix) so that norm(src\*dst - I) is +minimal, where I is an identity matrix. + +In case of the DECOMP_LU method, the function returns non-zero value if +the inverse has been successfully calculated and 0 if src is singular. + +In case of the DECOMP_SVD method, the function returns the inverse +condition number of src (the ratio of the smallest singular value to the +largest singular value) and 0 if src is singular. The SVD method +calculates a pseudo-inverse matrix if src is singular. + +Similarly to DECOMP_LU, the method DECOMP_CHOLESKY works only with +non-singular square matrices that should also be symmetrical and +positively defined. In this case, the function stores the inverted +matrix in dst and returns non-zero. Otherwise, it returns 0. + +@param src input floating-point M x N matrix. +@param dst output matrix of N x M size and the same type as src. +@param flags inversion method (cv::DecompTypes) +@sa solve, SVD +*/ +CV_EXPORTS_W double invert(InputArray src, OutputArray dst, int flags = DECOMP_LU); + +/** @brief Solves one or more linear systems or least-squares problems. + +The function cv::solve solves a linear system or least-squares problem (the +latter is possible with SVD or QR methods, or by specifying the flag +DECOMP_NORMAL ): +\f[\texttt{dst} = \arg \min _X \| \texttt{src1} \cdot \texttt{X} - \texttt{src2} \|\f] + +If DECOMP_LU or DECOMP_CHOLESKY method is used, the function returns 1 +if src1 (or \f$\texttt{src1}^T\texttt{src1}\f$ ) is non-singular. Otherwise, +it returns 0. In the latter case, dst is not valid. Other methods find a +pseudo-solution in case of a singular left-hand side part. + +@note If you want to find a unity-norm solution of an under-defined +singular system \f$\texttt{src1}\cdot\texttt{dst}=0\f$ , the function solve +will not do the work. Use SVD::solveZ instead. + +@param src1 input matrix on the left-hand side of the system. +@param src2 input matrix on the right-hand side of the system. +@param dst output solution. +@param flags solution (matrix inversion) method (cv::DecompTypes) +@sa invert, SVD, eigen +*/ +CV_EXPORTS_W bool solve(InputArray src1, InputArray src2, + OutputArray dst, int flags = DECOMP_LU); + +/** @brief Sorts each row or each column of a matrix. + +The function cv::sort sorts each matrix row or each matrix column in +ascending or descending order. So you should pass two operation flags to +get desired behaviour. If you want to sort matrix rows or columns +lexicographically, you can use STL std::sort generic function with the +proper comparison predicate. + +@param src input single-channel array. +@param dst output array of the same size and type as src. +@param flags operation flags, a combination of cv::SortFlags +@sa sortIdx, randShuffle +*/ +CV_EXPORTS_W void sort(InputArray src, OutputArray dst, int flags); + +/** @brief Sorts each row or each column of a matrix. + +The function cv::sortIdx sorts each matrix row or each matrix column in the +ascending or descending order. So you should pass two operation flags to +get desired behaviour. Instead of reordering the elements themselves, it +stores the indices of sorted elements in the output array. For example: +@code + Mat A = Mat::eye(3,3,CV_32F), B; + sortIdx(A, B, SORT_EVERY_ROW + SORT_ASCENDING); + // B will probably contain + // (because of equal elements in A some permutations are possible): + // [[1, 2, 0], [0, 2, 1], [0, 1, 2]] +@endcode +@param src input single-channel array. +@param dst output integer array of the same size as src. +@param flags operation flags that could be a combination of cv::SortFlags +@sa sort, randShuffle +*/ +CV_EXPORTS_W void sortIdx(InputArray src, OutputArray dst, int flags); + +/** @brief Finds the real roots of a cubic equation. + +The function solveCubic finds the real roots of a cubic equation: +- if coeffs is a 4-element vector: +\f[\texttt{coeffs} [0] x^3 + \texttt{coeffs} [1] x^2 + \texttt{coeffs} [2] x + \texttt{coeffs} [3] = 0\f] +- if coeffs is a 3-element vector: +\f[x^3 + \texttt{coeffs} [0] x^2 + \texttt{coeffs} [1] x + \texttt{coeffs} [2] = 0\f] + +The roots are stored in the roots array. +@param coeffs equation coefficients, an array of 3 or 4 elements. +@param roots output array of real roots that has 1 or 3 elements. +*/ +CV_EXPORTS_W int solveCubic(InputArray coeffs, OutputArray roots); + +/** @brief Finds the real or complex roots of a polynomial equation. + +The function cv::solvePoly finds real and complex roots of a polynomial equation: +\f[\texttt{coeffs} [n] x^{n} + \texttt{coeffs} [n-1] x^{n-1} + ... + \texttt{coeffs} [1] x + \texttt{coeffs} [0] = 0\f] +@param coeffs array of polynomial coefficients. +@param roots output (complex) array of roots. +@param maxIters maximum number of iterations the algorithm does. +*/ +CV_EXPORTS_W double solvePoly(InputArray coeffs, OutputArray roots, int maxIters = 300); + +/** @brief Calculates eigenvalues and eigenvectors of a symmetric matrix. + +The function cv::eigen calculates just eigenvalues, or eigenvalues and eigenvectors of the symmetric +matrix src: +@code + src*eigenvectors.row(i).t() = eigenvalues.at<srcType>(i)*eigenvectors.row(i).t() +@endcode +@note in the new and the old interfaces different ordering of eigenvalues and eigenvectors +parameters is used. +@param src input matrix that must have CV_32FC1 or CV_64FC1 type, square size and be symmetrical +(src ^T^ == src). +@param eigenvalues output vector of eigenvalues of the same type as src; the eigenvalues are stored +in the descending order. +@param eigenvectors output matrix of eigenvectors; it has the same size and type as src; the +eigenvectors are stored as subsequent matrix rows, in the same order as the corresponding +eigenvalues. +@sa completeSymm , PCA +*/ +CV_EXPORTS_W bool eigen(InputArray src, OutputArray eigenvalues, + OutputArray eigenvectors = noArray()); + +/** @brief Calculates the covariance matrix of a set of vectors. + +The function cv::calcCovarMatrix calculates the covariance matrix and, optionally, the mean vector of +the set of input vectors. +@param samples samples stored as separate matrices +@param nsamples number of samples +@param covar output covariance matrix of the type ctype and square size. +@param mean input or output (depending on the flags) array as the average value of the input vectors. +@param flags operation flags as a combination of cv::CovarFlags +@param ctype type of the matrixl; it equals 'CV_64F' by default. +@sa PCA, mulTransposed, Mahalanobis +@todo InputArrayOfArrays +*/ +CV_EXPORTS void calcCovarMatrix( const Mat* samples, int nsamples, Mat& covar, Mat& mean, + int flags, int ctype = CV_64F); + +/** @overload +@note use cv::COVAR_ROWS or cv::COVAR_COLS flag +@param samples samples stored as rows/columns of a single matrix. +@param covar output covariance matrix of the type ctype and square size. +@param mean input or output (depending on the flags) array as the average value of the input vectors. +@param flags operation flags as a combination of cv::CovarFlags +@param ctype type of the matrixl; it equals 'CV_64F' by default. +*/ +CV_EXPORTS_W void calcCovarMatrix( InputArray samples, OutputArray covar, + InputOutputArray mean, int flags, int ctype = CV_64F); + +/** wrap PCA::operator() */ +CV_EXPORTS_W void PCACompute(InputArray data, InputOutputArray mean, + OutputArray eigenvectors, int maxComponents = 0); + +/** wrap PCA::operator() */ +CV_EXPORTS_W void PCACompute(InputArray data, InputOutputArray mean, + OutputArray eigenvectors, double retainedVariance); + +/** wrap PCA::project */ +CV_EXPORTS_W void PCAProject(InputArray data, InputArray mean, + InputArray eigenvectors, OutputArray result); + +/** wrap PCA::backProject */ +CV_EXPORTS_W void PCABackProject(InputArray data, InputArray mean, + InputArray eigenvectors, OutputArray result); + +/** wrap SVD::compute */ +CV_EXPORTS_W void SVDecomp( InputArray src, OutputArray w, OutputArray u, OutputArray vt, int flags = 0 ); + +/** wrap SVD::backSubst */ +CV_EXPORTS_W void SVBackSubst( InputArray w, InputArray u, InputArray vt, + InputArray rhs, OutputArray dst ); + +/** @brief Calculates the Mahalanobis distance between two vectors. + +The function cv::Mahalanobis calculates and returns the weighted distance between two vectors: +\f[d( \texttt{vec1} , \texttt{vec2} )= \sqrt{\sum_{i,j}{\texttt{icovar(i,j)}\cdot(\texttt{vec1}(I)-\texttt{vec2}(I))\cdot(\texttt{vec1(j)}-\texttt{vec2(j)})} }\f] +The covariance matrix may be calculated using the cv::calcCovarMatrix function and then inverted using +the invert function (preferably using the cv::DECOMP_SVD method, as the most accurate). +@param v1 first 1D input vector. +@param v2 second 1D input vector. +@param icovar inverse covariance matrix. +*/ +CV_EXPORTS_W double Mahalanobis(InputArray v1, InputArray v2, InputArray icovar); + +/** @brief Performs a forward or inverse Discrete Fourier transform of a 1D or 2D floating-point array. + +The function cv::dft performs one of the following: +- Forward the Fourier transform of a 1D vector of N elements: + \f[Y = F^{(N)} \cdot X,\f] + where \f$F^{(N)}_{jk}=\exp(-2\pi i j k/N)\f$ and \f$i=\sqrt{-1}\f$ +- Inverse the Fourier transform of a 1D vector of N elements: + \f[\begin{array}{l} X'= \left (F^{(N)} \right )^{-1} \cdot Y = \left (F^{(N)} \right )^* \cdot y \\ X = (1/N) \cdot X, \end{array}\f] + where \f$F^*=\left(\textrm{Re}(F^{(N)})-\textrm{Im}(F^{(N)})\right)^T\f$ +- Forward the 2D Fourier transform of a M x N matrix: + \f[Y = F^{(M)} \cdot X \cdot F^{(N)}\f] +- Inverse the 2D Fourier transform of a M x N matrix: + \f[\begin{array}{l} X'= \left (F^{(M)} \right )^* \cdot Y \cdot \left (F^{(N)} \right )^* \\ X = \frac{1}{M \cdot N} \cdot X' \end{array}\f] + +In case of real (single-channel) data, the output spectrum of the forward Fourier transform or input +spectrum of the inverse Fourier transform can be represented in a packed format called *CCS* +(complex-conjugate-symmetrical). It was borrowed from IPL (Intel\* Image Processing Library). Here +is how 2D *CCS* spectrum looks: +\f[\begin{bmatrix} Re Y_{0,0} & Re Y_{0,1} & Im Y_{0,1} & Re Y_{0,2} & Im Y_{0,2} & \cdots & Re Y_{0,N/2-1} & Im Y_{0,N/2-1} & Re Y_{0,N/2} \\ Re Y_{1,0} & Re Y_{1,1} & Im Y_{1,1} & Re Y_{1,2} & Im Y_{1,2} & \cdots & Re Y_{1,N/2-1} & Im Y_{1,N/2-1} & Re Y_{1,N/2} \\ Im Y_{1,0} & Re Y_{2,1} & Im Y_{2,1} & Re Y_{2,2} & Im Y_{2,2} & \cdots & Re Y_{2,N/2-1} & Im Y_{2,N/2-1} & Im Y_{1,N/2} \\ \hdotsfor{9} \\ Re Y_{M/2-1,0} & Re Y_{M-3,1} & Im Y_{M-3,1} & \hdotsfor{3} & Re Y_{M-3,N/2-1} & Im Y_{M-3,N/2-1}& Re Y_{M/2-1,N/2} \\ Im Y_{M/2-1,0} & Re Y_{M-2,1} & Im Y_{M-2,1} & \hdotsfor{3} & Re Y_{M-2,N/2-1} & Im Y_{M-2,N/2-1}& Im Y_{M/2-1,N/2} \\ Re Y_{M/2,0} & Re Y_{M-1,1} & Im Y_{M-1,1} & \hdotsfor{3} & Re Y_{M-1,N/2-1} & Im Y_{M-1,N/2-1}& Re Y_{M/2,N/2} \end{bmatrix}\f] + +In case of 1D transform of a real vector, the output looks like the first row of the matrix above. + +So, the function chooses an operation mode depending on the flags and size of the input array: +- If DFT_ROWS is set or the input array has a single row or single column, the function + performs a 1D forward or inverse transform of each row of a matrix when DFT_ROWS is set. + Otherwise, it performs a 2D transform. +- If the input array is real and DFT_INVERSE is not set, the function performs a forward 1D or + 2D transform: + - When DFT_COMPLEX_OUTPUT is set, the output is a complex matrix of the same size as + input. + - When DFT_COMPLEX_OUTPUT is not set, the output is a real matrix of the same size as + input. In case of 2D transform, it uses the packed format as shown above. In case of a + single 1D transform, it looks like the first row of the matrix above. In case of + multiple 1D transforms (when using the DFT_ROWS flag), each row of the output matrix + looks like the first row of the matrix above. +- If the input array is complex and either DFT_INVERSE or DFT_REAL_OUTPUT are not set, the + output is a complex array of the same size as input. The function performs a forward or + inverse 1D or 2D transform of the whole input array or each row of the input array + independently, depending on the flags DFT_INVERSE and DFT_ROWS. +- When DFT_INVERSE is set and the input array is real, or it is complex but DFT_REAL_OUTPUT + is set, the output is a real array of the same size as input. The function performs a 1D or 2D + inverse transformation of the whole input array or each individual row, depending on the flags + DFT_INVERSE and DFT_ROWS. + +If DFT_SCALE is set, the scaling is done after the transformation. + +Unlike dct , the function supports arrays of arbitrary size. But only those arrays are processed +efficiently, whose sizes can be factorized in a product of small prime numbers (2, 3, and 5 in the +current implementation). Such an efficient DFT size can be calculated using the getOptimalDFTSize +method. + +The sample below illustrates how to calculate a DFT-based convolution of two 2D real arrays: +@code + void convolveDFT(InputArray A, InputArray B, OutputArray C) + { + // reallocate the output array if needed + C.create(abs(A.rows - B.rows)+1, abs(A.cols - B.cols)+1, A.type()); + Size dftSize; + // calculate the size of DFT transform + dftSize.width = getOptimalDFTSize(A.cols + B.cols - 1); + dftSize.height = getOptimalDFTSize(A.rows + B.rows - 1); + + // allocate temporary buffers and initialize them with 0's + Mat tempA(dftSize, A.type(), Scalar::all(0)); + Mat tempB(dftSize, B.type(), Scalar::all(0)); + + // copy A and B to the top-left corners of tempA and tempB, respectively + Mat roiA(tempA, Rect(0,0,A.cols,A.rows)); + A.copyTo(roiA); + Mat roiB(tempB, Rect(0,0,B.cols,B.rows)); + B.copyTo(roiB); + + // now transform the padded A & B in-place; + // use "nonzeroRows" hint for faster processing + dft(tempA, tempA, 0, A.rows); + dft(tempB, tempB, 0, B.rows); + + // multiply the spectrums; + // the function handles packed spectrum representations well + mulSpectrums(tempA, tempB, tempA); + + // transform the product back from the frequency domain. + // Even though all the result rows will be non-zero, + // you need only the first C.rows of them, and thus you + // pass nonzeroRows == C.rows + dft(tempA, tempA, DFT_INVERSE + DFT_SCALE, C.rows); + + // now copy the result back to C. + tempA(Rect(0, 0, C.cols, C.rows)).copyTo(C); + + // all the temporary buffers will be deallocated automatically + } +@endcode +To optimize this sample, consider the following approaches: +- Since nonzeroRows != 0 is passed to the forward transform calls and since A and B are copied to + the top-left corners of tempA and tempB, respectively, it is not necessary to clear the whole + tempA and tempB. It is only necessary to clear the tempA.cols - A.cols ( tempB.cols - B.cols) + rightmost columns of the matrices. +- This DFT-based convolution does not have to be applied to the whole big arrays, especially if B + is significantly smaller than A or vice versa. Instead, you can calculate convolution by parts. + To do this, you need to split the output array C into multiple tiles. For each tile, estimate + which parts of A and B are required to calculate convolution in this tile. If the tiles in C are + too small, the speed will decrease a lot because of repeated work. In the ultimate case, when + each tile in C is a single pixel, the algorithm becomes equivalent to the naive convolution + algorithm. If the tiles are too big, the temporary arrays tempA and tempB become too big and + there is also a slowdown because of bad cache locality. So, there is an optimal tile size + somewhere in the middle. +- If different tiles in C can be calculated in parallel and, thus, the convolution is done by + parts, the loop can be threaded. + +All of the above improvements have been implemented in matchTemplate and filter2D . Therefore, by +using them, you can get the performance even better than with the above theoretically optimal +implementation. Though, those two functions actually calculate cross-correlation, not convolution, +so you need to "flip" the second convolution operand B vertically and horizontally using flip . +@note +- An example using the discrete fourier transform can be found at + opencv_source_code/samples/cpp/dft.cpp +- (Python) An example using the dft functionality to perform Wiener deconvolution can be found + at opencv_source/samples/python/deconvolution.py +- (Python) An example rearranging the quadrants of a Fourier image can be found at + opencv_source/samples/python/dft.py +@param src input array that could be real or complex. +@param dst output array whose size and type depends on the flags . +@param flags transformation flags, representing a combination of the cv::DftFlags +@param nonzeroRows when the parameter is not zero, the function assumes that only the first +nonzeroRows rows of the input array (DFT_INVERSE is not set) or only the first nonzeroRows of the +output array (DFT_INVERSE is set) contain non-zeros, thus, the function can handle the rest of the +rows more efficiently and save some time; this technique is very useful for calculating array +cross-correlation or convolution using DFT. +@sa dct , getOptimalDFTSize , mulSpectrums, filter2D , matchTemplate , flip , cartToPolar , +magnitude , phase +*/ +CV_EXPORTS_W void dft(InputArray src, OutputArray dst, int flags = 0, int nonzeroRows = 0); + +/** @brief Calculates the inverse Discrete Fourier Transform of a 1D or 2D array. + +idft(src, dst, flags) is equivalent to dft(src, dst, flags | DFT_INVERSE) . +@note None of dft and idft scales the result by default. So, you should pass DFT_SCALE to one of +dft or idft explicitly to make these transforms mutually inverse. +@sa dft, dct, idct, mulSpectrums, getOptimalDFTSize +@param src input floating-point real or complex array. +@param dst output array whose size and type depend on the flags. +@param flags operation flags (see dft and cv::DftFlags). +@param nonzeroRows number of dst rows to process; the rest of the rows have undefined content (see +the convolution sample in dft description. +*/ +CV_EXPORTS_W void idft(InputArray src, OutputArray dst, int flags = 0, int nonzeroRows = 0); + +/** @brief Performs a forward or inverse discrete Cosine transform of 1D or 2D array. + +The function cv::dct performs a forward or inverse discrete Cosine transform (DCT) of a 1D or 2D +floating-point array: +- Forward Cosine transform of a 1D vector of N elements: + \f[Y = C^{(N)} \cdot X\f] + where + \f[C^{(N)}_{jk}= \sqrt{\alpha_j/N} \cos \left ( \frac{\pi(2k+1)j}{2N} \right )\f] + and + \f$\alpha_0=1\f$, \f$\alpha_j=2\f$ for *j \> 0*. +- Inverse Cosine transform of a 1D vector of N elements: + \f[X = \left (C^{(N)} \right )^{-1} \cdot Y = \left (C^{(N)} \right )^T \cdot Y\f] + (since \f$C^{(N)}\f$ is an orthogonal matrix, \f$C^{(N)} \cdot \left(C^{(N)}\right)^T = I\f$ ) +- Forward 2D Cosine transform of M x N matrix: + \f[Y = C^{(N)} \cdot X \cdot \left (C^{(N)} \right )^T\f] +- Inverse 2D Cosine transform of M x N matrix: + \f[X = \left (C^{(N)} \right )^T \cdot X \cdot C^{(N)}\f] + +The function chooses the mode of operation by looking at the flags and size of the input array: +- If (flags & DCT_INVERSE) == 0 , the function does a forward 1D or 2D transform. Otherwise, it + is an inverse 1D or 2D transform. +- If (flags & DCT_ROWS) != 0 , the function performs a 1D transform of each row. +- If the array is a single column or a single row, the function performs a 1D transform. +- If none of the above is true, the function performs a 2D transform. + +@note Currently dct supports even-size arrays (2, 4, 6 ...). For data analysis and approximation, you +can pad the array when necessary. +Also, the function performance depends very much, and not monotonically, on the array size (see +getOptimalDFTSize ). In the current implementation DCT of a vector of size N is calculated via DFT +of a vector of size N/2 . Thus, the optimal DCT size N1 \>= N can be calculated as: +@code + size_t getOptimalDCTSize(size_t N) { return 2*getOptimalDFTSize((N+1)/2); } + N1 = getOptimalDCTSize(N); +@endcode +@param src input floating-point array. +@param dst output array of the same size and type as src . +@param flags transformation flags as a combination of cv::DftFlags (DCT_*) +@sa dft , getOptimalDFTSize , idct +*/ +CV_EXPORTS_W void dct(InputArray src, OutputArray dst, int flags = 0); + +/** @brief Calculates the inverse Discrete Cosine Transform of a 1D or 2D array. + +idct(src, dst, flags) is equivalent to dct(src, dst, flags | DCT_INVERSE). +@param src input floating-point single-channel array. +@param dst output array of the same size and type as src. +@param flags operation flags. +@sa dct, dft, idft, getOptimalDFTSize +*/ +CV_EXPORTS_W void idct(InputArray src, OutputArray dst, int flags = 0); + +/** @brief Performs the per-element multiplication of two Fourier spectrums. + +The function cv::mulSpectrums performs the per-element multiplication of the two CCS-packed or complex +matrices that are results of a real or complex Fourier transform. + +The function, together with dft and idft , may be used to calculate convolution (pass conjB=false ) +or correlation (pass conjB=true ) of two arrays rapidly. When the arrays are complex, they are +simply multiplied (per element) with an optional conjugation of the second-array elements. When the +arrays are real, they are assumed to be CCS-packed (see dft for details). +@param a first input array. +@param b second input array of the same size and type as src1 . +@param c output array of the same size and type as src1 . +@param flags operation flags; currently, the only supported flag is cv::DFT_ROWS, which indicates that +each row of src1 and src2 is an independent 1D Fourier spectrum. If you do not want to use this flag, then simply add a `0` as value. +@param conjB optional flag that conjugates the second input array before the multiplication (true) +or not (false). +*/ +CV_EXPORTS_W void mulSpectrums(InputArray a, InputArray b, OutputArray c, + int flags, bool conjB = false); + +/** @brief Returns the optimal DFT size for a given vector size. + +DFT performance is not a monotonic function of a vector size. Therefore, when you calculate +convolution of two arrays or perform the spectral analysis of an array, it usually makes sense to +pad the input data with zeros to get a bit larger array that can be transformed much faster than the +original one. Arrays whose size is a power-of-two (2, 4, 8, 16, 32, ...) are the fastest to process. +Though, the arrays whose size is a product of 2's, 3's, and 5's (for example, 300 = 5\*5\*3\*2\*2) +are also processed quite efficiently. + +The function cv::getOptimalDFTSize returns the minimum number N that is greater than or equal to vecsize +so that the DFT of a vector of size N can be processed efficiently. In the current implementation N += 2 ^p^ \* 3 ^q^ \* 5 ^r^ for some integer p, q, r. + +The function returns a negative number if vecsize is too large (very close to INT_MAX ). + +While the function cannot be used directly to estimate the optimal vector size for DCT transform +(since the current DCT implementation supports only even-size vectors), it can be easily processed +as getOptimalDFTSize((vecsize+1)/2)\*2. +@param vecsize vector size. +@sa dft , dct , idft , idct , mulSpectrums +*/ +CV_EXPORTS_W int getOptimalDFTSize(int vecsize); + +/** @brief Returns the default random number generator. + +The function cv::theRNG returns the default random number generator. For each thread, there is a +separate random number generator, so you can use the function safely in multi-thread environments. +If you just need to get a single random number using this generator or initialize an array, you can +use randu or randn instead. But if you are going to generate many random numbers inside a loop, it +is much faster to use this function to retrieve the generator and then use RNG::operator _Tp() . +@sa RNG, randu, randn +*/ +CV_EXPORTS RNG& theRNG(); + +/** @brief Sets state of default random number generator. + +The function cv::setRNGSeed sets state of default random number generator to custom value. +@param seed new state for default random number generator +@sa RNG, randu, randn +*/ +CV_EXPORTS_W void setRNGSeed(int seed); + +/** @brief Generates a single uniformly-distributed random number or an array of random numbers. + +Non-template variant of the function fills the matrix dst with uniformly-distributed +random numbers from the specified range: +\f[\texttt{low} _c \leq \texttt{dst} (I)_c < \texttt{high} _c\f] +@param dst output array of random numbers; the array must be pre-allocated. +@param low inclusive lower boundary of the generated random numbers. +@param high exclusive upper boundary of the generated random numbers. +@sa RNG, randn, theRNG +*/ +CV_EXPORTS_W void randu(InputOutputArray dst, InputArray low, InputArray high); + +/** @brief Fills the array with normally distributed random numbers. + +The function cv::randn fills the matrix dst with normally distributed random numbers with the specified +mean vector and the standard deviation matrix. The generated random numbers are clipped to fit the +value range of the output array data type. +@param dst output array of random numbers; the array must be pre-allocated and have 1 to 4 channels. +@param mean mean value (expectation) of the generated random numbers. +@param stddev standard deviation of the generated random numbers; it can be either a vector (in +which case a diagonal standard deviation matrix is assumed) or a square matrix. +@sa RNG, randu +*/ +CV_EXPORTS_W void randn(InputOutputArray dst, InputArray mean, InputArray stddev); + +/** @brief Shuffles the array elements randomly. + +The function cv::randShuffle shuffles the specified 1D array by randomly choosing pairs of elements and +swapping them. The number of such swap operations will be dst.rows\*dst.cols\*iterFactor . +@param dst input/output numerical 1D array. +@param iterFactor scale factor that determines the number of random swap operations (see the details +below). +@param rng optional random number generator used for shuffling; if it is zero, theRNG () is used +instead. +@sa RNG, sort +*/ +CV_EXPORTS_W void randShuffle(InputOutputArray dst, double iterFactor = 1., RNG* rng = 0); + +/** @brief Principal Component Analysis + +The class is used to calculate a special basis for a set of vectors. The +basis will consist of eigenvectors of the covariance matrix calculated +from the input set of vectors. The class %PCA can also transform +vectors to/from the new coordinate space defined by the basis. Usually, +in this new coordinate system, each vector from the original set (and +any linear combination of such vectors) can be quite accurately +approximated by taking its first few components, corresponding to the +eigenvectors of the largest eigenvalues of the covariance matrix. +Geometrically it means that you calculate a projection of the vector to +a subspace formed by a few eigenvectors corresponding to the dominant +eigenvalues of the covariance matrix. And usually such a projection is +very close to the original vector. So, you can represent the original +vector from a high-dimensional space with a much shorter vector +consisting of the projected vector's coordinates in the subspace. Such a +transformation is also known as Karhunen-Loeve Transform, or KLT. +See http://en.wikipedia.org/wiki/Principal_component_analysis + +The sample below is the function that takes two matrices. The first +function stores a set of vectors (a row per vector) that is used to +calculate PCA. The second function stores another "test" set of vectors +(a row per vector). First, these vectors are compressed with PCA, then +reconstructed back, and then the reconstruction error norm is computed +and printed for each vector. : + +@code{.cpp} +using namespace cv; + +PCA compressPCA(const Mat& pcaset, int maxComponents, + const Mat& testset, Mat& compressed) +{ + PCA pca(pcaset, // pass the data + Mat(), // we do not have a pre-computed mean vector, + // so let the PCA engine to compute it + PCA::DATA_AS_ROW, // indicate that the vectors + // are stored as matrix rows + // (use PCA::DATA_AS_COL if the vectors are + // the matrix columns) + maxComponents // specify, how many principal components to retain + ); + // if there is no test data, just return the computed basis, ready-to-use + if( !testset.data ) + return pca; + CV_Assert( testset.cols == pcaset.cols ); + + compressed.create(testset.rows, maxComponents, testset.type()); + + Mat reconstructed; + for( int i = 0; i < testset.rows; i++ ) + { + Mat vec = testset.row(i), coeffs = compressed.row(i), reconstructed; + // compress the vector, the result will be stored + // in the i-th row of the output matrix + pca.project(vec, coeffs); + // and then reconstruct it + pca.backProject(coeffs, reconstructed); + // and measure the error + printf("%d. diff = %g\n", i, norm(vec, reconstructed, NORM_L2)); + } + return pca; +} +@endcode +@sa calcCovarMatrix, mulTransposed, SVD, dft, dct +*/ +class CV_EXPORTS PCA +{ +public: + enum Flags { DATA_AS_ROW = 0, //!< indicates that the input samples are stored as matrix rows + DATA_AS_COL = 1, //!< indicates that the input samples are stored as matrix columns + USE_AVG = 2 //! + }; + + /** @brief default constructor + + The default constructor initializes an empty %PCA structure. The other + constructors initialize the structure and call PCA::operator()(). + */ + PCA(); + + /** @overload + @param data input samples stored as matrix rows or matrix columns. + @param mean optional mean value; if the matrix is empty (@c noArray()), + the mean is computed from the data. + @param flags operation flags; currently the parameter is only used to + specify the data layout (PCA::Flags) + @param maxComponents maximum number of components that %PCA should + retain; by default, all the components are retained. + */ + PCA(InputArray data, InputArray mean, int flags, int maxComponents = 0); + + /** @overload + @param data input samples stored as matrix rows or matrix columns. + @param mean optional mean value; if the matrix is empty (noArray()), + the mean is computed from the data. + @param flags operation flags; currently the parameter is only used to + specify the data layout (PCA::Flags) + @param retainedVariance Percentage of variance that PCA should retain. + Using this parameter will let the PCA decided how many components to + retain but it will always keep at least 2. + */ + PCA(InputArray data, InputArray mean, int flags, double retainedVariance); + + /** @brief performs %PCA + + The operator performs %PCA of the supplied dataset. It is safe to reuse + the same PCA structure for multiple datasets. That is, if the structure + has been previously used with another dataset, the existing internal + data is reclaimed and the new @ref eigenvalues, @ref eigenvectors and @ref + mean are allocated and computed. + + The computed @ref eigenvalues are sorted from the largest to the smallest and + the corresponding @ref eigenvectors are stored as eigenvectors rows. + + @param data input samples stored as the matrix rows or as the matrix + columns. + @param mean optional mean value; if the matrix is empty (noArray()), + the mean is computed from the data. + @param flags operation flags; currently the parameter is only used to + specify the data layout. (Flags) + @param maxComponents maximum number of components that PCA should + retain; by default, all the components are retained. + */ + PCA& operator()(InputArray data, InputArray mean, int flags, int maxComponents = 0); + + /** @overload + @param data input samples stored as the matrix rows or as the matrix + columns. + @param mean optional mean value; if the matrix is empty (noArray()), + the mean is computed from the data. + @param flags operation flags; currently the parameter is only used to + specify the data layout. (PCA::Flags) + @param retainedVariance Percentage of variance that %PCA should retain. + Using this parameter will let the %PCA decided how many components to + retain but it will always keep at least 2. + */ + PCA& operator()(InputArray data, InputArray mean, int flags, double retainedVariance); + + /** @brief Projects vector(s) to the principal component subspace. + + The methods project one or more vectors to the principal component + subspace, where each vector projection is represented by coefficients in + the principal component basis. The first form of the method returns the + matrix that the second form writes to the result. So the first form can + be used as a part of expression while the second form can be more + efficient in a processing loop. + @param vec input vector(s); must have the same dimensionality and the + same layout as the input data used at %PCA phase, that is, if + DATA_AS_ROW are specified, then `vec.cols==data.cols` + (vector dimensionality) and `vec.rows` is the number of vectors to + project, and the same is true for the PCA::DATA_AS_COL case. + */ + Mat project(InputArray vec) const; + + /** @overload + @param vec input vector(s); must have the same dimensionality and the + same layout as the input data used at PCA phase, that is, if + DATA_AS_ROW are specified, then `vec.cols==data.cols` + (vector dimensionality) and `vec.rows` is the number of vectors to + project, and the same is true for the PCA::DATA_AS_COL case. + @param result output vectors; in case of PCA::DATA_AS_COL, the + output matrix has as many columns as the number of input vectors, this + means that `result.cols==vec.cols` and the number of rows match the + number of principal components (for example, `maxComponents` parameter + passed to the constructor). + */ + void project(InputArray vec, OutputArray result) const; + + /** @brief Reconstructs vectors from their PC projections. + + The methods are inverse operations to PCA::project. They take PC + coordinates of projected vectors and reconstruct the original vectors. + Unless all the principal components have been retained, the + reconstructed vectors are different from the originals. But typically, + the difference is small if the number of components is large enough (but + still much smaller than the original vector dimensionality). As a + result, PCA is used. + @param vec coordinates of the vectors in the principal component + subspace, the layout and size are the same as of PCA::project output + vectors. + */ + Mat backProject(InputArray vec) const; + + /** @overload + @param vec coordinates of the vectors in the principal component + subspace, the layout and size are the same as of PCA::project output + vectors. + @param result reconstructed vectors; the layout and size are the same as + of PCA::project input vectors. + */ + void backProject(InputArray vec, OutputArray result) const; + + /** @brief write PCA objects + + Writes @ref eigenvalues @ref eigenvectors and @ref mean to specified FileStorage + */ + void write(FileStorage& fs) const; + + /** @brief load PCA objects + + Loads @ref eigenvalues @ref eigenvectors and @ref mean from specified FileNode + */ + void read(const FileNode& fn); + + Mat eigenvectors; //!< eigenvectors of the covariation matrix + Mat eigenvalues; //!< eigenvalues of the covariation matrix + Mat mean; //!< mean value subtracted before the projection and added after the back projection +}; + +/** @example pca.cpp + An example using %PCA for dimensionality reduction while maintaining an amount of variance + */ + +/** + @brief Linear Discriminant Analysis + @todo document this class + */ +class CV_EXPORTS LDA +{ +public: + /** @brief constructor + Initializes a LDA with num_components (default 0). + */ + explicit LDA(int num_components = 0); + + /** Initializes and performs a Discriminant Analysis with Fisher's + Optimization Criterion on given data in src and corresponding labels + in labels. If 0 (or less) number of components are given, they are + automatically determined for given data in computation. + */ + LDA(InputArrayOfArrays src, InputArray labels, int num_components = 0); + + /** Serializes this object to a given filename. + */ + void save(const String& filename) const; + + /** Deserializes this object from a given filename. + */ + void load(const String& filename); + + /** Serializes this object to a given cv::FileStorage. + */ + void save(FileStorage& fs) const; + + /** Deserializes this object from a given cv::FileStorage. + */ + void load(const FileStorage& node); + + /** destructor + */ + ~LDA(); + + /** Compute the discriminants for data in src (row aligned) and labels. + */ + void compute(InputArrayOfArrays src, InputArray labels); + + /** Projects samples into the LDA subspace. + src may be one or more row aligned samples. + */ + Mat project(InputArray src); + + /** Reconstructs projections from the LDA subspace. + src may be one or more row aligned projections. + */ + Mat reconstruct(InputArray src); + + /** Returns the eigenvectors of this LDA. + */ + Mat eigenvectors() const { return _eigenvectors; } + + /** Returns the eigenvalues of this LDA. + */ + Mat eigenvalues() const { return _eigenvalues; } + + static Mat subspaceProject(InputArray W, InputArray mean, InputArray src); + static Mat subspaceReconstruct(InputArray W, InputArray mean, InputArray src); + +protected: + bool _dataAsRow; // unused, but needed for 3.0 ABI compatibility. + int _num_components; + Mat _eigenvectors; + Mat _eigenvalues; + void lda(InputArrayOfArrays src, InputArray labels); +}; + +/** @brief Singular Value Decomposition + +Class for computing Singular Value Decomposition of a floating-point +matrix. The Singular Value Decomposition is used to solve least-square +problems, under-determined linear systems, invert matrices, compute +condition numbers, and so on. + +If you want to compute a condition number of a matrix or an absolute value of +its determinant, you do not need `u` and `vt`. You can pass +flags=SVD::NO_UV|... . Another flag SVD::FULL_UV indicates that full-size u +and vt must be computed, which is not necessary most of the time. + +@sa invert, solve, eigen, determinant +*/ +class CV_EXPORTS SVD +{ +public: + enum Flags { + /** allow the algorithm to modify the decomposed matrix; it can save space and speed up + processing. currently ignored. */ + MODIFY_A = 1, + /** indicates that only a vector of singular values `w` is to be processed, while u and vt + will be set to empty matrices */ + NO_UV = 2, + /** when the matrix is not square, by default the algorithm produces u and vt matrices of + sufficiently large size for the further A reconstruction; if, however, FULL_UV flag is + specified, u and vt will be full-size square orthogonal matrices.*/ + FULL_UV = 4 + }; + + /** @brief the default constructor + + initializes an empty SVD structure + */ + SVD(); + + /** @overload + initializes an empty SVD structure and then calls SVD::operator() + @param src decomposed matrix. + @param flags operation flags (SVD::Flags) + */ + SVD( InputArray src, int flags = 0 ); + + /** @brief the operator that performs SVD. The previously allocated u, w and vt are released. + + The operator performs the singular value decomposition of the supplied + matrix. The u,`vt` , and the vector of singular values w are stored in + the structure. The same SVD structure can be reused many times with + different matrices. Each time, if needed, the previous u,`vt` , and w + are reclaimed and the new matrices are created, which is all handled by + Mat::create. + @param src decomposed matrix. + @param flags operation flags (SVD::Flags) + */ + SVD& operator ()( InputArray src, int flags = 0 ); + + /** @brief decomposes matrix and stores the results to user-provided matrices + + The methods/functions perform SVD of matrix. Unlike SVD::SVD constructor + and SVD::operator(), they store the results to the user-provided + matrices: + + @code{.cpp} + Mat A, w, u, vt; + SVD::compute(A, w, u, vt); + @endcode + + @param src decomposed matrix + @param w calculated singular values + @param u calculated left singular vectors + @param vt transposed matrix of right singular values + @param flags operation flags - see SVD::SVD. + */ + static void compute( InputArray src, OutputArray w, + OutputArray u, OutputArray vt, int flags = 0 ); + + /** @overload + computes singular values of a matrix + @param src decomposed matrix + @param w calculated singular values + @param flags operation flags - see SVD::Flags. + */ + static void compute( InputArray src, OutputArray w, int flags = 0 ); + + /** @brief performs back substitution + */ + static void backSubst( InputArray w, InputArray u, + InputArray vt, InputArray rhs, + OutputArray dst ); + + /** @brief solves an under-determined singular linear system + + The method finds a unit-length solution x of a singular linear system + A\*x = 0. Depending on the rank of A, there can be no solutions, a + single solution or an infinite number of solutions. In general, the + algorithm solves the following problem: + \f[dst = \arg \min _{x: \| x \| =1} \| src \cdot x \|\f] + @param src left-hand-side matrix. + @param dst found solution. + */ + static void solveZ( InputArray src, OutputArray dst ); + + /** @brief performs a singular value back substitution. + + The method calculates a back substitution for the specified right-hand + side: + + \f[\texttt{x} = \texttt{vt} ^T \cdot diag( \texttt{w} )^{-1} \cdot \texttt{u} ^T \cdot \texttt{rhs} \sim \texttt{A} ^{-1} \cdot \texttt{rhs}\f] + + Using this technique you can either get a very accurate solution of the + convenient linear system, or the best (in the least-squares terms) + pseudo-solution of an overdetermined linear system. + + @param rhs right-hand side of a linear system (u\*w\*v')\*dst = rhs to + be solved, where A has been previously decomposed. + + @param dst found solution of the system. + + @note Explicit SVD with the further back substitution only makes sense + if you need to solve many linear systems with the same left-hand side + (for example, src ). If all you need is to solve a single system + (possibly with multiple rhs immediately available), simply call solve + add pass DECOMP_SVD there. It does absolutely the same thing. + */ + void backSubst( InputArray rhs, OutputArray dst ) const; + + /** @todo document */ + template<typename _Tp, int m, int n, int nm> static + void compute( const Matx<_Tp, m, n>& a, Matx<_Tp, nm, 1>& w, Matx<_Tp, m, nm>& u, Matx<_Tp, n, nm>& vt ); + + /** @todo document */ + template<typename _Tp, int m, int n, int nm> static + void compute( const Matx<_Tp, m, n>& a, Matx<_Tp, nm, 1>& w ); + + /** @todo document */ + template<typename _Tp, int m, int n, int nm, int nb> static + void backSubst( const Matx<_Tp, nm, 1>& w, const Matx<_Tp, m, nm>& u, const Matx<_Tp, n, nm>& vt, const Matx<_Tp, m, nb>& rhs, Matx<_Tp, n, nb>& dst ); + + Mat u, w, vt; +}; + +/** @brief Random Number Generator + +Random number generator. It encapsulates the state (currently, a 64-bit +integer) and has methods to return scalar random values and to fill +arrays with random values. Currently it supports uniform and Gaussian +(normal) distributions. The generator uses Multiply-With-Carry +algorithm, introduced by G. Marsaglia ( +<http://en.wikipedia.org/wiki/Multiply-with-carry> ). +Gaussian-distribution random numbers are generated using the Ziggurat +algorithm ( <http://en.wikipedia.org/wiki/Ziggurat_algorithm> ), +introduced by G. Marsaglia and W. W. Tsang. +*/ +class CV_EXPORTS RNG +{ +public: + enum { UNIFORM = 0, + NORMAL = 1 + }; + + /** @brief constructor + + These are the RNG constructors. The first form sets the state to some + pre-defined value, equal to 2\*\*32-1 in the current implementation. The + second form sets the state to the specified value. If you passed state=0 + , the constructor uses the above default value instead to avoid the + singular random number sequence, consisting of all zeros. + */ + RNG(); + /** @overload + @param state 64-bit value used to initialize the RNG. + */ + RNG(uint64 state); + /**The method updates the state using the MWC algorithm and returns the + next 32-bit random number.*/ + unsigned next(); + + /**Each of the methods updates the state using the MWC algorithm and + returns the next random number of the specified type. In case of integer + types, the returned number is from the available value range for the + specified type. In case of floating-point types, the returned value is + from [0,1) range. + */ + operator uchar(); + /** @overload */ + operator schar(); + /** @overload */ + operator ushort(); + /** @overload */ + operator short(); + /** @overload */ + operator unsigned(); + /** @overload */ + operator int(); + /** @overload */ + operator float(); + /** @overload */ + operator double(); + + /** @brief returns a random integer sampled uniformly from [0, N). + + The methods transform the state using the MWC algorithm and return the + next random number. The first form is equivalent to RNG::next . The + second form returns the random number modulo N , which means that the + result is in the range [0, N) . + */ + unsigned operator ()(); + /** @overload + @param N upper non-inclusive boundary of the returned random number. + */ + unsigned operator ()(unsigned N); + + /** @brief returns uniformly distributed integer random number from [a,b) range + + The methods transform the state using the MWC algorithm and return the + next uniformly-distributed random number of the specified type, deduced + from the input parameter type, from the range [a, b) . There is a nuance + illustrated by the following sample: + + @code{.cpp} + RNG rng; + + // always produces 0 + double a = rng.uniform(0, 1); + + // produces double from [0, 1) + double a1 = rng.uniform((double)0, (double)1); + + // produces float from [0, 1) + double b = rng.uniform(0.f, 1.f); + + // produces double from [0, 1) + double c = rng.uniform(0., 1.); + + // may cause compiler error because of ambiguity: + // RNG::uniform(0, (int)0.999999)? or RNG::uniform((double)0, 0.99999)? + double d = rng.uniform(0, 0.999999); + @endcode + + The compiler does not take into account the type of the variable to + which you assign the result of RNG::uniform . The only thing that + matters to the compiler is the type of a and b parameters. So, if you + want a floating-point random number, but the range boundaries are + integer numbers, either put dots in the end, if they are constants, or + use explicit type cast operators, as in the a1 initialization above. + @param a lower inclusive boundary of the returned random numbers. + @param b upper non-inclusive boundary of the returned random numbers. + */ + int uniform(int a, int b); + /** @overload */ + float uniform(float a, float b); + /** @overload */ + double uniform(double a, double b); + + /** @brief Fills arrays with random numbers. + + @param mat 2D or N-dimensional matrix; currently matrices with more than + 4 channels are not supported by the methods, use Mat::reshape as a + possible workaround. + @param distType distribution type, RNG::UNIFORM or RNG::NORMAL. + @param a first distribution parameter; in case of the uniform + distribution, this is an inclusive lower boundary, in case of the normal + distribution, this is a mean value. + @param b second distribution parameter; in case of the uniform + distribution, this is a non-inclusive upper boundary, in case of the + normal distribution, this is a standard deviation (diagonal of the + standard deviation matrix or the full standard deviation matrix). + @param saturateRange pre-saturation flag; for uniform distribution only; + if true, the method will first convert a and b to the acceptable value + range (according to the mat datatype) and then will generate uniformly + distributed random numbers within the range [saturate(a), saturate(b)), + if saturateRange=false, the method will generate uniformly distributed + random numbers in the original range [a, b) and then will saturate them, + it means, for example, that + <tt>theRNG().fill(mat_8u, RNG::UNIFORM, -DBL_MAX, DBL_MAX)</tt> will likely + produce array mostly filled with 0's and 255's, since the range (0, 255) + is significantly smaller than [-DBL_MAX, DBL_MAX). + + Each of the methods fills the matrix with the random values from the + specified distribution. As the new numbers are generated, the RNG state + is updated accordingly. In case of multiple-channel images, every + channel is filled independently, which means that RNG cannot generate + samples from the multi-dimensional Gaussian distribution with + non-diagonal covariance matrix directly. To do that, the method + generates samples from multi-dimensional standard Gaussian distribution + with zero mean and identity covariation matrix, and then transforms them + using transform to get samples from the specified Gaussian distribution. + */ + void fill( InputOutputArray mat, int distType, InputArray a, InputArray b, bool saturateRange = false ); + + /** @brief Returns the next random number sampled from the Gaussian distribution + @param sigma standard deviation of the distribution. + + The method transforms the state using the MWC algorithm and returns the + next random number from the Gaussian distribution N(0,sigma) . That is, + the mean value of the returned random numbers is zero and the standard + deviation is the specified sigma . + */ + double gaussian(double sigma); + + uint64 state; +}; + +/** @brief Mersenne Twister random number generator + +Inspired by http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/MT2002/CODES/mt19937ar.c +@todo document + */ +class CV_EXPORTS RNG_MT19937 +{ +public: + RNG_MT19937(); + RNG_MT19937(unsigned s); + void seed(unsigned s); + + unsigned next(); + + operator int(); + operator unsigned(); + operator float(); + operator double(); + + unsigned operator ()(unsigned N); + unsigned operator ()(); + + /** @brief returns uniformly distributed integer random number from [a,b) range + +*/ + int uniform(int a, int b); + /** @brief returns uniformly distributed floating-point random number from [a,b) range + +*/ + float uniform(float a, float b); + /** @brief returns uniformly distributed double-precision floating-point random number from [a,b) range + +*/ + double uniform(double a, double b); + +private: + enum PeriodParameters {N = 624, M = 397}; + unsigned state[N]; + int mti; +}; + +//! @} core_array + +//! @addtogroup core_cluster +//! @{ + +/** @example kmeans.cpp + An example on K-means clustering +*/ + +/** @brief Finds centers of clusters and groups input samples around the clusters. + +The function kmeans implements a k-means algorithm that finds the centers of cluster_count clusters +and groups the input samples around the clusters. As an output, \f$\texttt{labels}_i\f$ contains a +0-based cluster index for the sample stored in the \f$i^{th}\f$ row of the samples matrix. + +@note +- (Python) An example on K-means clustering can be found at + opencv_source_code/samples/python/kmeans.py +@param data Data for clustering. An array of N-Dimensional points with float coordinates is needed. +Examples of this array can be: +- Mat points(count, 2, CV_32F); +- Mat points(count, 1, CV_32FC2); +- Mat points(1, count, CV_32FC2); +- std::vector\<cv::Point2f\> points(sampleCount); +@param K Number of clusters to split the set by. +@param bestLabels Input/output integer array that stores the cluster indices for every sample. +@param criteria The algorithm termination criteria, that is, the maximum number of iterations and/or +the desired accuracy. The accuracy is specified as criteria.epsilon. As soon as each of the cluster +centers moves by less than criteria.epsilon on some iteration, the algorithm stops. +@param attempts Flag to specify the number of times the algorithm is executed using different +initial labellings. The algorithm returns the labels that yield the best compactness (see the last +function parameter). +@param flags Flag that can take values of cv::KmeansFlags +@param centers Output matrix of the cluster centers, one row per each cluster center. +@return The function returns the compactness measure that is computed as +\f[\sum _i \| \texttt{samples} _i - \texttt{centers} _{ \texttt{labels} _i} \| ^2\f] +after every attempt. The best (minimum) value is chosen and the corresponding labels and the +compactness value are returned by the function. Basically, you can use only the core of the +function, set the number of attempts to 1, initialize labels each time using a custom algorithm, +pass them with the ( flags = KMEANS_USE_INITIAL_LABELS ) flag, and then choose the best +(most-compact) clustering. +*/ +CV_EXPORTS_W double kmeans( InputArray data, int K, InputOutputArray bestLabels, + TermCriteria criteria, int attempts, + int flags, OutputArray centers = noArray() ); + +//! @} core_cluster + +//! @addtogroup core_basic +//! @{ + +/////////////////////////////// Formatted output of cv::Mat /////////////////////////// + +/** @todo document */ +class CV_EXPORTS Formatted +{ +public: + virtual const char* next() = 0; + virtual void reset() = 0; + virtual ~Formatted(); +}; + +/** @todo document */ +class CV_EXPORTS Formatter +{ +public: + enum { FMT_DEFAULT = 0, + FMT_MATLAB = 1, + FMT_CSV = 2, + FMT_PYTHON = 3, + FMT_NUMPY = 4, + FMT_C = 5 + }; + + virtual ~Formatter(); + + virtual Ptr<Formatted> format(const Mat& mtx) const = 0; + + virtual void set32fPrecision(int p = 8) = 0; + virtual void set64fPrecision(int p = 16) = 0; + virtual void setMultiline(bool ml = true) = 0; + + static Ptr<Formatter> get(int fmt = FMT_DEFAULT); + +}; + +static inline +String& operator << (String& out, Ptr<Formatted> fmtd) +{ + fmtd->reset(); + for(const char* str = fmtd->next(); str; str = fmtd->next()) + out += cv::String(str); + return out; +} + +static inline +String& operator << (String& out, const Mat& mtx) +{ + return out << Formatter::get()->format(mtx); +} + +//////////////////////////////////////// Algorithm //////////////////////////////////// + +class CV_EXPORTS Algorithm; + +template<typename _Tp> struct ParamType {}; + + +/** @brief This is a base class for all more or less complex algorithms in OpenCV + +especially for classes of algorithms, for which there can be multiple implementations. The examples +are stereo correspondence (for which there are algorithms like block matching, semi-global block +matching, graph-cut etc.), background subtraction (which can be done using mixture-of-gaussians +models, codebook-based algorithm etc.), optical flow (block matching, Lucas-Kanade, Horn-Schunck +etc.). + +Here is example of SIFT use in your application via Algorithm interface: +@code + #include "opencv2/opencv.hpp" + #include "opencv2/xfeatures2d.hpp" + using namespace cv::xfeatures2d; + + Ptr<Feature2D> sift = SIFT::create(); + FileStorage fs("sift_params.xml", FileStorage::READ); + if( fs.isOpened() ) // if we have file with parameters, read them + { + sift->read(fs["sift_params"]); + fs.release(); + } + else // else modify the parameters and store them; user can later edit the file to use different parameters + { + sift->setContrastThreshold(0.01f); // lower the contrast threshold, compared to the default value + { + WriteStructContext ws(fs, "sift_params", CV_NODE_MAP); + sift->write(fs); + } + } + Mat image = imread("myimage.png", 0), descriptors; + vector<KeyPoint> keypoints; + sift->detectAndCompute(image, noArray(), keypoints, descriptors); +@endcode + */ +class CV_EXPORTS_W Algorithm +{ +public: + Algorithm(); + virtual ~Algorithm(); + + /** @brief Clears the algorithm state + */ + CV_WRAP virtual void clear() {} + + /** @brief Stores algorithm parameters in a file storage + */ + virtual void write(FileStorage& fs) const { (void)fs; } + + /** @brief Reads algorithm parameters from a file storage + */ + virtual void read(const FileNode& fn) { (void)fn; } + + /** @brief Returns true if the Algorithm is empty (e.g. in the very beginning or after unsuccessful read + */ + virtual bool empty() const { return false; } + + /** @brief Reads algorithm from the file node + + This is static template method of Algorithm. It's usage is following (in the case of SVM): + @code + cv::FileStorage fsRead("example.xml", FileStorage::READ); + Ptr<SVM> svm = Algorithm::read<SVM>(fsRead.root()); + @endcode + In order to make this method work, the derived class must overwrite Algorithm::read(const + FileNode& fn) and also have static create() method without parameters + (or with all the optional parameters) + */ + template<typename _Tp> static Ptr<_Tp> read(const FileNode& fn) + { + Ptr<_Tp> obj = _Tp::create(); + obj->read(fn); + return !obj->empty() ? obj : Ptr<_Tp>(); + } + + /** @brief Loads algorithm from the file + + @param filename Name of the file to read. + @param objname The optional name of the node to read (if empty, the first top-level node will be used) + + This is static template method of Algorithm. It's usage is following (in the case of SVM): + @code + Ptr<SVM> svm = Algorithm::load<SVM>("my_svm_model.xml"); + @endcode + In order to make this method work, the derived class must overwrite Algorithm::read(const + FileNode& fn). + */ + template<typename _Tp> static Ptr<_Tp> load(const String& filename, const String& objname=String()) + { + FileStorage fs(filename, FileStorage::READ); + FileNode fn = objname.empty() ? fs.getFirstTopLevelNode() : fs[objname]; + if (fn.empty()) return Ptr<_Tp>(); + Ptr<_Tp> obj = _Tp::create(); + obj->read(fn); + return !obj->empty() ? obj : Ptr<_Tp>(); + } + + /** @brief Loads algorithm from a String + + @param strModel The string variable containing the model you want to load. + @param objname The optional name of the node to read (if empty, the first top-level node will be used) + + This is static template method of Algorithm. It's usage is following (in the case of SVM): + @code + Ptr<SVM> svm = Algorithm::loadFromString<SVM>(myStringModel); + @endcode + */ + template<typename _Tp> static Ptr<_Tp> loadFromString(const String& strModel, const String& objname=String()) + { + FileStorage fs(strModel, FileStorage::READ + FileStorage::MEMORY); + FileNode fn = objname.empty() ? fs.getFirstTopLevelNode() : fs[objname]; + Ptr<_Tp> obj = _Tp::create(); + obj->read(fn); + return !obj->empty() ? obj : Ptr<_Tp>(); + } + + /** Saves the algorithm to a file. + In order to make this method work, the derived class must implement Algorithm::write(FileStorage& fs). */ + CV_WRAP virtual void save(const String& filename) const; + + /** Returns the algorithm string identifier. + This string is used as top level xml/yml node tag when the object is saved to a file or string. */ + CV_WRAP virtual String getDefaultName() const; + +protected: + void writeFormat(FileStorage& fs) const; +}; + +struct Param { + enum { INT=0, BOOLEAN=1, REAL=2, STRING=3, MAT=4, MAT_VECTOR=5, ALGORITHM=6, FLOAT=7, + UNSIGNED_INT=8, UINT64=9, UCHAR=11 }; +}; + + + +template<> struct ParamType<bool> +{ + typedef bool const_param_type; + typedef bool member_type; + + enum { type = Param::BOOLEAN }; +}; + +template<> struct ParamType<int> +{ + typedef int const_param_type; + typedef int member_type; + + enum { type = Param::INT }; +}; + +template<> struct ParamType<double> +{ + typedef double const_param_type; + typedef double member_type; + + enum { type = Param::REAL }; +}; + +template<> struct ParamType<String> +{ + typedef const String& const_param_type; + typedef String member_type; + + enum { type = Param::STRING }; +}; + +template<> struct ParamType<Mat> +{ + typedef const Mat& const_param_type; + typedef Mat member_type; + + enum { type = Param::MAT }; +}; + +template<> struct ParamType<std::vector<Mat> > +{ + typedef const std::vector<Mat>& const_param_type; + typedef std::vector<Mat> member_type; + + enum { type = Param::MAT_VECTOR }; +}; + +template<> struct ParamType<Algorithm> +{ + typedef const Ptr<Algorithm>& const_param_type; + typedef Ptr<Algorithm> member_type; + + enum { type = Param::ALGORITHM }; +}; + +template<> struct ParamType<float> +{ + typedef float const_param_type; + typedef float member_type; + + enum { type = Param::FLOAT }; +}; + +template<> struct ParamType<unsigned> +{ + typedef unsigned const_param_type; + typedef unsigned member_type; + + enum { type = Param::UNSIGNED_INT }; +}; + +template<> struct ParamType<uint64> +{ + typedef uint64 const_param_type; + typedef uint64 member_type; + + enum { type = Param::UINT64 }; +}; + +template<> struct ParamType<uchar> +{ + typedef uchar const_param_type; + typedef uchar member_type; + + enum { type = Param::UCHAR }; +}; + +//! @} core_basic + +} //namespace cv + +#include "opencv2/core/operations.hpp" +#include "opencv2/core/cvstd.inl.hpp" +#include "opencv2/core/utility.hpp" +#include "opencv2/core/optim.hpp" +#include "opencv2/core/ovx.hpp" + +#endif /*OPENCV_CORE_HPP*/ |