Operations on arrays
[Core functionality]

Various border types, image boundaries are denoted with `|`.

See also:

borderInterpolate, copyMakeBorder

Enumerator:

BORDER_CONSTANT	`iiiiii|abcdefgh|iiiiiii` with some specified `i`
BORDER_REPLICATE	`aaaaaa|abcdefgh|hhhhhhh`
BORDER_REFLECT	`fedcba|abcdefgh|hgfedcb`
BORDER_WRAP	`cdefgh|abcdefgh|abcdefg`
BORDER_REFLECT_101	`gfedcb|abcdefgh|gfedcba`
BORDER_TRANSPARENT	`uvwxyz|absdefgh|ijklmno`
BORDER_REFLECT101	same as BORDER_REFLECT_101
BORDER_DEFAULT	same as BORDER_REFLECT_101
BORDER_ISOLATED	do not look outside of ROI

Definition at line 251 of file base.hpp.

comparison types

Enumerator:

CMP_EQ	src1 is equal to src2.
CMP_GT	src1 is greater than src2.
CMP_GE	src1 is greater than or equal to src2.
CMP_LT	src1 is less than src2.
CMP_LE	src1 is less than or equal to src2.
CMP_NE	src1 is unequal to src2.

Definition at line 198 of file base.hpp.

matrix decomposition types

Enumerator:

DECOMP_LU	Gaussian elimination with the optimal pivot element chosen.
DECOMP_SVD	singular value decomposition (SVD) method; the system can be over-defined and/or the matrix src1 can be singular
DECOMP_EIG	eigenvalue decomposition; the matrix src1 must be symmetrical
DECOMP_CHOLESKY	Cholesky factorization; the matrix src1 must be symmetrical and positively defined.
DECOMP_QR	QR factorization; the system can be over-defined and/or the matrix src1 can be singular.
DECOMP_NORMAL	while all the previous flags are mutually exclusive, this flag can be used together with any of the previous; it means that the normal equations are solved instead of the original system

Definition at line 131 of file base.hpp.

Enumerator:

DFT_INVERSE	performs an inverse 1D or 2D transform instead of the default forward transform.
DFT_SCALE	scales the result: divide it by the number of array elements. Normally, it is combined with DFT_INVERSE.
DFT_ROWS	performs a forward or inverse transform of every individual row of the input matrix; this flag enables you to transform multiple vectors simultaneously and can be used to decrease the overhead (which is sometimes several times larger than the processing itself) to perform 3D and higher-dimensional transformations and so forth.
DFT_COMPLEX_OUTPUT	performs a forward transformation of 1D or 2D real array; the result, though being a complex array, has complex-conjugate symmetry (*CCS*, see the function description below for details), and such an array can be packed into a real array of the same size as input, which is the fastest option and which is what the function does by default; however, you may wish to get a full complex array (for simpler spectrum analysis, and so on) - pass the flag to enable the function to produce a full-size complex output array.
DFT_REAL_OUTPUT	performs an inverse transformation of a 1D or 2D complex array; the result is normally a complex array of the same size, however, if the input array has conjugate-complex symmetry (for example, it is a result of forward transformation with DFT_COMPLEX_OUTPUT flag), the output is a real array; while the function itself does not check whether the input is symmetrical or not, you can pass the flag and then the function will assume the symmetry and produce the real output array (note that when the input is packed into a real array and inverse transformation is executed, the function treats the input as a packed complex-conjugate symmetrical array, and the output will also be a real array).
DCT_INVERSE	performs an inverse 1D or 2D transform instead of the default forward transform.
DCT_ROWS	performs a forward or inverse transform of every individual row of the input matrix. This flag enables you to transform multiple vectors simultaneously and can be used to decrease the overhead (which is sometimes several times larger than the processing itself) to perform 3D and higher-dimensional transforms and so forth.

Definition at line 212 of file base.hpp.

generalized matrix multiplication flags

Enumerator:

GEMM_1_T	transposes src1
GEMM_2_T	transposes src2
GEMM_3_T	transposes src3

Definition at line 207 of file base.hpp.

norm types

• For one array:

  

• Absolute norm for two arrays

  

• Relative norm for two arrays

  

As example for one array consider the function . The and norm for the sample value is calculated as follows

and for the calculation is

The following graphic shows all values for the three norm functions and . It is notable that the norm forms the upper and the norm forms the lower border for the example function . 

Enumerator:

NORM_RELATIVE	flag
NORM_MINMAX	flag

Definition at line 186 of file base.hpp.

Calculates the per-element absolute difference between two arrays or between an array and a scalar.

The function absdiff calculates: Absolute difference between two arrays when they have the same size and type:

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`:

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`:

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.

Parameters:

src1	first input array or a scalar.
src2	second input array or a scalar.
dst	output array that has the same size and type as input arrays.

See also:

cv::abs(const Mat&)

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:

  

• Sum of an array and a scalar when src2 is constructed from Scalar or has the same number of elements as `src1.channels()`:

  

• Sum of a scalar and an array when src1 is constructed from Scalar or has the same number of elements as `src2.channels()`:

  

  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:

 {.cpp}
    dst = src1 + src2;
    dst += src1; // equivalent to add(dst, src1, dst);

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.

Parameters:

src1	first input array or a scalar.
src2	second input array or a scalar.
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.
mask	optional operation mask - 8-bit single channel array, that specifies elements of the output array to be changed.
dtype	optional depth of the output array (see the discussion below).

See also:

subtract, addWeighted, scaleAdd, Mat::convertTo

Calculates the weighted sum of two arrays.

The function addWeighted calculates the weighted sum of two arrays as follows:

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:

 {.cpp}
    dst = src1*alpha + src2*beta + gamma;

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.

Parameters:

src1	first input array.
alpha	weight of the first array elements.
src2	second input array of the same size and channel number as src1.
beta	weight of the second array elements.
gamma	scalar added to each sum.
dst	output array that has the same size and number of channels as the input arrays.
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().

See also:

add, subtract, scaleAdd, Mat::convertTo

naive nearest neighbor finder

see http://en.wikipedia.org/wiki/Nearest_neighbor_search

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 calculates the per-element bit-wise logical conjunction for: Two arrays when src1 and src2 have the same size:

An array and a scalar when src2 is constructed from Scalar or has the same number of elements as `src1.channels()`:

A scalar and an array when src1 is constructed from Scalar or has the same number of elements as `src2.channels()`:

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.

Parameters:

src1	first input array or a scalar.
src2	second input array or a scalar.
dst	output array that has the same size and type as the input arrays.
mask	optional operation mask, 8-bit single channel array, that specifies elements of the output array to be changed.

Inverts every bit of an array.

The function calculates per-element bit-wise inversion of the input array:

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.

Parameters:

src	input array.
dst	output array that has the same size and type as the input array.
mask	optional operation mask, 8-bit single channel array, that specifies elements of the output array to be changed.

Calculates the per-element bit-wise disjunction of two arrays or an array and a scalar.

The function calculates the per-element bit-wise logical disjunction for: Two arrays when src1 and src2 have the same size:

An array and a scalar when src2 is constructed from Scalar or has the same number of elements as `src1.channels()`:

A scalar and an array when src1 is constructed from Scalar or has the same number of elements as `src2.channels()`:

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.

Parameters:

src1	first input array or a scalar.
src2	second input array or a scalar.
dst	output array that has the same size and type as the input arrays.
mask	optional operation mask, 8-bit single channel array, that specifies elements of the output array to be changed.

Calculates the per-element bit-wise "exclusive or" operation on two arrays or an array and a scalar.

The function calculates the per-element bit-wise logical "exclusive-or" operation for: Two arrays when src1 and src2 have the same size:

An array and a scalar when src2 is constructed from Scalar or has the same number of elements as `src1.channels()`:

A scalar and an array when src1 is constructed from Scalar or has the same number of elements as `src2.channels()`:

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.

Parameters:

src1	first input array or a scalar.
src2	second input array or a scalar.
dst	output array that has the same size and type as the input arrays.
mask	optional operation mask, 8-bit single channel array, that specifies elements of the output array to be changed.

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:

 {.cpp}
    float val = img.at<float>(borderInterpolate(100, img.rows, cv::BORDER_REFLECT_101),
                              borderInterpolate(-5, img.cols, cv::BORDER_WRAP));

Normally, the function is not called directly. It is used inside filtering functions and also in copyMakeBorder.

Parameters:

p	0-based coordinate of the extrapolated pixel along one of the axes, likely <0 or >= len
len	Length of the array along the corresponding axis.
borderType	Border type, one of the cv::BorderTypes, except for cv::BORDER_TRANSPARENT and cv::BORDER_ISOLATED . When borderType==cvBORDER_CONSTANT , the function always returns -1, regardless of p and len.

See also:

copyMakeBorder

Calculates the covariance matrix of a set of vectors.

The functions calcCovarMatrix calculate the covariance matrix and, optionally, the mean vector of the set of input vectors.

Parameters:

samples	samples stored as separate matrices
nsamples	number of samples
covar	output covariance matrix of the type ctype and square size.
mean	input or output (depending on the flags) array as the average value of the input vectors.
flags	operation flags as a combination of cv::CovarFlags
ctype	type of the matrixl; it equals 'CV_64F' by default.

See also:

PCA, mulTransposed, Mahalanobis

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Note:

use cv::COVAR_ROWS or cv::COVAR_COLS flag

Parameters:

samples	samples stored as rows/columns of a single matrix.
covar	output covariance matrix of the type ctype and square size.
mean	input or output (depending on the flags) array as the average value of the input vectors.
flags	operation flags as a combination of cv::CovarFlags
ctype	type of the matrixl; it equals 'CV_64F' by default.

Calculates the magnitude and angle of 2D vectors.

The function cartToPolar calculates either the magnitude, angle, or both for every 2D vector (x(I),y(I)):

The angles are calculated with accuracy about 0.3 degrees. For the point (0,0), the angle is set to 0.

Parameters:

x	array of x-coordinates; this must be a single-precision or double-precision floating-point array.
y	array of y-coordinates, that must have the same size and same type as x.
magnitude	output array of magnitudes of the same size and type as x.
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).
angleInDegrees	a flag, indicating whether the angles are measured in radians (which is by default), or in degrees.

See also:

Sobel, Scharr

Checks every element of an input array for invalid values.

The functions checkRange check that every array element is neither NaN nor infinite. When minVal > -DBL_MAX and maxVal < DBL_MAX, the functions also check 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 functions either return false (when quiet=true) or throw an exception.

Parameters:

a	input array.
quiet	a flag, indicating whether the functions quietly return false when the array elements are out of range or they throw an exception.
pos	optional output parameter, when not NULL, must be a pointer to array of src.dims elements.
minVal	inclusive lower boundary of valid values range.
maxVal	exclusive upper boundary of valid values range.

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:

Elements of src1 with a scalar src2 when src2 is constructed from Scalar or has a single element:

src1 with elements of src2 when src1 is constructed from Scalar or has a single element:

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:

 {.cpp}
    Mat dst1 = src1 >= src2;
    Mat dst2 = src1 < 8;
    ...

Parameters:

src1	first input array or a scalar; when it is an array, it must have a single channel.
src2	second input array or a scalar; when it is an array, it must have a single channel.
dst	output array of type ref CV_8U that has the same size and the same number of channels as the input arrays.
cmpop	a flag, that specifies correspondence between the arrays (cv::CmpTypes)

See also:

checkRange, min, max, threshold

Copies the lower or the upper half of a square matrix to another half.

The function completeSymm copies the lower half of a square matrix to its another half. The matrix diagonal remains unchanged: for if lowerToUpper=false for if lowerToUpper=true

Parameters:

mtx	input-output floating-point square matrix.
lowerToUpper	operation flag; if true, the lower half is copied to the upper half. Otherwise, the upper half is copied to the lower half.

See also:

flip, transpose

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:

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:

 {.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

Parameters:

src	input array.
dst	output array.
alpha	optional scale factor.
beta	optional delta added to the scaled values.

See also:

Mat::convertTo, cv::abs(const Mat&)

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:

 {.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 ...
    ...

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.

Parameters:

src	Source image.
dst	Destination image of the same type as src and the size Size(src.cols+left+right, src.rows+top+bottom) .
top
bottom
left
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.
borderType	Border type. See borderInterpolate for details.
value	Border value if borderType==BORDER_CONSTANT .

See also:

borderInterpolate

Counts non-zero array elements.

The function returns the number of non-zero elements in src :

Parameters:

src	single-channel array.

See also:

mean, meanStdDev, norm, minMaxLoc, calcCovarMatrix

Calculates the sum of array elements.

The functions sum calculate and return the sum of array elements, independently for each channel.

Parameters:

src	input array that must have from 1 to 4 channels.

See also:

countNonZero, mean, meanStdDev, norm, minMaxLoc, reduce

Performs a forward or inverse discrete Cosine transform of 1D or 2D array.

The function 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:

  

  where

  

  and , for *j > 0*.
• Inverse Cosine transform of a 1D vector of N elements:

  

  (since is an orthogonal matrix, )
• Forward 2D Cosine transform of M x N matrix:

  

• Inverse 2D Cosine transform of M x N matrix:

  

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:

    size_t getOptimalDCTSize(size_t N) { return 2*getOptimalDFTSize((N+1)/2); }
    N1 = getOptimalDCTSize(N);

Parameters:

src	input floating-point array.
dst	output array of the same size and type as src .
flags	transformation flags as a combination of cv::DftFlags (DCT_*)

See also:

dft , getOptimalDFTSize , idct

Returns the determinant of a square floating-point matrix.

The function 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.

Parameters:

mtx	input matrix that must have CV_32FC1 or CV_64FC1 type and square size.

See also:

trace, invert, solve, eigen, MatrixExpressions

Performs a forward or inverse Discrete Fourier transform of a 1D or 2D floating-point array.

The function performs one of the following:

• Forward the Fourier transform of a 1D vector of N elements:

  

  where and
• Inverse the Fourier transform of a 1D vector of N elements:

  

  where
• Forward the 2D Fourier transform of a M x N matrix:

  

• Inverse the 2D Fourier transform of a M x N matrix:

  

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:

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:

    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
    }

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

Parameters:

src	input array that could be real or complex.
dst	output array whose size and type depends on the flags .
flags	transformation flags, representing a combination of the cv::DftFlags
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.

See also:

dct , getOptimalDFTSize , mulSpectrums, filter2D , matchTemplate , flip , cartToPolar , magnitude , phase

Performs per-element division of two arrays or a scalar by an array.

The functions divide divide one array by another:

or a scalar by an array when there is no src1 :

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.

Parameters:

src1	first input array.
src2	second input array of the same size and type as src1.
scale	scalar factor.
dst	output array of the same size and type as src2.
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().

See also:

multiply, add, subtract

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Calculates eigenvalues and eigenvectors of a symmetric matrix.

The functions eigen calculate just eigenvalues, or eigenvalues and eigenvectors of the symmetric matrix src:

    src*eigenvectors.row(i).t() = eigenvalues.at<srcType>(i)*eigenvectors.row(i).t()

Note:

in the new and the old interfaces different ordering of eigenvalues and eigenvectors parameters is used.

Parameters:

src	input matrix that must have CV_32FC1 or CV_64FC1 type, square size and be symmetrical (src ^T^ == src).
eigenvalues	output vector of eigenvalues of the same type as src; the eigenvalues are stored in the descending order.
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.

See also:

completeSymm , PCA

Calculates the exponent of every array element.

The function exp calculates the exponent of every element of the input array:

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.

Parameters:

src	input array.
dst	output array of the same size and type as src.

See also:

log , cartToPolar , polarToCart , phase , pow , sqrt , magnitude

extracts a single channel from src (coi is 0-based index)

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:

 {.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);

or

 {.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];

Parameters:

src	single-channel array (type CV_8UC1)
idx	the output array, type of cv::Mat or std::vector<Point>, corresponding to non-zero indices in the input

Flips a 2D array around vertical, horizontal, or both axes.

The function flip flips the array in one of three different ways (row and column indices are 0-based):

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).

Parameters:

src	input array.
dst	output array of the same size and type as src.
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.

See also:

transpose , repeat , completeSymm

Performs generalized matrix multiplication.

The function 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

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:

 {.cpp}
    dst = alpha*src1.t()*src2 + beta*src3.t();

Parameters:

src1	first multiplied input matrix that could be real(CV_32FC1, CV_64FC1) or complex(CV_32FC2, CV_64FC2).
src2	second multiplied input matrix of the same type as src1.
alpha	weight of the matrix product.
src3	third optional delta matrix added to the matrix product; it should have the same type as src1 and src2.
beta	weight of src3.
dst	output matrix; it has the proper size and the same type as input matrices.
flags	operation flags (cv::GemmFlags)

See also:

mulTransposed , transform

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 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.

Parameters:

vecsize

vector size.

See also:

dft , dct , idft , idct , mulSpectrums

Applies horizontal concatenation to given matrices.

The function horizontally concatenates two or more cv::Mat matrices (with the same number of rows).

 {.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]

Parameters:

src	input array or vector of matrices. all of the matrices must have the same number of rows and the same depth.
nsrc	number of matrices in src.
dst	output array. It has the same number of rows and depth as the src, and the sum of cols of the src.

See also:

cv::vconcat(const Mat*, size_t, OutputArray),

cv::vconcat(InputArrayOfArrays, OutputArray) and

cv::vconcat(InputArray, InputArray, OutputArray)

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

 {.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]

Parameters:

src1	first input array to be considered for horizontal concatenation.
src2	second input array to be considered for horizontal concatenation.
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.

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

 {.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]

Parameters:

src	input array or vector of matrices. all of the matrices must have the same number of rows and the same depth.
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.

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).

Parameters:

src	input floating-point single-channel array.
dst	output array of the same size and type as src.
flags	operation flags.

See also:

dct, dft, idft, getOptimalDFTSize

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.

See also:

dft, dct, idct, mulSpectrums, getOptimalDFTSize

Parameters:

src	input floating-point real or complex array.
dst	output array whose size and type depend on the flags.
flags	operation flags (see dft and cv::DftFlags).
nonzeroRows	number of dst rows to process; the rest of the rows have undefined content (see the convolution sample in dft description.

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:

  

• For two-channel arrays:

  

• 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.

Parameters:

src	first input array.
lowerb	inclusive lower boundary array or a scalar.
upperb	inclusive upper boundary array or a scalar.
dst	output array of the same size as src and CV_8U type.

inserts a single channel to dst (coi is 0-based index)

Finds the inverse or pseudo-inverse of a matrix.

The function 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.

Parameters:

src	input floating-point M x N matrix.
dst	output matrix of N x M size and the same type as src.
flags	inversion method (cv::DecompTypes)

See also:

solve, SVD

Calculates the natural logarithm of every array element.

The function log calculates the natural logarithm of the absolute value of every element of the input array:

where C is a large negative number (about -700 in the current implementation). The maximum relative error is about 7e-6 for single-precision input and less than 1e-10 for double-precision input. Special values (NaN, Inf) are not handled.

Parameters:

src	input array.
dst	output array of the same size and type as src .

See also:

exp, cartToPolar, polarToCart, phase, pow, sqrt, magnitude

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:

where

Parameters:

src	input array of 8-bit elements.
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.
dst	output array of the same size and number of channels as src, and the same depth as lut.

See also:

convertScaleAbs, Mat::convertTo

Calculates the magnitude of 2D vectors.

The function magnitude calculates the magnitude of 2D vectors formed from the corresponding elements of x and y arrays:

Parameters:

x	floating-point array of x-coordinates of the vectors.
y	floating-point array of y-coordinates of the vectors; it must have the same size as x.
magnitude	output array of the same size and type as x.

See also:

cartToPolar, polarToCart, phase, sqrt

Calculates the Mahalanobis distance between two vectors.

The function Mahalanobis calculates and returns the weighted distance between two vectors:

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).

Parameters:

v1	first 1D input vector.
v2	second 1D input vector.
icovar	inverse covariance matrix.

Calculates per-element maximum of two arrays or an array and a scalar.

The functions max calculate the per-element maximum of two arrays:

or array and a scalar:

Parameters:

src1	first input array.
src2	second input array of the same size and type as src1 .
dst	output array of the same size and type as src1.

See also:

min, compare, inRange, minMaxLoc, MatrixExpressions

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.needed to avoid conflicts with const _Tp& std::min(const _Tp&, const _Tp&, _Compare)

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.needed to avoid conflicts with const _Tp& std::min(const _Tp&, const _Tp&, _Compare)

Calculates an average (mean) of array elements.

The function mean calculates the mean value M of array elements, independently for each channel, and return it:

When all the mask elements are 0's, the functions return Scalar::all(0)

Parameters:

src	input array that should have from 1 to 4 channels so that the result can be stored in Scalar_ .
mask	optional operation mask.

See also:

countNonZero, meanStdDev, norm, minMaxLoc

Calculates a mean and standard deviation of array elements.

The function meanStdDev calculates the mean and the standard deviation M of array elements independently for each channel and returns it via the output parameters:

When all the mask elements are 0's, the functions return mean=stddev=Scalarall(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 .

Parameters:

src	input array that should have from 1 to 4 channels so that the results can be stored in Scalar_ 's.
mean	output parameter: calculated mean value.
stddev	output parameter: calculateded standard deviation.
mask	optional operation mask.

See also:

countNonZero, mean, norm, minMaxLoc, calcCovarMatrix

Creates one multi-channel array out of several single-channel ones.

The function 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.

Parameters:

mv	input array of matrices to be merged; all the matrices in mv must have the same size and the same depth.
count	number of input matrices when mv is a plain C array; it must be greater than zero.
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.

See also:

mixChannels, split, Mat::reshape

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Parameters:

mv	input vector of matrices to be merged; all the matrices in mv must have the same size and the same depth.
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.

Calculates per-element minimum of two arrays or an array and a scalar.

The functions min calculate the per-element minimum of two arrays:

or array and a scalar:

Parameters:

src1	first input array.
src2	second input array of the same size and type as src1.
dst	output array of the same size and type as src1.

See also:

max, compare, inRange, minMaxLoc

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.needed to avoid conflicts with const _Tp& std::min(const _Tp&, const _Tp&, _Compare)

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.needed to avoid conflicts with const _Tp& std::min(const _Tp&, const _Tp&, _Compare)

Finds the global minimum and maximum in an array.

The function 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)).

Parameters:

src	input single-channel array.
minVal	pointer to the returned minimum value; NULL is used if not required.
maxVal	pointer to the returned maximum value; NULL is used if not required.
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.
maxIdx	pointer to the returned maximum location (in nD case). NULL is used if not required.
mask	specified array region

Finds the global minimum and maximum in an array.

The functions minMaxLoc find 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 functions 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 .

Parameters:

src	input single-channel array.
minVal	pointer to the returned minimum value; NULL is used if not required.
maxVal	pointer to the returned maximum value; NULL is used if not required.
minLoc	pointer to the returned minimum location (in 2D case); NULL is used if not required.
maxLoc	pointer to the returned maximum location (in 2D case); NULL is used if not required.
mask	optional mask used to select a sub-array.

See also:

max, min, compare, inRange, extractImageCOI, mixChannels, split, Mat::reshape

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Parameters:

a	input single-channel array.
minVal	pointer to the returned minimum value; NULL is used if not required.
maxVal	pointer to the returned maximum value; NULL is used if not required.
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.
maxIdx	pointer to the returned maximum location (in nD case). NULL is used if not required.

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 and cv::merge 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:

 {.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 );

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.

Parameters:

src	input array or vector of matrices; all of the matrices must have the same size and the same depth.
nsrcs	number of matrices in `src`.
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]`.
ndsts	number of matrices in `dst`.
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 .
npairs	number of index pairs in `fromTo`.

See also:

cv::split, cv::merge, cv::cvtColor

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Parameters:

src	input array or vector of matrices; all of the matrices must have the same size and the same depth.
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].
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 .
npairs	number of index pairs in fromTo.

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Parameters:

src	input array or vector of matrices; all of the matrices must have the same size and the same depth.
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].
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 .

Performs the per-element multiplication of two Fourier spectrums.

The function 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).

Parameters:

a	first input array.
b	second input array of the same size and type as src1 .
c	output array of the same size and type as src1 .
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.
conjB	optional flag that conjugates the second input array before the multiplication (true) or not (false).

Calculates the per-element scaled product of two arrays.

The function multiply calculates the per-element product of two arrays:

There is also a 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.

Parameters:

src1	first input array.
src2	second input array of the same size and the same type as src1.
dst	output array of the same size and type as src1.
scale	optional scale factor.
dtype	optional depth of the output array

See also:

add, subtract, divide, scaleAdd, addWeighted, accumulate, accumulateProduct, accumulateSquare, Mat::convertTo

Calculates the product of a matrix and its transposition.

The function mulTransposed calculates the product of src and its transposition:

if aTa=true , and

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'

Parameters:

src	input single-channel matrix. Note that unlike gemm, the function can multiply not only floating-point matrices.
dst	output square matrix.
aTa	Flag specifying the multiplication ordering. See the description below.
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.
scale	Optional scale factor for the matrix product.
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 .

See also:

calcCovarMatrix, gemm, repeat, reduce

Calculates an absolute array norm, an absolute difference norm, or a relative difference norm.

The functions norm calculate an absolute norm of src1 (when there is no src2 ):

or an absolute or relative difference norm if src2 is there:

or

The functions norm return 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.

Parameters:

src1	first input array.
normType	type of the norm (see cv::NormTypes).
mask	optional operation mask; it must have the same size as src1 and CV_8UC1 type.

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Parameters:

src1	first input array.
src2	second input array of the same size and the same type as src1.
normType	type of the norm (cv::NormTypes).
mask	optional operation mask; it must have the same size as src1 and CV_8UC1 type.

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Parameters:

src	first input array.
normType	type of the norm (see cv::NormTypes).

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Parameters:

src	input array.
dst	output array of the same size as src .
alpha	norm value to normalize to or the lower range boundary in case of the range normalization.
normType	normalization type (see cv::NormTypes).

Normalizes the norm or value range of an array.

The functions normalize scale and shift the input array elements so that

(where p=Inf, 1 or 2) when normType=NORM_INF, NORM_L1, or NORM_L2, respectively; or so that

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:

 {.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);

Parameters:

src	input array.
dst	output array of the same size as src .
alpha	norm value to normalize to or the lower range boundary in case of the range normalization.
beta	upper range boundary in case of the range normalization; it is not used for the norm normalization.
norm_type	normalization type (see cv::NormTypes).
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).
mask	optional operation mask.

See also:

norm, Mat::convertTo, SparseMat::convertTo

converts NaN's to the given number

wrap PCA::backProject

wrap PCA::operator()

wrap PCA::operator()

wrap PCA::project

Performs the perspective matrix transformation of vectors.

The function perspectiveTransform transforms every element of src by treating it as a 2D or 3D vector, in the following way:

where

and

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 .

Parameters:

src	input two-channel or three-channel floating-point array; each element is a 2D/3D vector to be transformed.
dst	output array of the same size and type as src.
m	3x3 or 4x4 floating-point transformation matrix.

See also:

transform, warpPerspective, getPerspectiveTransform, findHomography

Calculates the rotation angle of 2D vectors.

The function phase calculates the rotation angle of each 2D vector that is formed from the corresponding elements of x and y :

The angle estimation accuracy is about 0.3 degrees. When x(I)=y(I)=0 , the corresponding angle(I) is set to 0.

Parameters:

x	input floating-point array of x-coordinates of 2D vectors.
y	input array of y-coordinates of 2D vectors; it must have the same size and the same type as x.
angle	output array of vector angles; it has the same size and same type as x .
angleInDegrees	when true, the function calculates the angle in degrees, otherwise, they are measured in radians.

Calculates x and y coordinates of 2D vectors from their magnitude and angle.

The function polarToCart calculates the Cartesian coordinates of each 2D vector represented by the corresponding elements of magnitude and angle:

The relative accuracy of the estimated coordinates is about 1e-6.

Parameters:

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.
angle	input floating-point array of angles of 2D vectors.
x	output array of x-coordinates of 2D vectors; it has the same size and type as angle.
y	output array of y-coordinates of 2D vectors; it has the same size and type as angle.
angleInDegrees	when true, the input angles are measured in degrees, otherwise, they are measured in radians.

See also:

cartToPolar, magnitude, phase, exp, log, pow, sqrt

Raises every array element to a power.

The function pow raises every element of the input array to power :

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:

 {.cpp}
    Mat mask = src < 0;
    pow(src, 1./5, dst);
    subtract(Scalar::all(0), dst, dst, mask);

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.

Parameters:

src	input array.
power	exponent of power.
dst	output array of the same size and type as src.

See also:

sqrt, exp, log, cartToPolar, polarToCart

computes PSNR image/video quality metric

see http://en.wikipedia.org/wiki/Peak_signal-to-noise_ratio for details

Fills the array with normally distributed random numbers.

The function 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.

Parameters:

dst	output array of random numbers; the array must be pre-allocated and have 1 to 4 channels.
mean	mean value (expectation) of the generated random numbers.
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.

See also:

RNG, randu

Shuffles the array elements randomly.

The function 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 .

Parameters:

dst	input/output numerical 1D array.
iterFactor	scale factor that determines the number of random swap operations (see the details below).
rng	optional random number generator used for shuffling; if it is zero, theRNG () is used instead.

See also:

RNG, sort

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:

Parameters:

dst	output array of random numbers; the array must be pre-allocated.
low	inclusive lower boundary of the generated random numbers.
high	exclusive upper boundary of the generated random numbers.

See also:

RNG, randn, theRNG

Reduces a matrix to a vector.

The function 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_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.

Parameters:

src	input 2D matrix.
dst	output vector. Its size and type is defined by dim and dtype parameters.
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.
rtype	reduction operation that could be one of cv::ReduceTypes
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()).

See also:

repeat

Fills the output array with repeated copies of the input array.

The functions repeat duplicate the input array one or more times along each of the two axes:

The second variant of the function is more convenient to use with MatrixExpressions.

Parameters:

src	input array to replicate.
dst	output array of the same type as src.
ny	Flag to specify how many times the src is repeated along the vertical axis.
nx	Flag to specify how many times the src is repeated along the horizontal axis.

See also:

reduce

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Parameters:

src	input array to replicate.
ny	Flag to specify how many times the src is repeated along the vertical axis.
nx	Flag to specify how many times the src is repeated along the horizontal axis.

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:

The function can also be emulated with a matrix expression, for example:

 {.cpp}
    Mat A(3, 3, CV_64F);
    ...
    A.row(0) = A.row(1)*2 + A.row(2);

Parameters:

src1	first input array.
alpha	scale factor for the first array.
src2	second input array of the same size and type as src1.
dst	output array of the same size and type as src1.

See also:

add, addWeighted, subtract, Mat::dot, Mat::convertTo

Initializes a scaled identity matrix.

The function setIdentity initializes a scaled identity matrix:

The function can also be emulated using the matrix initializers and the matrix expressions:

    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]]

Parameters:

mtx	matrix to initialize (not necessarily square).
s	value to assign to diagonal elements.

See also:

Mat::zeros, Mat::ones, Mat::setTo, Mat::operator=

Solves one or more linear systems or least-squares problems.

The function 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 ):

If DECOMP_LU or DECOMP_CHOLESKY method is used, the function returns 1 if src1 (or ) 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 , the function solve will not do the work. Use SVD::solveZ instead.

Parameters:

src1	input matrix on the left-hand side of the system.
src2	input matrix on the right-hand side of the system.
dst	output solution.
flags	solution (matrix inversion) method (cv::DecompTypes)

See also:

invert, SVD, eigen

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:

  

• if coeffs is a 3-element vector:

  

The roots are stored in the roots array.

Parameters:

coeffs	equation coefficients, an array of 3 or 4 elements.
roots	output array of real roots that has 1 or 3 elements.

Finds the real or complex roots of a polynomial equation.

The function solvePoly finds real and complex roots of a polynomial equation:

Parameters:

coeffs	array of polynomial coefficients.
roots	output (complex) array of roots.
maxIters	maximum number of iterations the algorithm does.

Sorts each row or each column of a matrix.

The function 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.

Parameters:

src	input single-channel array.
dst	output array of the same size and type as src.
flags	operation flags, a combination of cv::SortFlags

See also:

sortIdx, randShuffle

Sorts each row or each column of a matrix.

The function 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:

    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]]

Parameters:

src	input single-channel array.
dst	output integer array of the same size as src.
flags	operation flags that could be a combination of cv::SortFlags

See also:

sort, randShuffle

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Parameters:

m	input multi-channel array.
mv	output vector of arrays; the arrays themselves are reallocated, if needed.

Divides a multi-channel array into several single-channel arrays.

The functions split split a multi-channel array into separate single-channel arrays:

If you need to extract a single channel or do some other sophisticated channel permutation, use mixChannels .

Parameters:

src	input multi-channel array.
mvbegin	output array; the number of arrays must match src.channels(); the arrays themselves are reallocated, if needed.

See also:

merge, mixChannels, cvtColor

Calculates a square root of array elements.

The functions sqrt calculate 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 .

Parameters:

src	input floating-point array.
dst	output array of the same size and type as src.

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:

  

• Difference between an array and a scalar, when src2 is constructed from Scalar or has the same number of elements as `src1.channels()`:

  

• Difference between a scalar and an array, when src1 is constructed from Scalar or has the same number of elements as `src2.channels()`:

  

• The reverse difference between a scalar and an array in the case of `SubRS`:

  

  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:

 {.cpp}
    dst = src1 - src2;
    dst -= src1; // equivalent to subtract(dst, src1, dst);

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.

Parameters:

src1	first input array or a scalar.
src2	second input array or a scalar.
dst	output array of the same size and the same number of channels as the input array.
mask	optional operation mask; this is an 8-bit single channel array that specifies elements of the output array to be changed.
dtype	optional depth of the output array

See also:

add, addWeighted, scaleAdd, Mat::convertTo

wrap SVD::backSubst

wrap SVD::compute

Returns the default random number generator.

The function 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() .

See also:

RNG, randu, randn

Returns the trace of a matrix.

The function trace returns the sum of the diagonal elements of the matrix mtx .

Parameters:

mtx	input matrix.

Performs the matrix transformation of every array element.

The function transform performs the matrix transformation of every element of the array src and stores the results in dst :

(when m.cols=src.channels() ), or

(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.

Parameters:

src	input array that must have as many channels (1 to 4) as m.cols or m.cols-1.
dst	output array of the same size and depth as src; it has as many channels as m.rows.
m	transformation 2x2 or 2x3 floating-point matrix.

See also:

perspectiveTransform, getAffineTransform, estimateRigidTransform, warpAffine, warpPerspective

Transposes a matrix.

The function transpose transposes the matrix src :

Note:

No complex conjugation is done in case of a complex matrix. It it should be done separately if needed.

Parameters:

src	input array.
dst	output array of the same type as src.

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

 {.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]

Parameters:

src	input array or vector of matrices. all of the matrices must have the same number of cols and the same depth
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.

Applies vertical concatenation to given matrices.

The function vertically concatenates two or more cv::Mat matrices (with the same number of cols).

 {.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]

Parameters:

src	input array or vector of matrices. all of the matrices must have the same number of cols and the same depth.
nsrc	number of matrices in src.
dst	output array. It has the same number of cols and depth as the src, and the sum of rows of the src.

See also:

cv::hconcat(const Mat*, size_t, OutputArray),

cv::hconcat(InputArrayOfArrays, OutputArray) and

cv::hconcat(InputArray, InputArray, OutputArray)

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

 {.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]

Parameters:

src1	first input array to be considered for vertical concatenation.
src2	second input array to be considered for vertical concatenation.
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.