OpenCV  3.3.0-dev
Open Source Computer Vision
Classes | Enumerations | Functions
Operations on arrays

Classes

class  cv::LDA
 Linear Discriminant Analysis. More...
 
class  cv::PCA
 Principal Component Analysis. More...
 
class  cv::RNG
 Random Number Generator. More...
 
class  cv::RNG_MT19937
 Mersenne Twister random number generator. More...
 
class  cv::SVD
 Singular Value Decomposition. More...
 

Enumerations

enum  cv::BorderTypes {
  cv::BORDER_CONSTANT = 0,
  cv::BORDER_REPLICATE = 1,
  cv::BORDER_REFLECT = 2,
  cv::BORDER_WRAP = 3,
  cv::BORDER_REFLECT_101 = 4,
  cv::BORDER_TRANSPARENT = 5,
  cv::BORDER_REFLECT101 = BORDER_REFLECT_101,
  cv::BORDER_DEFAULT = BORDER_REFLECT_101,
  cv::BORDER_ISOLATED = 16
}
 
enum  cv::CmpTypes {
  cv::CMP_EQ = 0,
  cv::CMP_GT = 1,
  cv::CMP_GE = 2,
  cv::CMP_LT = 3,
  cv::CMP_LE = 4,
  cv::CMP_NE = 5
}
 comparison types More...
 
enum  cv::DecompTypes {
  cv::DECOMP_LU = 0,
  cv::DECOMP_SVD = 1,
  cv::DECOMP_EIG = 2,
  cv::DECOMP_CHOLESKY = 3,
  cv::DECOMP_QR = 4,
  cv::DECOMP_NORMAL = 16
}
 matrix decomposition types More...
 
enum  cv::DftFlags {
  cv::DFT_INVERSE = 1,
  cv::DFT_SCALE = 2,
  cv::DFT_ROWS = 4,
  cv::DFT_COMPLEX_OUTPUT = 16,
  cv::DFT_REAL_OUTPUT = 32,
  cv::DFT_COMPLEX_INPUT = 64,
  cv::DCT_INVERSE = DFT_INVERSE,
  cv::DCT_ROWS = DFT_ROWS
}
 
enum  cv::GemmFlags {
  cv::GEMM_1_T = 1,
  cv::GEMM_2_T = 2,
  cv::GEMM_3_T = 4
}
 generalized matrix multiplication flags More...
 
enum  cv::NormTypes {
  cv::NORM_INF = 1,
  cv::NORM_L1 = 2,
  cv::NORM_L2 = 4,
  cv::NORM_L2SQR = 5,
  cv::NORM_HAMMING = 6,
  cv::NORM_HAMMING2 = 7,
  cv::NORM_TYPE_MASK = 7,
  cv::NORM_RELATIVE = 8,
  cv::NORM_MINMAX = 32
}
 
enum  cv::RotateFlags {
  cv::ROTATE_90_CLOCKWISE = 0,
  cv::ROTATE_180 = 1,
  cv::ROTATE_90_COUNTERCLOCKWISE = 2
}
 

Functions

void cv::absdiff (InputArray src1, InputArray src2, OutputArray dst)
 Calculates the per-element absolute difference between two arrays or between an array and a scalar. More...
 
void cv::add (InputArray src1, InputArray src2, OutputArray dst, InputArray mask=noArray(), int dtype=-1)
 Calculates the per-element sum of two arrays or an array and a scalar. More...
 
void cv::addWeighted (InputArray src1, double alpha, InputArray src2, double beta, double gamma, OutputArray dst, int dtype=-1)
 Calculates the weighted sum of two arrays. More...
 
void cv::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)
 naive nearest neighbor finder More...
 
void cv::bitwise_and (InputArray src1, InputArray src2, OutputArray dst, InputArray mask=noArray())
 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. More...
 
void cv::bitwise_not (InputArray src, OutputArray dst, InputArray mask=noArray())
 Inverts every bit of an array. More...
 
void cv::bitwise_or (InputArray src1, InputArray src2, OutputArray dst, InputArray mask=noArray())
 Calculates the per-element bit-wise disjunction of two arrays or an array and a scalar. More...
 
void cv::bitwise_xor (InputArray src1, InputArray src2, OutputArray dst, InputArray mask=noArray())
 Calculates the per-element bit-wise "exclusive or" operation on two arrays or an array and a scalar. More...
 
int cv::borderInterpolate (int p, int len, int borderType)
 Computes the source location of an extrapolated pixel. More...
 
void cv::calcCovarMatrix (const Mat *samples, int nsamples, Mat &covar, Mat &mean, int flags, int ctype=CV_64F)
 Calculates the covariance matrix of a set of vectors. More...
 
void cv::calcCovarMatrix (InputArray samples, OutputArray covar, InputOutputArray mean, int flags, int ctype=CV_64F)
 
void cv::cartToPolar (InputArray x, InputArray y, OutputArray magnitude, OutputArray angle, bool angleInDegrees=false)
 Calculates the magnitude and angle of 2D vectors. More...
 
bool cv::checkRange (InputArray a, bool quiet=true, Point *pos=0, double minVal=-DBL_MAX, double maxVal=DBL_MAX)
 Checks every element of an input array for invalid values. More...
 
void cv::compare (InputArray src1, InputArray src2, OutputArray dst, int cmpop)
 Performs the per-element comparison of two arrays or an array and scalar value. More...
 
void cv::completeSymm (InputOutputArray mtx, bool lowerToUpper=false)
 Copies the lower or the upper half of a square matrix to another half. More...
 
void cv::convertFp16 (InputArray src, OutputArray dst)
 Converts an array to half precision floating number. More...
 
void cv::convertScaleAbs (InputArray src, OutputArray dst, double alpha=1, double beta=0)
 Scales, calculates absolute values, and converts the result to 8-bit. More...
 
void cv::copyMakeBorder (InputArray src, OutputArray dst, int top, int bottom, int left, int right, int borderType, const Scalar &value=Scalar())
 Forms a border around an image. More...
 
int cv::countNonZero (InputArray src)
 Counts non-zero array elements. More...
 
void cv::dct (InputArray src, OutputArray dst, int flags=0)
 Performs a forward or inverse discrete Cosine transform of 1D or 2D array. More...
 
double cv::determinant (InputArray mtx)
 Returns the determinant of a square floating-point matrix. More...
 
void cv::dft (InputArray src, OutputArray dst, int flags=0, int nonzeroRows=0)
 Performs a forward or inverse Discrete Fourier transform of a 1D or 2D floating-point array. More...
 
void cv::divide (InputArray src1, InputArray src2, OutputArray dst, double scale=1, int dtype=-1)
 Performs per-element division of two arrays or a scalar by an array. More...
 
void cv::divide (double scale, InputArray src2, OutputArray dst, int dtype=-1)
 
bool cv::eigen (InputArray src, OutputArray eigenvalues, OutputArray eigenvectors=noArray())
 Calculates eigenvalues and eigenvectors of a symmetric matrix. More...
 
void cv::exp (InputArray src, OutputArray dst)
 Calculates the exponent of every array element. More...
 
void cv::extractChannel (InputArray src, OutputArray dst, int coi)
 Extracts a single channel from src (coi is 0-based index) More...
 
void cv::findNonZero (InputArray src, OutputArray idx)
 Returns the list of locations of non-zero pixels. More...
 
void cv::flip (InputArray src, OutputArray dst, int flipCode)
 Flips a 2D array around vertical, horizontal, or both axes. More...
 
void cv::gemm (InputArray src1, InputArray src2, double alpha, InputArray src3, double beta, OutputArray dst, int flags=0)
 Performs generalized matrix multiplication. More...
 
int cv::getOptimalDFTSize (int vecsize)
 Returns the optimal DFT size for a given vector size. More...
 
void cv::hconcat (const Mat *src, size_t nsrc, OutputArray dst)
 Applies horizontal concatenation to given matrices. More...
 
void cv::hconcat (InputArray src1, InputArray src2, OutputArray dst)
 
void cv::hconcat (InputArrayOfArrays src, OutputArray dst)
 
void cv::idct (InputArray src, OutputArray dst, int flags=0)
 Calculates the inverse Discrete Cosine Transform of a 1D or 2D array. More...
 
void cv::idft (InputArray src, OutputArray dst, int flags=0, int nonzeroRows=0)
 Calculates the inverse Discrete Fourier Transform of a 1D or 2D array. More...
 
void cv::inRange (InputArray src, InputArray lowerb, InputArray upperb, OutputArray dst)
 Checks if array elements lie between the elements of two other arrays. More...
 
void cv::insertChannel (InputArray src, InputOutputArray dst, int coi)
 Inserts a single channel to dst (coi is 0-based index) More...
 
double cv::invert (InputArray src, OutputArray dst, int flags=DECOMP_LU)
 Finds the inverse or pseudo-inverse of a matrix. More...
 
void cv::log (InputArray src, OutputArray dst)
 Calculates the natural logarithm of every array element. More...
 
void cv::LUT (InputArray src, InputArray lut, OutputArray dst)
 Performs a look-up table transform of an array. More...
 
void cv::magnitude (InputArray x, InputArray y, OutputArray magnitude)
 Calculates the magnitude of 2D vectors. More...
 
double cv::Mahalanobis (InputArray v1, InputArray v2, InputArray icovar)
 Calculates the Mahalanobis distance between two vectors. More...
 
void cv::max (InputArray src1, InputArray src2, OutputArray dst)
 Calculates per-element maximum of two arrays or an array and a scalar. More...
 
void cv::max (const Mat &src1, const Mat &src2, Mat &dst)
 
void cv::max (const UMat &src1, const UMat &src2, UMat &dst)
 
Scalar cv::mean (InputArray src, InputArray mask=noArray())
 Calculates an average (mean) of array elements. More...
 
void cv::meanStdDev (InputArray src, OutputArray mean, OutputArray stddev, InputArray mask=noArray())
 
void cv::merge (const Mat *mv, size_t count, OutputArray dst)
 Creates one multi-channel array out of several single-channel ones. More...
 
void cv::merge (InputArrayOfArrays mv, OutputArray dst)
 
void cv::min (InputArray src1, InputArray src2, OutputArray dst)
 Calculates per-element minimum of two arrays or an array and a scalar. More...
 
void cv::min (const Mat &src1, const Mat &src2, Mat &dst)
 
void cv::min (const UMat &src1, const UMat &src2, UMat &dst)
 
void cv::minMaxIdx (InputArray src, double *minVal, double *maxVal=0, int *minIdx=0, int *maxIdx=0, InputArray mask=noArray())
 Finds the global minimum and maximum in an array. More...
 
void cv::minMaxLoc (InputArray src, double *minVal, double *maxVal=0, Point *minLoc=0, Point *maxLoc=0, InputArray mask=noArray())
 Finds the global minimum and maximum in an array. More...
 
void cv::minMaxLoc (const SparseMat &a, double *minVal, double *maxVal, int *minIdx=0, int *maxIdx=0)
 
void cv::mixChannels (const Mat *src, size_t nsrcs, Mat *dst, size_t ndsts, const int *fromTo, size_t npairs)
 Copies specified channels from input arrays to the specified channels of output arrays. More...
 
void cv::mixChannels (InputArrayOfArrays src, InputOutputArrayOfArrays dst, const int *fromTo, size_t npairs)
 
void cv::mixChannels (InputArrayOfArrays src, InputOutputArrayOfArrays dst, const std::vector< int > &fromTo)
 
void cv::mulSpectrums (InputArray a, InputArray b, OutputArray c, int flags, bool conjB=false)
 Performs the per-element multiplication of two Fourier spectrums. More...
 
void cv::multiply (InputArray src1, InputArray src2, OutputArray dst, double scale=1, int dtype=-1)
 Calculates the per-element scaled product of two arrays. More...
 
void cv::mulTransposed (InputArray src, OutputArray dst, bool aTa, InputArray delta=noArray(), double scale=1, int dtype=-1)
 Calculates the product of a matrix and its transposition. More...
 
double cv::norm (InputArray src1, int normType=NORM_L2, InputArray mask=noArray())
 Calculates the absolute norm of an array. More...
 
double cv::norm (InputArray src1, InputArray src2, int normType=NORM_L2, InputArray mask=noArray())
 Calculates an absolute difference norm or a relative difference norm. More...
 
double cv::norm (const SparseMat &src, int normType)
 
void cv::normalize (InputArray src, InputOutputArray dst, double alpha=1, double beta=0, int norm_type=NORM_L2, int dtype=-1, InputArray mask=noArray())
 Normalizes the norm or value range of an array. More...
 
void cv::normalize (const SparseMat &src, SparseMat &dst, double alpha, int normType)
 
void cv::patchNaNs (InputOutputArray a, double val=0)
 converts NaN's to the given number More...
 
void cv::PCABackProject (InputArray data, InputArray mean, InputArray eigenvectors, OutputArray result)
 
void cv::PCACompute (InputArray data, InputOutputArray mean, OutputArray eigenvectors, int maxComponents=0)
 
void cv::PCACompute (InputArray data, InputOutputArray mean, OutputArray eigenvectors, double retainedVariance)
 
void cv::PCAProject (InputArray data, InputArray mean, InputArray eigenvectors, OutputArray result)
 
void cv::perspectiveTransform (InputArray src, OutputArray dst, InputArray m)
 Performs the perspective matrix transformation of vectors. More...
 
void cv::phase (InputArray x, InputArray y, OutputArray angle, bool angleInDegrees=false)
 Calculates the rotation angle of 2D vectors. More...
 
void cv::polarToCart (InputArray magnitude, InputArray angle, OutputArray x, OutputArray y, bool angleInDegrees=false)
 Calculates x and y coordinates of 2D vectors from their magnitude and angle. More...
 
void cv::pow (InputArray src, double power, OutputArray dst)
 Raises every array element to a power. More...
 
double cv::PSNR (InputArray src1, InputArray src2)
 Computes the Peak Signal-to-Noise Ratio (PSNR) image quality metric. More...
 
void cv::randn (InputOutputArray dst, InputArray mean, InputArray stddev)
 Fills the array with normally distributed random numbers. More...
 
void cv::randShuffle (InputOutputArray dst, double iterFactor=1., RNG *rng=0)
 Shuffles the array elements randomly. More...
 
void cv::randu (InputOutputArray dst, InputArray low, InputArray high)
 Generates a single uniformly-distributed random number or an array of random numbers. More...
 
void cv::reduce (InputArray src, OutputArray dst, int dim, int rtype, int dtype=-1)
 Reduces a matrix to a vector. More...
 
void cv::repeat (InputArray src, int ny, int nx, OutputArray dst)
 Fills the output array with repeated copies of the input array. More...
 
Mat cv::repeat (const Mat &src, int ny, int nx)
 
void cv::rotate (InputArray src, OutputArray dst, int rotateCode)
 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). More...
 
void cv::scaleAdd (InputArray src1, double alpha, InputArray src2, OutputArray dst)
 Calculates the sum of a scaled array and another array. More...
 
void cv::setIdentity (InputOutputArray mtx, const Scalar &s=Scalar(1))
 Initializes a scaled identity matrix. More...
 
void cv::setRNGSeed (int seed)
 Sets state of default random number generator. More...
 
bool cv::solve (InputArray src1, InputArray src2, OutputArray dst, int flags=DECOMP_LU)
 Solves one or more linear systems or least-squares problems. More...
 
int cv::solveCubic (InputArray coeffs, OutputArray roots)
 Finds the real roots of a cubic equation. More...
 
double cv::solvePoly (InputArray coeffs, OutputArray roots, int maxIters=300)
 Finds the real or complex roots of a polynomial equation. More...
 
void cv::sort (InputArray src, OutputArray dst, int flags)
 Sorts each row or each column of a matrix. More...
 
void cv::sortIdx (InputArray src, OutputArray dst, int flags)
 Sorts each row or each column of a matrix. More...
 
void cv::split (const Mat &src, Mat *mvbegin)
 Divides a multi-channel array into several single-channel arrays. More...
 
void cv::split (InputArray m, OutputArrayOfArrays mv)
 
void cv::sqrt (InputArray src, OutputArray dst)
 Calculates a square root of array elements. More...
 
void cv::subtract (InputArray src1, InputArray src2, OutputArray dst, InputArray mask=noArray(), int dtype=-1)
 Calculates the per-element difference between two arrays or array and a scalar. More...
 
Scalar cv::sum (InputArray src)
 Calculates the sum of array elements. More...
 
void cv::SVBackSubst (InputArray w, InputArray u, InputArray vt, InputArray rhs, OutputArray dst)
 
void cv::SVDecomp (InputArray src, OutputArray w, OutputArray u, OutputArray vt, int flags=0)
 
RNGcv::theRNG ()
 Returns the default random number generator. More...
 
Scalar cv::trace (InputArray mtx)
 Returns the trace of a matrix. More...
 
void cv::transform (InputArray src, OutputArray dst, InputArray m)
 Performs the matrix transformation of every array element. More...
 
void cv::transpose (InputArray src, OutputArray dst)
 Transposes a matrix. More...
 
void cv::vconcat (const Mat *src, size_t nsrc, OutputArray dst)
 Applies vertical concatenation to given matrices. More...
 
void cv::vconcat (InputArray src1, InputArray src2, OutputArray dst)
 
void cv::vconcat (InputArrayOfArrays src, OutputArray dst)
 

Detailed Description

Enumeration Type Documentation

§ BorderTypes

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

§ CmpTypes

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.

§ DecompTypes

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 \(LL^T\) 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 \(\texttt{src1}^T\cdot\texttt{src1}\cdot\texttt{dst}=\texttt{src1}^T\texttt{src2}\) are solved instead of the original system \(\texttt{src1}\cdot\texttt{dst}=\texttt{src2}\)

§ DftFlags

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).

DFT_COMPLEX_INPUT 

specifies that input is complex input. If this flag is set, the input must have 2 channels. On the other hand, for backwards compatibility reason, if input has 2 channels, input is already considered complex.

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.

§ GemmFlags

generalized matrix multiplication flags

Enumerator
GEMM_1_T 

transposes src1

GEMM_2_T 

transposes src2

GEMM_3_T 

transposes src3

§ NormTypes

norm types

src1 and src2 denote input arrays.

Enumerator
NORM_INF 

\[ norm = \forkthree {\|\texttt{src1}\|_{L_{\infty}} = \max _I | \texttt{src1} (I)|}{if \(\texttt{normType} = \texttt{NORM_INF}\) } {\|\texttt{src1}-\texttt{src2}\|_{L_{\infty}} = \max _I | \texttt{src1} (I) - \texttt{src2} (I)|}{if \(\texttt{normType} = \texttt{NORM_INF}\) } {\frac{\|\texttt{src1}-\texttt{src2}\|_{L_{\infty}} }{\|\texttt{src2}\|_{L_{\infty}} }}{if \(\texttt{normType} = \texttt{NORM_RELATIVE | NORM_INF}\) } \]

NORM_L1 

\[ norm = \forkthree {\| \texttt{src1} \| _{L_1} = \sum _I | \texttt{src1} (I)|}{if \(\texttt{normType} = \texttt{NORM_L1}\)} { \| \texttt{src1} - \texttt{src2} \| _{L_1} = \sum _I | \texttt{src1} (I) - \texttt{src2} (I)|}{if \(\texttt{normType} = \texttt{NORM_L1}\) } { \frac{\|\texttt{src1}-\texttt{src2}\|_{L_1} }{\|\texttt{src2}\|_{L_1}} }{if \(\texttt{normType} = \texttt{NORM_RELATIVE | NORM_L1}\) } \]

NORM_L2 

\[ norm = \forkthree { \| \texttt{src1} \| _{L_2} = \sqrt{\sum_I \texttt{src1}(I)^2} }{if \(\texttt{normType} = \texttt{NORM_L2}\) } { \| \texttt{src1} - \texttt{src2} \| _{L_2} = \sqrt{\sum_I (\texttt{src1}(I) - \texttt{src2}(I))^2} }{if \(\texttt{normType} = \texttt{NORM_L2}\) } { \frac{\|\texttt{src1}-\texttt{src2}\|_{L_2} }{\|\texttt{src2}\|_{L_2}} }{if \(\texttt{normType} = \texttt{NORM_RELATIVE | NORM_L2}\) } \]

NORM_L2SQR 

\[ norm = \forkthree { \| \texttt{src1} \| _{L_2} ^{2} = \sum_I \texttt{src1}(I)^2} {if \(\texttt{normType} = \texttt{NORM_L2SQR}\)} { \| \texttt{src1} - \texttt{src2} \| _{L_2} ^{2} = \sum_I (\texttt{src1}(I) - \texttt{src2}(I))^2 }{if \(\texttt{normType} = \texttt{NORM_L2SQR}\) } { \left(\frac{\|\texttt{src1}-\texttt{src2}\|_{L_2} }{\|\texttt{src2}\|_{L_2}}\right)^2 }{if \(\texttt{normType} = \texttt{NORM_RELATIVE | NORM_L2}\) } \]

NORM_HAMMING 

In the case of one input array, calculates the Hamming distance of the array from zero, In the case of two input arrays, calculates the Hamming distance between the arrays.

NORM_HAMMING2 

Similar to NORM_HAMMING, but in the calculation, each two bits of the input sequence will be added and treated as a single bit to be used in the same calculation as NORM_HAMMING.

NORM_TYPE_MASK 

bit-mask which can be used to separate norm type from norm flags

NORM_RELATIVE 

flag

NORM_MINMAX 

flag

§ RotateFlags

Enumerator
ROTATE_90_CLOCKWISE 
ROTATE_180 
ROTATE_90_COUNTERCLOCKWISE 

Function Documentation

§ absdiff()

void cv::absdiff ( InputArray  src1,
InputArray  src2,
OutputArray  dst 
)

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:

\[\texttt{dst}(I) = \texttt{saturate} (| \texttt{src1}(I) - \texttt{src2}(I)|)\]

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:

\[\texttt{dst}(I) = \texttt{saturate} (| \texttt{src1}(I) - \texttt{src2} |)\]

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:

\[\texttt{dst}(I) = \texttt{saturate} (| \texttt{src1} - \texttt{src2}(I) |)\]

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
src1first input array or a scalar.
src2second input array or a scalar.
dstoutput array that has the same size and type as input arrays.
See also
cv::abs(const Mat&)

§ add()

void cv::add ( InputArray  src1,
InputArray  src2,
OutputArray  dst,
InputArray  mask = noArray(),
int  dtype = -1 
)

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:

    \[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src1}(I) + \texttt{src2}(I)) \quad \texttt{if mask}(I) \ne0\]

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

    \[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src1}(I) + \texttt{src2} ) \quad \texttt{if mask}(I) \ne0\]

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

    \[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src1} + \texttt{src2}(I) ) \quad \texttt{if mask}(I) \ne0\]

    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:

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
src1first input array or a scalar.
src2second input array or a scalar.
dstoutput array that has the same size and number of channels as the input array(s); the depth is defined by dtype or src1/src2.
maskoptional operation mask - 8-bit single channel array, that specifies elements of the output array to be changed.
dtypeoptional depth of the output array (see the discussion below).
See also
subtract, addWeighted, scaleAdd, Mat::convertTo
Examples:
shape_example.cpp.

§ addWeighted()

void cv::addWeighted ( InputArray  src1,
double  alpha,
InputArray  src2,
double  beta,
double  gamma,
OutputArray  dst,
int  dtype = -1 
)

Calculates the weighted sum of two arrays.

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

\[\texttt{dst} (I)= \texttt{saturate} ( \texttt{src1} (I)* \texttt{alpha} + \texttt{src2} (I)* \texttt{beta} + \texttt{gamma} )\]

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:

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
src1first input array.
alphaweight of the first array elements.
src2second input array of the same size and channel number as src1.
betaweight of the second array elements.
gammascalar added to each sum.
dstoutput array that has the same size and number of channels as the input arrays.
dtypeoptional 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
Examples:
AddingImagesTrackbar.cpp, and Sobel_Demo.cpp.

§ batchDistance()

void cv::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 
)

naive nearest neighbor finder

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

Todo:
document

§ bitwise_and()

void cv::bitwise_and ( InputArray  src1,
InputArray  src2,
OutputArray  dst,
InputArray  mask = noArray() 
)

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:

\[\texttt{dst} (I) = \texttt{src1} (I) \wedge \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0\]

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

\[\texttt{dst} (I) = \texttt{src1} (I) \wedge \texttt{src2} \quad \texttt{if mask} (I) \ne0\]

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

\[\texttt{dst} (I) = \texttt{src1} \wedge \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0\]

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
src1first input array or a scalar.
src2second input array or a scalar.
dstoutput array that has the same size and type as the input arrays.
maskoptional operation mask, 8-bit single channel array, that specifies elements of the output array to be changed.

§ bitwise_not()

void cv::bitwise_not ( InputArray  src,
OutputArray  dst,
InputArray  mask = noArray() 
)

Inverts every bit of an array.

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

\[\texttt{dst} (I) = \neg \texttt{src} (I)\]

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
srcinput array.
dstoutput array that has the same size and type as the input array.
maskoptional operation mask, 8-bit single channel array, that specifies elements of the output array to be changed.
Examples:
camshiftdemo.cpp.

§ bitwise_or()

void cv::bitwise_or ( InputArray  src1,
InputArray  src2,
OutputArray  dst,
InputArray  mask = noArray() 
)

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:

\[\texttt{dst} (I) = \texttt{src1} (I) \vee \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0\]

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

\[\texttt{dst} (I) = \texttt{src1} (I) \vee \texttt{src2} \quad \texttt{if mask} (I) \ne0\]

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

\[\texttt{dst} (I) = \texttt{src1} \vee \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0\]

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
src1first input array or a scalar.
src2second input array or a scalar.
dstoutput array that has the same size and type as the input arrays.
maskoptional operation mask, 8-bit single channel array, that specifies elements of the output array to be changed.

§ bitwise_xor()

void cv::bitwise_xor ( InputArray  src1,
InputArray  src2,
OutputArray  dst,
InputArray  mask = noArray() 
)

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:

\[\texttt{dst} (I) = \texttt{src1} (I) \oplus \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0\]

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

\[\texttt{dst} (I) = \texttt{src1} (I) \oplus \texttt{src2} \quad \texttt{if mask} (I) \ne0\]

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

\[\texttt{dst} (I) = \texttt{src1} \oplus \texttt{src2} (I) \quad \texttt{if mask} (I) \ne0\]

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
src1first input array or a scalar.
src2second input array or a scalar.
dstoutput array that has the same size and type as the input arrays.
maskoptional operation mask, 8-bit single channel array, that specifies elements of the output array to be changed.

§ borderInterpolate()

int cv::borderInterpolate ( int  p,
int  len,
int  borderType 
)

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:

float val = img.at<float>(borderInterpolate(100, img.rows, cv::BORDER_REFLECT_101),

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

Parameters
p0-based coordinate of the extrapolated pixel along one of the axes, likely <0 or >= len
lenLength of the array along the corresponding axis.
borderTypeBorder 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.
See also
copyMakeBorder

§ calcCovarMatrix() [1/2]

void cv::calcCovarMatrix ( const Mat samples,
int  nsamples,
Mat covar,
Mat mean,
int  flags,
int  ctype = CV_64F 
)

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.

Parameters
samplessamples stored as separate matrices
nsamplesnumber of samples
covaroutput covariance matrix of the type ctype and square size.
meaninput or output (depending on the flags) array as the average value of the input vectors.
flagsoperation flags as a combination of cv::CovarFlags
ctypetype of the matrixl; it equals 'CV_64F' by default.
See also
PCA, mulTransposed, Mahalanobis
Todo:
InputArrayOfArrays

§ calcCovarMatrix() [2/2]

void cv::calcCovarMatrix ( InputArray  samples,
OutputArray  covar,
InputOutputArray  mean,
int  flags,
int  ctype = CV_64F 
)

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

§ cartToPolar()

void cv::cartToPolar ( InputArray  x,
InputArray  y,
OutputArray  magnitude,
OutputArray  angle,
bool  angleInDegrees = false 
)

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)):

\[\begin{array}{l} \texttt{magnitude} (I)= \sqrt{\texttt{x}(I)^2+\texttt{y}(I)^2} , \\ \texttt{angle} (I)= \texttt{atan2} ( \texttt{y} (I), \texttt{x} (I))[ \cdot180 / \pi ] \end{array}\]

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

Parameters
xarray of x-coordinates; this must be a single-precision or double-precision floating-point array.
yarray of y-coordinates, that must have the same size and same type as x.
magnitudeoutput array of magnitudes of the same size and type as x.
angleoutput 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).
angleInDegreesa flag, indicating whether the angles are measured in radians (which is by default), or in degrees.
See also
Sobel, Scharr

§ checkRange()

bool cv::checkRange ( InputArray  a,
bool  quiet = true,
Point pos = 0,
double  minVal = -DBL_MAX,
double  maxVal = DBL_MAX 
)

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.

Parameters
ainput array.
quieta flag, indicating whether the functions quietly return false when the array elements are out of range or they throw an exception.
posoptional output parameter, when not NULL, must be a pointer to array of src.dims elements.
minValinclusive lower boundary of valid values range.
maxValexclusive upper boundary of valid values range.

§ compare()

void cv::compare ( InputArray  src1,
InputArray  src2,
OutputArray  dst,
int  cmpop 
)

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:

\[\texttt{dst} (I) = \texttt{src1} (I) \,\texttt{cmpop}\, \texttt{src2} (I)\]

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

\[\texttt{dst} (I) = \texttt{src1}(I) \,\texttt{cmpop}\, \texttt{src2}\]

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

\[\texttt{dst} (I) = \texttt{src1} \,\texttt{cmpop}\, \texttt{src2} (I)\]

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:

Mat dst1 = src1 >= src2;
Mat dst2 = src1 < 8;
...
Parameters
src1first input array or a scalar; when it is an array, it must have a single channel.
src2second input array or a scalar; when it is an array, it must have a single channel.
dstoutput array of type ref CV_8U that has the same size and the same number of channels as the input arrays.
cmpopa flag, that specifies correspondence between the arrays (cv::CmpTypes)
See also
checkRange, min, max, threshold

§ completeSymm()

void cv::completeSymm ( InputOutputArray  mtx,
bool  lowerToUpper = false 
)

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: \(\texttt{mtx}_{ij}=\texttt{mtx}_{ji}\) for \(i > j\) if lowerToUpper=false \(\texttt{mtx}_{ij}=\texttt{mtx}_{ji}\) for \(i < j\) if lowerToUpper=true

Parameters
mtxinput-output floating-point square matrix.
lowerToUpperoperation 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

§ convertFp16()

void cv::convertFp16 ( InputArray  src,
OutputArray  dst 
)

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.

Parameters
srcinput array.
dstoutput array.

§ convertScaleAbs()

void cv::convertScaleAbs ( InputArray  src,
OutputArray  dst,
double  alpha = 1,
double  beta = 0 
)

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:

\[\texttt{dst} (I)= \texttt{saturate\_cast<uchar>} (| \texttt{src} (I)* \texttt{alpha} + \texttt{beta} |)\]

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:

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
srcinput array.
dstoutput array.
alphaoptional scale factor.
betaoptional delta added to the scaled values.
See also
Mat::convertTo, cv::abs(const Mat&)
Examples:
laplace.cpp, and Sobel_Demo.cpp.

§ copyMakeBorder()

void cv::copyMakeBorder ( InputArray  src,
OutputArray  dst,
int  top,
int  bottom,
int  left,
int  right,
int  borderType,
const Scalar value = Scalar() 
)

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:

// 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
// 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
srcSource image.
dstDestination image of the same type as src and the size Size(src.cols+left+right, src.rows+top+bottom) .
top
bottom
left
rightParameter 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.
borderTypeBorder type. See borderInterpolate for details.
valueBorder value if borderType==BORDER_CONSTANT .
See also
borderInterpolate
Examples:
copyMakeBorder_demo.cpp.

§ countNonZero()

int cv::countNonZero ( InputArray  src)

Counts non-zero array elements.

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

\[\sum _{I: \; \texttt{src} (I) \ne0 } 1\]

Parameters
srcsingle-channel array.
See also
mean, meanStdDev, norm, minMaxLoc, calcCovarMatrix

§ dct()

void cv::dct ( InputArray  src,
OutputArray  dst,
int  flags = 0 
)

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:

    \[Y = C^{(N)} \cdot X\]

    where

    \[C^{(N)}_{jk}= \sqrt{\alpha_j/N} \cos \left ( \frac{\pi(2k+1)j}{2N} \right )\]

    and \(\alpha_0=1\), \(\alpha_j=2\) for j > 0.
  • Inverse Cosine transform of a 1D vector of N elements:

    \[X = \left (C^{(N)} \right )^{-1} \cdot Y = \left (C^{(N)} \right )^T \cdot Y\]

    (since \(C^{(N)}\) is an orthogonal matrix, \(C^{(N)} \cdot \left(C^{(N)}\right)^T = I\) )
  • Forward 2D Cosine transform of M x N matrix:

    \[Y = C^{(N)} \cdot X \cdot \left (C^{(N)} \right )^T\]

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

    \[X = \left (C^{(N)} \right )^T \cdot X \cdot C^{(N)}\]

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
srcinput floating-point array.
dstoutput array of the same size and type as src .
flagstransformation flags as a combination of cv::DftFlags (DCT_*)
See also
dft , getOptimalDFTSize , idct

§ determinant()

double cv::determinant ( InputArray  mtx)

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.

Parameters
mtxinput matrix that must have CV_32FC1 or CV_64FC1 type and square size.
See also
trace, invert, solve, eigen, MatrixExpressions

§ dft()

void cv::dft ( InputArray  src,
OutputArray  dst,
int  flags = 0,
int  nonzeroRows = 0 
)

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:

    \[Y = F^{(N)} \cdot X,\]

    where \(F^{(N)}_{jk}=\exp(-2\pi i j k/N)\) and \(i=\sqrt{-1}\)
  • Inverse the Fourier transform of a 1D vector of N elements:

    \[\begin{array}{l} X'= \left (F^{(N)} \right )^{-1} \cdot Y = \left (F^{(N)} \right )^* \cdot y \\ X = (1/N) \cdot X, \end{array}\]

    where \(F^*=\left(\textrm{Re}(F^{(N)})-\textrm{Im}(F^{(N)})\right)^T\)
  • Forward the 2D Fourier transform of a M x N matrix:

    \[Y = F^{(M)} \cdot X \cdot F^{(N)}\]

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

    \[\begin{array}{l} X'= \left (F^{(M)} \right )^* \cdot Y \cdot \left (F^{(N)} \right )^* \\ X = \frac{1}{M \cdot N} \cdot X' \end{array}\]

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:

\[\begin{bmatrix} Re Y_{0,0} & Re Y_{0,1} & Im Y_{0,1} & Re Y_{0,2} & Im Y_{0,2} & \cdots & Re Y_{0,N/2-1} & Im Y_{0,N/2-1} & Re Y_{0,N/2} \\ Re Y_{1,0} & Re Y_{1,1} & Im Y_{1,1} & Re Y_{1,2} & Im Y_{1,2} & \cdots & Re Y_{1,N/2-1} & Im Y_{1,N/2-1} & Re Y_{1,N/2} \\ Im Y_{1,0} & Re Y_{2,1} & Im Y_{2,1} & Re Y_{2,2} & Im Y_{2,2} & \cdots & Re Y_{2,N/2-1} & Im Y_{2,N/2-1} & Im Y_{1,N/2} \\ \hdotsfor{9} \\ Re Y_{M/2-1,0} & Re Y_{M-3,1} & Im Y_{M-3,1} & \hdotsfor{3} & Re Y_{M-3,N/2-1} & Im Y_{M-3,N/2-1}& Re Y_{M/2-1,N/2} \\ Im Y_{M/2-1,0} & Re Y_{M-2,1} & Im Y_{M-2,1} & \hdotsfor{3} & Re Y_{M-2,N/2-1} & Im Y_{M-2,N/2-1}& Im Y_{M/2-1,N/2} \\ Re Y_{M/2,0} & Re Y_{M-1,1} & Im Y_{M-1,1} & \hdotsfor{3} & Re Y_{M-1,N/2-1} & Im Y_{M-1,N/2-1}& Re Y_{M/2,N/2} \end{bmatrix}\]

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
srcinput array that could be real or complex.
dstoutput array whose size and type depends on the flags .
flagstransformation flags, representing a combination of the cv::DftFlags
nonzeroRowswhen 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

§ divide() [1/2]

void cv::divide ( InputArray  src1,
InputArray  src2,
OutputArray  dst,
double  scale = 1,
int  dtype = -1 
)

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

The function cv::divide divides one array by another:

\[\texttt{dst(I) = saturate(src1(I)*scale/src2(I))}\]

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

\[\texttt{dst(I) = saturate(scale/src2(I))}\]

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
src1first input array.
src2second input array of the same size and type as src1.
scalescalar factor.
dstoutput array of the same size and type as src2.
dtypeoptional 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

§ divide() [2/2]

void cv::divide ( double  scale,
InputArray  src2,
OutputArray  dst,
int  dtype = -1 
)

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

§ eigen()

bool cv::eigen ( InputArray  src,
OutputArray  eigenvalues,
OutputArray  eigenvectors = noArray() 
)

Calculates eigenvalues and eigenvectors of a symmetric matrix.

The function cv::eigen calculates 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
srcinput matrix that must have CV_32FC1 or CV_64FC1 type, square size and be symmetrical (src ^T^ == src).
eigenvaluesoutput vector of eigenvalues of the same type as src; the eigenvalues are stored in the descending order.
eigenvectorsoutput 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

§ exp()

void cv::exp ( InputArray  src,
OutputArray  dst 
)

Calculates the exponent of every array element.

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

\[\texttt{dst} [I] = e^{ src(I) }\]

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
srcinput array.
dstoutput array of the same size and type as src.
See also
log , cartToPolar , polarToCart , phase , pow , sqrt , magnitude

§ extractChannel()

void cv::extractChannel ( InputArray  src,
OutputArray  dst,
int  coi 
)

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

Parameters
srcinput array
dstoutput array
coiindex of channel to extract
See also
mixChannels, split

§ findNonZero()

void cv::findNonZero ( InputArray  src,
OutputArray  idx 
)

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:

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

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

§ flip()

void cv::flip ( InputArray  src,
OutputArray  dst,
int  flipCode 
)

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):

\[\texttt{dst} _{ij} = \left\{ \begin{array}{l l} \texttt{src} _{\texttt{src.rows}-i-1,j} & if\; \texttt{flipCode} = 0 \\ \texttt{src} _{i, \texttt{src.cols} -j-1} & if\; \texttt{flipCode} > 0 \\ \texttt{src} _{ \texttt{src.rows} -i-1, \texttt{src.cols} -j-1} & if\; \texttt{flipCode} < 0 \\ \end{array} \right.\]

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
srcinput array.
dstoutput array of the same size and type as src.
flipCodea 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
Examples:
facedetect.cpp.

§ gemm()

void cv::gemm ( InputArray  src1,
InputArray  src2,
double  alpha,
InputArray  src3,
double  beta,
OutputArray  dst,
int  flags = 0 
)

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

\[\texttt{dst} = \texttt{alpha} \cdot \texttt{src1} ^T \cdot \texttt{src2} + \texttt{beta} \cdot \texttt{src3} ^T\]

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:

dst = alpha*src1.t()*src2 + beta*src3.t();
Parameters
src1first multiplied input matrix that could be real(CV_32FC1, CV_64FC1) or complex(CV_32FC2, CV_64FC2).
src2second multiplied input matrix of the same type as src1.
alphaweight of the matrix product.
src3third optional delta matrix added to the matrix product; it should have the same type as src1 and src2.
betaweight of src3.
dstoutput matrix; it has the proper size and the same type as input matrices.
flagsoperation flags (cv::GemmFlags)
See also
mulTransposed , transform
Examples:
image_alignment.cpp.

§ getOptimalDFTSize()

int cv::getOptimalDFTSize ( int  vecsize)

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.

Parameters
vecsizevector size.
See also
dft , dct , idft , idct , mulSpectrums

§ hconcat() [1/3]

void cv::hconcat ( const Mat src,
size_t  nsrc,
OutputArray  dst 
)

Applies horizontal concatenation to given matrices.

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

cv::Mat matArray[] = { cv::Mat(4, 1, CV_8UC1, cv::Scalar(1)),
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
srcinput array or vector of matrices. all of the matrices must have the same number of rows and the same depth.
nsrcnumber of matrices in src.
dstoutput 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)

§ hconcat() [2/3]

void cv::hconcat ( InputArray  src1,
InputArray  src2,
OutputArray  dst 
)

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

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::hconcat(A, B, C);
//C:
//[1, 4, 7, 10;
// 2, 5, 8, 11;
// 3, 6, 9, 12]
Parameters
src1first input array to be considered for horizontal concatenation.
src2second input array to be considered for horizontal concatenation.
dstoutput 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.

§ hconcat() [3/3]

void cv::hconcat ( InputArrayOfArrays  src,
OutputArray  dst 
)

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

std::vector<cv::Mat> matrices = { cv::Mat(4, 1, CV_8UC1, cv::Scalar(1)),
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
srcinput array or vector of matrices. all of the matrices must have the same number of rows and the same depth.
dstoutput array. It has the same number of rows and depth as the src, and the sum of cols of the src. same depth.

§ idct()

void cv::idct ( InputArray  src,
OutputArray  dst,
int  flags = 0 
)

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
srcinput floating-point single-channel array.
dstoutput array of the same size and type as src.
flagsoperation flags.
See also
dct, dft, idft, getOptimalDFTSize

§ idft()

void cv::idft ( InputArray  src,
OutputArray  dst,
int  flags = 0,
int  nonzeroRows = 0 
)

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
srcinput floating-point real or complex array.
dstoutput array whose size and type depend on the flags.
flagsoperation flags (see dft and cv::DftFlags).
nonzeroRowsnumber of dst rows to process; the rest of the rows have undefined content (see the convolution sample in dft description.

§ inRange()

void cv::inRange ( InputArray  src,
InputArray  lowerb,
InputArray  upperb,
OutputArray  dst 
)

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:

    \[\texttt{dst} (I)= \texttt{lowerb} (I)_0 \leq \texttt{src} (I)_0 \leq \texttt{upperb} (I)_0\]

  • For two-channel arrays:

    \[\texttt{dst} (I)= \texttt{lowerb} (I)_0 \leq \texttt{src} (I)_0 \leq \texttt{upperb} (I)_0 \land \texttt{lowerb} (I)_1 \leq \texttt{src} (I)_1 \leq \texttt{upperb} (I)_1\]

  • 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
srcfirst input array.
lowerbinclusive lower boundary array or a scalar.
upperbinclusive upper boundary array or a scalar.
dstoutput array of the same size as src and CV_8U type.
Examples:
camshiftdemo.cpp.

§ insertChannel()

void cv::insertChannel ( InputArray  src,
InputOutputArray  dst,
int  coi 
)

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

Parameters
srcinput array
dstoutput array
coiindex of channel for insertion
See also
mixChannels, merge

§ invert()

double cv::invert ( InputArray  src,
OutputArray  dst,
int  flags = DECOMP_LU 
)

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.

Parameters
srcinput floating-point M x N matrix.
dstoutput matrix of N x M size and the same type as src.
flagsinversion method (cv::DecompTypes)
See also
solve, SVD

§ log()

void cv::log ( InputArray  src,
OutputArray  dst 
)

Calculates the natural logarithm of every array element.

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

\[\texttt{dst} (I) = \log (\texttt{src}(I)) \]

Output on zero, negative and special (NaN, Inf) values is undefined.

Parameters
srcinput array.
dstoutput array of the same size and type as src .
See also
exp, cartToPolar, polarToCart, phase, pow, sqrt, magnitude

§ LUT()

void cv::LUT ( InputArray  src,
InputArray  lut,
OutputArray  dst 
)

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:

\[\texttt{dst} (I) \leftarrow \texttt{lut(src(I) + d)}\]

where

\[d = \fork{0}{if \(\texttt{src}\) has depth \(\texttt{CV_8U}\)}{128}{if \(\texttt{src}\) has depth \(\texttt{CV_8S}\)}\]

Parameters
srcinput array of 8-bit elements.
lutlook-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.
dstoutput array of the same size and number of channels as src, and the same depth as lut.
See also
convertScaleAbs, Mat::convertTo

§ magnitude()

void cv::magnitude ( InputArray  x,
InputArray  y,
OutputArray  magnitude 
)

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:

\[\texttt{dst} (I) = \sqrt{\texttt{x}(I)^2 + \texttt{y}(I)^2}\]

Parameters
xfloating-point array of x-coordinates of the vectors.
yfloating-point array of y-coordinates of the vectors; it must have the same size as x.
magnitudeoutput array of the same size and type as x.
See also
cartToPolar, polarToCart, phase, sqrt

§ Mahalanobis()

double cv::Mahalanobis ( InputArray  v1,
InputArray  v2,
InputArray  icovar 
)

Calculates the Mahalanobis distance between two vectors.

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

\[d( \texttt{vec1} , \texttt{vec2} )= \sqrt{\sum_{i,j}{\texttt{icovar(i,j)}\cdot(\texttt{vec1}(I)-\texttt{vec2}(I))\cdot(\texttt{vec1(j)}-\texttt{vec2(j)})} }\]

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
v1first 1D input vector.
v2second 1D input vector.
icovarinverse covariance matrix.

§ max() [1/3]

void cv::max ( InputArray  src1,
InputArray  src2,
OutputArray  dst 
)

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:

\[\texttt{dst} (I)= \max ( \texttt{src1} (I), \texttt{src2} (I))\]

or array and a scalar:

\[\texttt{dst} (I)= \max ( \texttt{src1} (I), \texttt{value} )\]

Parameters
src1first input array.
src2second input array of the same size and type as src1 .
dstoutput array of the same size and type as src1.
See also
min, compare, inRange, minMaxLoc, MatrixExpressions

§ max() [2/3]

void cv::max ( const Mat src1,
const Mat src2,
Mat dst 
)

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)

§ max() [3/3]

void cv::max ( const UMat src1,
const UMat src2,
UMat dst 
)

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)

§ mean()

Scalar cv::mean ( InputArray  src,
InputArray  mask = noArray() 
)

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:

\[\begin{array}{l} N = \sum _{I: \; \texttt{mask} (I) \ne 0} 1 \\ M_c = \left ( \sum _{I: \; \texttt{mask} (I) \ne 0}{ \texttt{mtx} (I)_c} \right )/N \end{array}\]

When all the mask elements are 0's, the function returns Scalar::all(0)

Parameters
srcinput array that should have from 1 to 4 channels so that the result can be stored in Scalar_ .
maskoptional operation mask.
See also
countNonZero, meanStdDev, norm, minMaxLoc

§ meanStdDev()

void cv::meanStdDev ( InputArray  src,
OutputArray  mean,
OutputArray  stddev,
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:

\[\begin{array}{l} N = \sum _{I, \texttt{mask} (I) \ne 0} 1 \\ \texttt{mean} _c = \frac{\sum_{ I: \; \texttt{mask}(I) \ne 0} \texttt{src} (I)_c}{N} \\ \texttt{stddev} _c = \sqrt{\frac{\sum_{ I: \; \texttt{mask}(I) \ne 0} \left ( \texttt{src} (I)_c - \texttt{mean} _c \right )^2}{N}} \end{array}\]

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 .
Parameters
srcinput array that should have from 1 to 4 channels so that the results can be stored in Scalar_ 's.
meanoutput parameter: calculated mean value.
stddevoutput parameter: calculated standard deviation.
maskoptional operation mask.
See also
countNonZero, mean, norm, minMaxLoc, calcCovarMatrix

§ merge() [1/2]

void cv::merge ( const Mat mv,
size_t  count,
OutputArray  dst 
)

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.

The following example shows how to merge 3 single channel matrices into a single 3-channel matrix.

Mat m1 = (Mat_<uchar>(2,2) << 1,4,7,10);
Mat m2 = (Mat_<uchar>(2,2) << 2,5,8,11);
Mat m3 = (Mat_<uchar>(2,2) << 3,6,9,12);
Mat channels[3] = {m1, m2, m3};
Mat m;
merge(channels, 3, m);
/*
m =
[ 1, 2, 3, 4, 5, 6;
7, 8, 9, 10, 11, 12]
m.channels() = 3
*/
Parameters
mvinput array of matrices to be merged; all the matrices in mv must have the same size and the same depth.
countnumber of input matrices when mv is a plain C array; it must be greater than zero.
dstoutput 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
Examples:
distrans.cpp.

§ merge() [2/2]

void cv::merge ( InputArrayOfArrays  mv,
OutputArray  dst 
)

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

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

§ min() [1/3]

void cv::min ( InputArray  src1,
InputArray  src2,
OutputArray  dst 
)

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:

\[\texttt{dst} (I)= \min ( \texttt{src1} (I), \texttt{src2} (I))\]

or array and a scalar:

\[\texttt{dst} (I)= \min ( \texttt{src1} (I), \texttt{value} )\]

Parameters
src1first input array.
src2second input array of the same size and type as src1.
dstoutput array of the same size and type as src1.
See also
max, compare, inRange, minMaxLoc

§ min() [2/3]

void cv::min ( const Mat src1,
const Mat src2,
Mat dst 
)

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)

§ min() [3/3]

void cv::min ( const UMat src1,
const UMat src2,
UMat dst 
)

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)

§ minMaxIdx()

void cv::minMaxIdx ( InputArray  src,
double *  minVal,
double *  maxVal = 0,
int *  minIdx = 0,
int *  maxIdx = 0,
InputArray  mask = noArray() 
)

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)).
Parameters
srcinput single-channel array.
minValpointer to the returned minimum value; NULL is used if not required.
maxValpointer to the returned maximum value; NULL is used if not required.
minIdxpointer 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.
maxIdxpointer to the returned maximum location (in nD case). NULL is used if not required.
maskspecified array region

§ minMaxLoc() [1/2]

void cv::minMaxLoc ( InputArray  src,
double *  minVal,
double *  maxVal = 0,
Point minLoc = 0,
Point maxLoc = 0,
InputArray  mask = noArray() 
)

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 .

Parameters
srcinput single-channel array.
minValpointer to the returned minimum value; NULL is used if not required.
maxValpointer to the returned maximum value; NULL is used if not required.
minLocpointer to the returned minimum location (in 2D case); NULL is used if not required.
maxLocpointer to the returned maximum location (in 2D case); NULL is used if not required.
maskoptional mask used to select a sub-array.
See also
max, min, compare, inRange, extractImageCOI, mixChannels, split, Mat::reshape
Examples:
image_alignment.cpp, and MatchTemplate_Demo.cpp.

§ minMaxLoc() [2/2]

void cv::minMaxLoc ( const SparseMat a,
double *  minVal,
double *  maxVal,
int *  minIdx = 0,
int *  maxIdx = 0 
)

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

Parameters
ainput single-channel array.
minValpointer to the returned minimum value; NULL is used if not required.
maxValpointer to the returned maximum value; NULL is used if not required.
minIdxpointer 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.
maxIdxpointer to the returned maximum location (in nD case). NULL is used if not required.

§ mixChannels() [1/3]

void cv::mixChannels ( const Mat src,
size_t  nsrcs,
Mat dst,
size_t  ndsts,
const int *  fromTo,
size_t  npairs 
)

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:

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
srcinput array or vector of matrices; all of the matrices must have the same size and the same depth.
nsrcsnumber of matrices in src.
dstoutput array or vector of matrices; all the matrices must be allocated; their size and depth must be the same as in src[0].
ndstsnumber of matrices in dst.
fromToarray 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 .
npairsnumber of index pairs in fromTo.
See also
split, merge, extractChannel, insertChannel, cvtColor
Examples:
camshiftdemo.cpp.

§ mixChannels() [2/3]

void cv::mixChannels ( InputArrayOfArrays  src,
InputOutputArrayOfArrays  dst,
const int *  fromTo,
size_t  npairs 
)

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

Parameters
srcinput array or vector of matrices; all of the matrices must have the same size and the same depth.
dstoutput array or vector of matrices; all the matrices must be allocated; their size and depth must be the same as in src[0].
fromToarray 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 .
npairsnumber of index pairs in fromTo.

§ mixChannels() [3/3]

void cv::mixChannels ( InputArrayOfArrays  src,
InputOutputArrayOfArrays  dst,
const std::vector< int > &  fromTo 
)

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

Parameters
srcinput array or vector of matrices; all of the matrices must have the same size and the same depth.
dstoutput array or vector of matrices; all the matrices must be allocated; their size and depth must be the same as in src[0].
fromToarray 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 .

§ mulSpectrums()

void cv::mulSpectrums ( InputArray  a,
InputArray  b,
OutputArray  c,
int  flags,
bool  conjB = false 
)

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).

Parameters
afirst input array.
bsecond input array of the same size and type as src1 .
coutput array of the same size and type as src1 .
flagsoperation 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.
conjBoptional flag that conjugates the second input array before the multiplication (true) or not (false).

§ multiply()

void cv::multiply ( InputArray  src1,
InputArray  src2,
OutputArray  dst,
double  scale = 1,
int  dtype = -1 
)

Calculates the per-element scaled product of two arrays.

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

\[\texttt{dst} (I)= \texttt{saturate} ( \texttt{scale} \cdot \texttt{src1} (I) \cdot \texttt{src2} (I))\]

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
src1first input array.
src2second input array of the same size and the same type as src1.
dstoutput array of the same size and type as src1.
scaleoptional scale factor.
dtypeoptional depth of the output array
See also
add, subtract, divide, scaleAdd, addWeighted, accumulate, accumulateProduct, accumulateSquare, Mat::convertTo

§ mulTransposed()

void cv::mulTransposed ( InputArray  src,
OutputArray  dst,
bool  aTa,
InputArray  delta = noArray(),
double  scale = 1,
int  dtype = -1 
)

Calculates the product of a matrix and its transposition.

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

\[\texttt{dst} = \texttt{scale} ( \texttt{src} - \texttt{delta} )^T ( \texttt{src} - \texttt{delta} )\]

if aTa=true , and

\[\texttt{dst} = \texttt{scale} ( \texttt{src} - \texttt{delta} ) ( \texttt{src} - \texttt{delta} )^T\]

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
srcinput single-channel matrix. Note that unlike gemm, the function can multiply not only floating-point matrices.
dstoutput square matrix.
aTaFlag specifying the multiplication ordering. See the description below.
deltaOptional 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.
scaleOptional scale factor for the matrix product.
dtypeOptional 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

§ norm() [1/3]

double cv::norm ( InputArray  src1,
int  normType = NORM_L2,
InputArray  mask = noArray() 
)

Calculates the absolute norm of an array.

This version of cv::norm calculates the absolute norm of src1. The type of norm to calculate is specified using cv::NormTypes.

As example for one array consider the function \(r(x)= \begin{pmatrix} x \\ 1-x \end{pmatrix}, x \in [-1;1]\). The \( L_{1}, L_{2} \) and \( L_{\infty} \) norm for the sample value \(r(-1) = \begin{pmatrix} -1 \\ 2 \end{pmatrix}\) is calculated as follows

\begin{align*} \| r(-1) \|_{L_1} &= |-1| + |2| = 3 \\ \| r(-1) \|_{L_2} &= \sqrt{(-1)^{2} + (2)^{2}} = \sqrt{5} \\ \| r(-1) \|_{L_\infty} &= \max(|-1|,|2|) = 2 \end{align*}

and for \(r(0.5) = \begin{pmatrix} 0.5 \\ 0.5 \end{pmatrix}\) the calculation is

\begin{align*} \| r(0.5) \|_{L_1} &= |0.5| + |0.5| = 1 \\ \| r(0.5) \|_{L_2} &= \sqrt{(0.5)^{2} + (0.5)^{2}} = \sqrt{0.5} \\ \| r(0.5) \|_{L_\infty} &= \max(|0.5|,|0.5|) = 0.5. \end{align*}

The following graphic shows all values for the three norm functions \(\| r(x) \|_{L_1}, \| r(x) \|_{L_2}\) and \(\| r(x) \|_{L_\infty}\). It is notable that the \( L_{1} \) norm forms the upper and the \( L_{\infty} \) norm forms the lower border for the example function \( r(x) \).

NormTypes_OneArray_1-2-INF.png
Graphs for the different norm functions from the above example

When the mask parameter is specified and it is not empty, the norm is

If normType is not specified, NORM_L2 is used. calculated only over the region specified by the mask.

Multi-channel input arrays are treated as single-channel arrays, that is, the results for all channels are combined.

Hamming norms can only be calculated with CV_8U depth arrays.

Parameters
src1first input array.
normTypetype of the norm (see cv::NormTypes).
maskoptional operation mask; it must have the same size as src1 and CV_8UC1 type.

§ norm() [2/3]

double cv::norm ( InputArray  src1,
InputArray  src2,
int  normType = NORM_L2,
InputArray  mask = noArray() 
)

Calculates an absolute difference norm or a relative difference norm.

This version of cv::norm calculates the absolute difference norm or the relative difference norm of arrays src1 and src2. The type of norm to calculate is specified using cv::NormTypes.

Parameters
src1first input array.
src2second input array of the same size and the same type as src1.
normTypetype of the norm (cv::NormTypes).
maskoptional operation mask; it must have the same size as src1 and CV_8UC1 type.

§ norm() [3/3]

double cv::norm ( const SparseMat src,
int  normType 
)

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

Parameters
srcfirst input array.
normTypetype of the norm (see cv::NormTypes).

§ normalize() [1/2]

void cv::normalize ( InputArray  src,
InputOutputArray  dst,
double  alpha = 1,
double  beta = 0,
int  norm_type = NORM_L2,
int  dtype = -1,
InputArray  mask = noArray() 
)

Normalizes the norm or value range of an array.

The function cv::normalize normalizes scale and shift the input array elements so that

\[\| \texttt{dst} \| _{L_p}= \texttt{alpha}\]

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

\[\min _I \texttt{dst} (I)= \texttt{alpha} , \, \, \max _I \texttt{dst} (I)= \texttt{beta}\]

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:

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
srcinput array.
dstoutput array of the same size as src .
alphanorm value to normalize to or the lower range boundary in case of the range normalization.
betaupper range boundary in case of the range normalization; it is not used for the norm normalization.
norm_typenormalization type (see cv::NormTypes).
dtypewhen 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).
maskoptional operation mask.
See also
norm, Mat::convertTo, SparseMat::convertTo

§ normalize() [2/2]

void cv::normalize ( const SparseMat src,
SparseMat dst,
double  alpha,
int  normType 
)

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

Parameters
srcinput array.
dstoutput array of the same size as src .
alphanorm value to normalize to or the lower range boundary in case of the range normalization.
normTypenormalization type (see cv::NormTypes).

§ patchNaNs()

void cv::patchNaNs ( InputOutputArray  a,
double  val = 0 
)

converts NaN's to the given number

§ PCABackProject()

void cv::PCABackProject ( InputArray  data,
InputArray  mean,
InputArray  eigenvectors,
OutputArray  result 
)

§ PCACompute() [1/2]

void cv::PCACompute ( InputArray  data,
InputOutputArray  mean,
OutputArray  eigenvectors,
int  maxComponents = 0 
)

wrap PCA::operator()

§ PCACompute() [2/2]

void cv::PCACompute ( InputArray  data,
InputOutputArray  mean,
OutputArray  eigenvectors,
double  retainedVariance 
)

wrap PCA::operator()

§ PCAProject()

void cv::PCAProject ( InputArray  data,
InputArray  mean,
InputArray  eigenvectors,
OutputArray  result 
)

§ perspectiveTransform()

void cv::perspectiveTransform ( InputArray  src,
OutputArray  dst,
InputArray  m 
)

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:

\[(x, y, z) \rightarrow (x'/w, y'/w, z'/w)\]

where

\[(x', y', z', w') = \texttt{mat} \cdot \begin{bmatrix} x & y & z & 1 \end{bmatrix}\]

and

\[w = \fork{w'}{if \(w' \ne 0\)}{\infty}{otherwise}\]

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
srcinput two-channel or three-channel floating-point array; each element is a 2D/3D vector to be transformed.
dstoutput array of the same size and type as src.
m3x3 or 4x4 floating-point transformation matrix.
See also
transform, warpPerspective, getPerspectiveTransform, findHomography

§ phase()

void cv::phase ( InputArray  x,
InputArray  y,
OutputArray  angle,
bool  angleInDegrees = false 
)

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 :

\[\texttt{angle} (I) = \texttt{atan2} ( \texttt{y} (I), \texttt{x} (I))\]

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

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

§ polarToCart()

void cv::polarToCart ( InputArray  magnitude,
InputArray  angle,
OutputArray  x,
OutputArray  y,
bool  angleInDegrees = false 
)

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:

\[\begin{array}{l} \texttt{x} (I) = \texttt{magnitude} (I) \cos ( \texttt{angle} (I)) \\ \texttt{y} (I) = \texttt{magnitude} (I) \sin ( \texttt{angle} (I)) \\ \end{array}\]

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

Parameters
magnitudeinput 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.
angleinput floating-point array of angles of 2D vectors.
xoutput array of x-coordinates of 2D vectors; it has the same size and type as angle.
youtput array of y-coordinates of 2D vectors; it has the same size and type as angle.
angleInDegreeswhen true, the input angles are measured in degrees, otherwise, they are measured in radians.
See also
cartToPolar, magnitude, phase, exp, log, pow, sqrt

§ pow()

void cv::pow ( InputArray  src,
double  power,
OutputArray  dst 
)

Raises every array element to a power.

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

\[\texttt{dst} (I) = \fork{\texttt{src}(I)^{power}}{if \(\texttt{power}\) is integer}{|\texttt{src}(I)|^{power}}{otherwise}\]

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:

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
srcinput array.
powerexponent of power.
dstoutput array of the same size and type as src.
See also
sqrt, exp, log, cartToPolar, polarToCart

§ PSNR()

double cv::PSNR ( InputArray  src1,
InputArray  src2 
)

Computes the Peak Signal-to-Noise Ratio (PSNR) image quality metric.

This function calculates the Peak Signal-to-Noise Ratio (PSNR) image quality metric in decibels (dB), between two input arrays src1 and src2. Arrays must have depth CV_8U.

The PSNR is calculated as follows:

\[ \texttt{PSNR} = 10 \cdot \log_{10}{\left( \frac{R^2}{MSE} \right) } \]

where R is the maximum integer value of depth CV_8U (255) and MSE is the mean squared error between the two arrays.

Parameters
src1first input array.
src2second input array of the same size as src1.

§ randn()

void cv::randn ( InputOutputArray  dst,
InputArray  mean,
InputArray  stddev 
)

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.

Parameters
dstoutput array of random numbers; the array must be pre-allocated and have 1 to 4 channels.
meanmean value (expectation) of the generated random numbers.
stddevstandard 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
Examples:
kalman.cpp.

§ randShuffle()

void cv::randShuffle ( InputOutputArray  dst,
double  iterFactor = 1.,
RNG rng = 0 
)

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 .

Parameters
dstinput/output numerical 1D array.
iterFactorscale factor that determines the number of random swap operations (see the details below).
rngoptional random number generator used for shuffling; if it is zero, theRNG () is used instead.
See also
RNG, sort
Examples:
kmeans.cpp.

§ randu()

void cv::randu ( InputOutputArray  dst,
InputArray  low,
InputArray  high 
)

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:

\[\texttt{low} _c \leq \texttt{dst} (I)_c < \texttt{high} _c\]

Parameters
dstoutput array of random numbers; the array must be pre-allocated.
lowinclusive lower boundary of the generated random numbers.
highexclusive upper boundary of the generated random numbers.
See also
RNG, randn, theRNG
Examples:
cout_mat.cpp.

§ reduce()

void cv::reduce ( InputArray  src,
OutputArray  dst,
int  dim,
int  rtype,
int  dtype = -1 
)

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.

The following code demonstrates its usage for a single channel matrix.

Mat m = (Mat_<uchar>(3,2) << 1,2,3,4,5,6);
Mat col_sum, row_sum;
reduce(m, col_sum, 0, CV_REDUCE_SUM, CV_32F);
reduce(m, row_sum, 1, CV_REDUCE_SUM, CV_32F);
/*
m =
[ 1, 2;
3, 4;
5, 6]
col_sum =
[9, 12]
row_sum =
[3;
7;
11]
*/

And the following code demonstrates its usage for a two-channel matrix.

// two channels
char d[] = {1,2,3,4,5,6};
Mat m(3, 1, CV_8UC2, d);
Mat col_sum_per_channel;
reduce(m, col_sum_per_channel, 0, CV_REDUCE_SUM, CV_32F);
/*
col_sum_per_channel =
[9, 12]
*/
Parameters
srcinput 2D matrix.
dstoutput vector. Its size and type is defined by dim and dtype parameters.
dimdimension 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.
rtypereduction operation that could be one of cv::ReduceTypes
dtypewhen 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

§ repeat() [1/2]

void cv::repeat ( InputArray  src,
int  ny,
int  nx,
OutputArray  dst 
)

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:

\[\texttt{dst} _{ij}= \texttt{src} _{i\mod src.rows, \; j\mod src.cols }\]

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

Parameters
srcinput array to replicate.
nyFlag to specify how many times the src is repeated along the vertical axis.
nxFlag to specify how many times the src is repeated along the horizontal axis.
dstoutput array of the same type as src.
See also
cv::reduce

§ repeat() [2/2]

Mat cv::repeat ( const Mat src,
int  ny,
int  nx 
)

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

Parameters
srcinput array to replicate.
nyFlag to specify how many times the src is repeated along the vertical axis.
nxFlag to specify how many times the src is repeated along the horizontal axis.

§ rotate()

void cv::rotate ( InputArray  src,
OutputArray  dst,
int  rotateCode 
)

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).

Parameters
srcinput array.
dstoutput 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.
rotateCodean enum to specify how to rotate the array; see the enum RotateFlags
See also
transpose , repeat , completeSymm, flip, RotateFlags

§ scaleAdd()

void cv::scaleAdd ( InputArray  src1,
double  alpha,
InputArray  src2,
OutputArray  dst 
)

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. It calculates the sum of a scaled array and another array:

\[\texttt{dst} (I)= \texttt{scale} \cdot \texttt{src1} (I) + \texttt{src2} (I)\]

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

Mat A(3, 3, CV_64F);
...
A.row(0) = A.row(1)*2 + A.row(2);
Parameters
src1first input array.
alphascale factor for the first array.
src2second input array of the same size and type as src1.
dstoutput array of the same size and type as src1.
See also
add, addWeighted, subtract, Mat::dot, Mat::convertTo

§ setIdentity()

void cv::setIdentity ( InputOutputArray  mtx,
const Scalar s = Scalar(1) 
)

Initializes a scaled identity matrix.

The function cv::setIdentity initializes a scaled identity matrix:

\[\texttt{mtx} (i,j)= \fork{\texttt{value}}{ if \(i=j\)}{0}{otherwise}\]

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
mtxmatrix to initialize (not necessarily square).
svalue to assign to diagonal elements.
See also
Mat::zeros, Mat::ones, Mat::setTo, Mat::operator=
Examples:
kalman.cpp.

§ setRNGSeed()

void cv::setRNGSeed ( int  seed)

Sets state of default random number generator.

The function cv::setRNGSeed sets state of default random number generator to custom value.

Parameters
seednew state for default random number generator
See also
RNG, randu, randn

§ solve()

bool cv::solve ( InputArray  src1,
InputArray  src2,
OutputArray  dst,
int  flags = DECOMP_LU 
)

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 ):

\[\texttt{dst} = \arg \min _X \| \texttt{src1} \cdot \texttt{X} - \texttt{src2} \|\]

If DECOMP_LU or DECOMP_CHOLESKY method is used, the function returns 1 if src1 (or \(\texttt{src1}^T\texttt{src1}\) ) 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 \(\texttt{src1}\cdot\texttt{dst}=0\) , the function solve will not do the work. Use SVD::solveZ instead.
Parameters
src1input matrix on the left-hand side of the system.
src2input matrix on the right-hand side of the system.
dstoutput solution.
flagssolution (matrix inversion) method (cv::DecompTypes)
See also
invert, SVD, eigen

§ solveCubic()

int cv::solveCubic ( InputArray  coeffs,
OutputArray  roots 
)

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:

    \[\texttt{coeffs} [0] x^3 + \texttt{coeffs} [1] x^2 + \texttt{coeffs} [2] x + \texttt{coeffs} [3] = 0\]

  • if coeffs is a 3-element vector:

    \[x^3 + \texttt{coeffs} [0] x^2 + \texttt{coeffs} [1] x + \texttt{coeffs} [2] = 0\]

The roots are stored in the roots array.

Parameters
coeffsequation coefficients, an array of 3 or 4 elements.
rootsoutput array of real roots that has 1 or 3 elements.

§ solvePoly()

double cv::solvePoly ( InputArray  coeffs,
OutputArray  roots,
int  maxIters = 300 
)

Finds the real or complex roots of a polynomial equation.

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

\[\texttt{coeffs} [n] x^{n} + \texttt{coeffs} [n-1] x^{n-1} + ... + \texttt{coeffs} [1] x + \texttt{coeffs} [0] = 0\]

Parameters
coeffsarray of polynomial coefficients.
rootsoutput (complex) array of roots.
maxItersmaximum number of iterations the algorithm does.

§ sort()

void cv::sort ( InputArray  src,
OutputArray  dst,
int  flags 
)

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.

Parameters
srcinput single-channel array.
dstoutput array of the same size and type as src.
flagsoperation flags, a combination of cv::SortFlags
See also
sortIdx, randShuffle

§ sortIdx()

void cv::sortIdx ( InputArray  src,
OutputArray  dst,
int  flags 
)

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:

Mat A = Mat::eye(3,3,CV_32F), B;
// B will probably contain
// (because of equal elements in A some permutations are possible):
// [[1, 2, 0], [0, 2, 1], [0, 1, 2]]
Parameters
srcinput single-channel array.
dstoutput integer array of the same size as src.
flagsoperation flags that could be a combination of cv::SortFlags
See also
sort, randShuffle

§ split() [1/2]

void cv::split ( const Mat src,
Mat mvbegin 
)

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

The function cv::split splits a multi-channel array into separate single-channel arrays:

\[\texttt{mv} [c](I) = \texttt{src} (I)_c\]

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

The following example demonstrates how to split a 3-channel matrix into 3 single channel matrices.

char d[] = {1,2,3,4,5,6,7,8,9,10,11,12};
Mat m(2, 2, CV_8UC3, d);
Mat channels[3];
split(m, channels);
/*
channels[0] =
[ 1, 4;
7, 10]
channels[1] =
[ 2, 5;
8, 11]
channels[2] =
[ 3, 6;
9, 12]
*/
Parameters
srcinput multi-channel array.
mvbeginoutput array; the number of arrays must match src.channels(); the arrays themselves are reallocated, if needed.
See also
merge, mixChannels, cvtColor

§ split() [2/2]

void cv::split ( InputArray  m,
OutputArrayOfArrays  mv 
)

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

Parameters
minput multi-channel array.
mvoutput vector of arrays; the arrays themselves are reallocated, if needed.

§ sqrt()

void cv::sqrt ( InputArray  src,
OutputArray  dst 
)

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 .

Parameters
srcinput floating-point array.
dstoutput array of the same size and type as src.

§ subtract()

void cv::subtract ( InputArray  src1,
InputArray  src2,
OutputArray  dst,
InputArray  mask = noArray(),
int  dtype = -1 
)

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:

    \[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src1}(I) - \texttt{src2}(I)) \quad \texttt{if mask}(I) \ne0\]

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

    \[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src1}(I) - \texttt{src2} ) \quad \texttt{if mask}(I) \ne0\]

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

    \[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src1} - \texttt{src2}(I) ) \quad \texttt{if mask}(I) \ne0\]

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

    \[\texttt{dst}(I) = \texttt{saturate} ( \texttt{src2} - \texttt{src1}(I) ) \quad \texttt{if mask}(I) \ne0\]

    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:

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
src1first input array or a scalar.
src2second input array or a scalar.
dstoutput array of the same size and the same number of channels as the input array.
maskoptional operation mask; this is an 8-bit single channel array that specifies elements of the output array to be changed.
dtypeoptional depth of the output array
See also
add, addWeighted, scaleAdd, Mat::convertTo
Examples:
image_alignment.cpp.

§ sum()

Scalar cv::sum ( InputArray  src)

Calculates the sum of array elements.

The function cv::sum calculates and returns the sum of array elements, independently for each channel.

Parameters
srcinput array that must have from 1 to 4 channels.
See also
countNonZero, mean, meanStdDev, norm, minMaxLoc, reduce

§ SVBackSubst()

void cv::SVBackSubst ( InputArray  w,
InputArray  u,
InputArray  vt,
InputArray  rhs,
OutputArray  dst 
)

§ SVDecomp()

void cv::SVDecomp ( InputArray  src,
OutputArray  w,
OutputArray  u,
OutputArray  vt,
int  flags = 0 
)

§ theRNG()

RNG& cv::theRNG ( )

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() .

See also
RNG, randu, randn
Examples:
convexhull.cpp, ffilldemo.cpp, kalman.cpp, minarea.cpp, and watershed.cpp.

§ trace()

Scalar cv::trace ( InputArray  mtx)

Returns the trace of a matrix.

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

\[\mathrm{tr} ( \texttt{mtx} ) = \sum _i \texttt{mtx} (i,i)\]

Parameters
mtxinput matrix.

§ transform()

void cv::transform ( InputArray  src,
OutputArray  dst,
InputArray  m 
)

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 :

\[\texttt{dst} (I) = \texttt{m} \cdot \texttt{src} (I)\]

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

\[\texttt{dst} (I) = \texttt{m} \cdot [ \texttt{src} (I); 1]\]

(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
srcinput array that must have as many channels (1 to 4) as m.cols or m.cols-1.
dstoutput array of the same size and depth as src; it has as many channels as m.rows.
mtransformation 2x2 or 2x3 floating-point matrix.
See also
perspectiveTransform, getAffineTransform, estimateAffine2D, warpAffine, warpPerspective

§ transpose()

void cv::transpose ( InputArray  src,
OutputArray  dst 
)

Transposes a matrix.

The function cv::transpose transposes the matrix src :

\[\texttt{dst} (i,j) = \texttt{src} (j,i)\]

Note
No complex conjugation is done in case of a complex matrix. It should be done separately if needed.
Parameters
srcinput array.
dstoutput array of the same type as src.

§ vconcat() [1/3]

void cv::vconcat ( const Mat src,
size_t  nsrc,
OutputArray  dst 
)

Applies vertical concatenation to given matrices.

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

cv::Mat matArray[] = { cv::Mat(1, 4, CV_8UC1, cv::Scalar(1)),
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
srcinput array or vector of matrices. all of the matrices must have the same number of cols and the same depth.
nsrcnumber of matrices in src.
dstoutput 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)

§ vconcat() [2/3]

void cv::vconcat ( InputArray  src1,
InputArray  src2,
OutputArray  dst 
)

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

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::vconcat(A, B, C);
//C:
//[1, 7;
// 2, 8;
// 3, 9;
// 4, 10;
// 5, 11;
// 6, 12]
Parameters
src1first input array to be considered for vertical concatenation.
src2second input array to be considered for vertical concatenation.
dstoutput 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.

§ vconcat() [3/3]

void cv::vconcat ( InputArrayOfArrays  src,
OutputArray  dst 
)

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

std::vector<cv::Mat> matrices = { cv::Mat(1, 4, CV_8UC1, cv::Scalar(1)),
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
srcinput array or vector of matrices. all of the matrices must have the same number of cols and the same depth
dstoutput array. It has the same number of cols and depth as the src, and the sum of rows of the src. same depth.