Various border types, image boundaries are denoted with |
[borderInterpolate], [copyMakeBorder]
Various border types, image boundaries are denoted with |
[borderInterpolate], [copyMakeBorder]
Various border types, image boundaries are denoted with |
[borderInterpolate], [copyMakeBorder]
Various border types, image boundaries are denoted with |
[borderInterpolate], [copyMakeBorder]
Various border types, image boundaries are denoted with |
[borderInterpolate], [copyMakeBorder]
Various border types, image boundaries are denoted with |
[borderInterpolate], [copyMakeBorder]
performs an inverse 1D or 2D transform instead of the default forward transform.
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.
Cholesky $LL^T$ factorization; the matrix src1 must be symmetrical and positively defined
eigenvalue decomposition; the matrix src1 must be symmetrical
Gaussian elimination with the optimal pivot element chosen.
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 $\\texttt{src1}\\cdot\\texttt{dst}=\\texttt{src2}$
QR factorization; the system can be over-defined and/or the matrix src1 can be singular
singular value decomposition ([SVD]) method; the system can be over-defined and/or the matrix src1 can be singular
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.
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.
performs an inverse 1D or 2D transform instead of the default forward transform.
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).
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.
scales the result: divide it by the number of array elements. Normally, it is combined with DFT_INVERSE.
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.
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 = \\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 = \\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 = \\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 = \\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_L2SQR}\\) } \\]
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}\\)}\\]
[convertScaleAbs], [Mat::convertTo]
input array of 8-bit elements.
look-up table of 256 elements; in case of multi-channel input array, the table should either have a single channel (in this case the same table is used for all channels) or the same number of channels as in the input array.
output array of the same size and number of channels as src, and the same depth as lut.
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 [calcCovarMatrix] function and then inverted
using the invert function (preferably using the [DECOMP_SVD] method, as the most accurate).
first 1D input vector.
second 1D input vector.
inverse covariance matrix.
wrap [PCA::backProject]
wrap PCA::operator()
wrap PCA::operator() and add eigenvalues output parameter
wrap PCA::operator()
wrap PCA::operator() and add eigenvalues output parameter
wrap [PCA::project]
This function calculates the Peak Signal-to-Noise Ratio (PSNR) image quality metric in decibels (dB), between two input arrays src1 and src2. The arrays must have the same type.
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 (e.g. 255 in the case of CV_8U data) and MSE is the mean squared error between the two arrays.
first input array.
second input array of the same size as src1.
the maximum pixel value (255 by default)
wrap [SVD::backSubst]
wrap [SVD::compute]
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.
Saturation is not applied when the arrays have the depth CV_32S. You may even get a negative value in the case of overflow.
cv::abs(const Mat&)
first input array or a scalar.
second input array or a scalar.
output array that has the same size and type as input arrays.
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.
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.
[subtract], [addWeighted], [scaleAdd], [Mat::convertTo]
first input array or a scalar.
second input array or a scalar.
output array that has the same size and number of channels as the input array(s); the depth is defined by dtype or src1/src2.
optional operation mask - 8-bit single channel array, that specifies elements of the output array to be changed.
optional depth of the output array (see the discussion below).
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;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.
[add], [subtract], [scaleAdd], [Mat::convertTo]
first input array.
weight of the first array elements.
second input array of the same size and channel number as src1.
weight of the second array elements.
scalar added to each sum.
output array that has the same size and number of channels as the input arrays.
optional depth of the output array; when both input arrays have the same depth, dtype can be set to -1, which will be equivalent to src1.depth().
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.
first input array or a scalar.
second input array or a scalar.
output array that has the same size and type as the input arrays.
optional operation mask, 8-bit single channel array, that specifies elements of the output array to be changed.
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.
input array.
output array that has the same size and type as the input array.
optional operation mask, 8-bit single channel array, that specifies elements of the output array to be changed.
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.
first input array or a scalar.
second input array or a scalar.
output array that has the same size and type as the input arrays.
optional operation mask, 8-bit single channel array, that specifies elements of the output array to be changed.
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.
first input array or a scalar.
second input array or a scalar.
output array that has the same size and type as the input arrays.
optional operation mask, 8-bit single channel array, that specifies elements of the output array to be changed.
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),
borderInterpolate(-5, img.cols, cv::BORDER_WRAP));Normally, the function is not called directly. It is used inside filtering functions and also in copyMakeBorder.
[copyMakeBorder]
0-based coordinate of the extrapolated pixel along one of the axes, likely <0 or >= len
Length of the array along the corresponding axis.
Border type, one of the BorderTypes, except for BORDER_TRANSPARENT and BORDER_ISOLATED . When borderType==BORDER_CONSTANT , the function always returns -1, regardless of p and len.
The function [cv::calcCovarMatrix] calculates the covariance matrix and, optionally, the mean vector of the set of input vectors.
[PCA], [mulTransposed], [Mahalanobis]
samples stored as separate matrices
number of samples
output covariance matrix of the type ctype and square size.
input or output (depending on the flags) array as the average value of the input vectors.
operation flags as a combination of CovarFlags
type of the matrixl; it equals 'CV_64F' by default.
This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
use [COVAR_ROWS] or [COVAR_COLS] flag
samples stored as rows/columns of a single matrix.
output covariance matrix of the type ctype and square size.
input or output (depending on the flags) array as the average value of the input vectors.
operation flags as a combination of CovarFlags
type of the matrixl; it equals 'CV_64F' by default.
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.
[Sobel], [Scharr]
array of x-coordinates; this must be a single-precision or double-precision floating-point array.
array of y-coordinates, that must have the same size and same type as x.
output array of magnitudes of the same size and type as x.
output array of angles that has the same size and type as x; the angles are measured in radians (from 0 to 2*Pi) or in degrees (0 to 360 degrees).
a flag, indicating whether the angles are measured in radians (which is by default), or in degrees.
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.
input array.
a flag, indicating whether the functions quietly return false when the array elements are out of range or they throw an exception.
optional output parameter, when not NULL, must be a pointer to array of src.dims elements.
inclusive lower boundary of valid values range.
exclusive upper boundary of valid values range.
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;
...[checkRange], [min], [max], [threshold]
first input array or a scalar; when it is an array, it must have a single channel.
second input array or a scalar; when it is an array, it must have a single channel.
output array of type ref CV_8U that has the same size and the same number of channels as the input arrays.
a flag, that specifies correspondence between the arrays (cv::CmpTypes)
The function [cv::completeSymm] copies the lower or the upper half of a square matrix to its another half. The matrix diagonal remains unchanged:
$\\texttt{m}_{ij}=\\texttt{m}_{ji}$ for $i > j$ if lowerToUpper=false
$\\texttt{m}_{ij}=\\texttt{m}_{ji}$ for $i < j$ if lowerToUpper=true
[flip], [transpose]
input-output floating-point square matrix.
operation flag; if true, the lower half is copied to the upper half. Otherwise, the upper half is copied to the lower half.
This function converts FP32 (single precision floating point) from/to FP16 (half precision floating point). CV_16S format is used to represent FP16 data. There are two use modes (src -> dst): CV_32F -> CV_16S and CV_16S -> CV_32F. 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.
input array.
output array.
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[Mat::convertTo], cv::abs(const Mat&)
input array.
output array.
optional scale factor.
optional delta added to the scaled values.
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
cvtColor(rgb, gray, COLOR_RGB2GRAY);
// form a border in-place
copyMakeBorder(gray, gray_buf, border, border,
border, border, BORDER_REPLICATE);
// now do some custom filtering ...
...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].
[borderInterpolate]
Source image.
Destination image of the same type as src and the size Size(src.cols+left+right, src.rows+top+bottom) .
the top pixels
the bottom pixels
the left pixels
Parameter specifying how many pixels in each direction from the source image rectangle to extrapolate. For example, top=1, bottom=1, left=1, right=1 mean that 1 pixel-wide border needs to be built.
Border type. See borderInterpolate for details.
Border value if borderType==BORDER_CONSTANT .
source matrix.
Destination matrix. If it does not have a proper size or type before the operation, it is reallocated.
Operation mask of the same size as *this. Its non-zero elements indicate which matrix elements need to be copied. The mask has to be of type CV_8U and can have 1 or multiple channels.
The function returns the number of non-zero elements in src : \\[\\sum _{I: \\; \\texttt{src} (I)
\\ne0 } 1\\]
[mean], [meanStdDev], [norm], [minMaxLoc], [calcCovarMatrix]
single-channel 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.
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);[dft] , [getOptimalDFTSize] , [idct]
input floating-point array.
output array of the same size and type as src .
transformation flags as a combination of cv::DftFlags (DCT_*)
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.
[trace], [invert], [solve], [eigen], [MatrixExpressions]
input matrix that must have CV_32FC1 or CV_64FC1 type and square size.
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 .
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
[dct] , [getOptimalDFTSize] , [mulSpectrums], [filter2D] , [matchTemplate] , [flip] , [cartToPolar] , [magnitude] , [phase]
input array that could be real or complex.
output array whose size and type depends on the flags .
transformation flags, representing a combination of the DftFlags
when the parameter is not zero, the function assumes that only the first nonzeroRows rows of the input array (DFT_INVERSE is not set) or only the first nonzeroRows of the output array (DFT_INVERSE is set) contain non-zeros, thus, the function can handle the rest of the rows more efficiently and save some time; this technique is very useful for calculating array cross-correlation or convolution using DFT.
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))}\\]
Different channels of multi-channel arrays are processed independently.
For integer types when src2(I) is zero, dst(I) will also be zero.
In case of floating point data there is no special defined behavior for zero src2(I) values. Regular floating-point division is used. Expect correct IEEE-754 behaviour for floating-point data (with NaN, Inf result values).
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.
[multiply], [add], [subtract]
first input array.
second input array of the same size and type as src1.
output array of the same size and type as src2.
scalar factor.
optional depth of the output array; if -1, dst will have depth src2.depth(), but in case of an array-by-array division, you can only pass -1 when src1.depth()==src2.depth().
This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
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()Use [cv::eigenNonSymmetric] for calculation of real eigenvalues and eigenvectors of non-symmetric matrix.
[eigenNonSymmetric], [completeSymm] , [PCA]
input matrix that must have CV_32FC1 or CV_64FC1 type, square size and be symmetrical (src ^T^ == src).
output vector of eigenvalues of the same type as src; the eigenvalues are stored in the descending order.
output matrix of eigenvectors; it has the same size and type as src; the eigenvectors are stored as subsequent matrix rows, in the same order as the corresponding eigenvalues.
Assumes real eigenvalues. The function calculates eigenvalues and eigenvectors (optional) of the square matrix src:
src*eigenvectors.row(i).t() = eigenvalues.at<srcType>(i)*eigenvectors.row(i).t()[eigen]
input matrix (CV_32FC1 or CV_64FC1 type).
output vector of eigenvalues (type is the same type as src).
output matrix of eigenvectors (type is the same type as src). The eigenvectors are stored as subsequent matrix rows, in the same order as the corresponding eigenvalues.
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.
[log] , [cartToPolar] , [polarToCart] , [phase] , [pow] , [sqrt] , [magnitude]
input array.
output array of the same size and type as src.
[mixChannels], [split]
input array
output array
index of channel to extract
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::vectorcv::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];single-channel array
the output array, type of cv::Mat or std::vector
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).
[transpose] , [repeat] , [completeSymm]
input array.
output array of the same size and type as src.
a flag to specify how to flip the array; 0 means flipping around the x-axis and positive value (for example, 1) means flipping around y-axis. Negative value (for example, -1) means flipping around both axes.
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();[mulTransposed] , [transform]
first multiplied input matrix that could be real(CV_32FC1, CV_64FC1) or complex(CV_32FC2, CV_64FC2).
second multiplied input matrix of the same type as src1.
weight of the matrix product.
third optional delta matrix added to the matrix product; it should have the same type as src1 and src2.
weight of src3.
output matrix; it has the proper size and the same type as input matrices.
operation flags (cv::GemmFlags)
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 = 55322) 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.
[dft] , [dct] , [idft] , [idct] , [mulSpectrums]
vector size.
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(2)),
cv::Mat(4, 1, CV_8UC1, cv::Scalar(3)),};
cv::Mat out;
cv::hconcat( matArray, 3, out );
//out:
//[1, 2, 3;
// 1, 2, 3;
// 1, 2, 3;
// 1, 2, 3][cv::vconcat(const Mat*, size_t, OutputArray)],
[cv::vconcat(InputArrayOfArrays, OutputArray)] and
[cv::vconcat(InputArray, InputArray, OutputArray)]
input array or vector of matrices. all of the matrices must have the same number of rows and the same depth.
number of matrices in src.
output array. It has the same number of rows and depth as the src, and the sum of cols of the src.
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::Mat C;
cv::hconcat(A, B, C);
//C:
//[1, 4, 7, 10;
// 2, 5, 8, 11;
// 3, 6, 9, 12]first input array to be considered for horizontal concatenation.
second input array to be considered for horizontal concatenation.
output array. It has the same number of rows and depth as the src1 and src2, and the sum of cols of the src1 and src2.
This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
std::vector<cv::Mat> matrices = { cv::Mat(4, 1, CV_8UC1, cv::Scalar(1)),
cv::Mat(4, 1, CV_8UC1, cv::Scalar(2)),
cv::Mat(4, 1, CV_8UC1, cv::Scalar(3)),};
cv::Mat out;
cv::hconcat( matrices, out );
//out:
//[1, 2, 3;
// 1, 2, 3;
// 1, 2, 3;
// 1, 2, 3]input array or vector of matrices. all of the matrices must have the same number of rows and the same depth.
output array. It has the same number of rows and depth as the src, and the sum of cols of the src. same depth.
idct(src, dst, flags) is equivalent to dct(src, dst, flags | DCT_INVERSE).
[dct], [dft], [idft], [getOptimalDFTSize]
input floating-point single-channel array.
output array of the same size and type as src.
operation flags.
idft(src, dst, flags) is equivalent to dft(src, dst, flags | [DFT_INVERSE]) .
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.
[dft], [dct], [idct], [mulSpectrums], [getOptimalDFTSize]
input floating-point real or complex array.
output array whose size and type depend on the flags.
operation flags (see dft and DftFlags).
number of dst rows to process; the rest of the rows have undefined content (see the convolution sample in dft description.
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.
first input array.
inclusive lower boundary array or a scalar.
inclusive upper boundary array or a scalar.
output array of the same size as src and CV_8U type.
[mixChannels], [merge]
input array
output array
index of channel for insertion
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.
[solve], [SVD]
input floating-point M x N matrix.
output matrix of N x M size and the same type as src.
inversion method (cv::DecompTypes)
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.
[exp], [cartToPolar], [polarToCart], [phase], [pow], [sqrt], [magnitude]
input array.
output array of the same size and type as src .
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}\\]
[cartToPolar], [polarToCart], [phase], [sqrt]
floating-point array of x-coordinates of the vectors.
floating-point array of y-coordinates of the vectors; it must have the same size as x.
output array of the same size and type as x.
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} )\\]
[min], [compare], [inRange], [minMaxLoc], [MatrixExpressions]
first input array.
second input array of the same size and type as src1 .
output array of the same size and type as src1.
This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. needed to avoid conflicts with const _Tp& std::min(const _Tp&, const _Tp&, _Compare)
This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. needed to avoid conflicts with const _Tp& std::min(const _Tp&, const _Tp&, _Compare)
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)
[countNonZero], [meanStdDev], [norm], [minMaxLoc]
input array that should have from 1 to 4 channels so that the result can be stored in Scalar_ .
optional operation mask.
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).
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 .
[countNonZero], [mean], [norm], [minMaxLoc], [calcCovarMatrix]
input array that should have from 1 to 4 channels so that the results can be stored in Scalar_ 's.
output parameter: calculated mean value.
output parameter: calculated standard deviation.
optional operation mask.
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
\/[mixChannels], [split], [Mat::reshape]
input array of matrices to be merged; all the matrices in mv must have the same size and the same depth.
number of input matrices when mv is a plain C array; it must be greater than zero.
output array of the same size and the same depth as mv[0]; The number of channels will be equal to the parameter count.
This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
input vector of matrices to be merged; all the matrices in mv must have the same size and the same depth.
output array of the same size and the same depth as mv[0]; The number of channels will be the total number of channels in the matrix array.
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} )\\]
[max], [compare], [inRange], [minMaxLoc]
first input array.
second input array of the same size and type as src1.
output array of the same size and type as src1.
This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. needed to avoid conflicts with const _Tp& std::min(const _Tp&, const _Tp&, _Compare)
This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. needed to avoid conflicts with const _Tp& std::min(const _Tp&, const _Tp&, _Compare)
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.
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)).
input single-channel array.
pointer to the returned minimum value; NULL is used if not required.
pointer to the returned maximum value; NULL is used if not required.
pointer to the returned minimum location (in nD case); NULL is used if not required; Otherwise, it must point to an array of src.dims elements, the coordinates of the minimum element in each dimension are stored there sequentially.
pointer to the returned maximum location (in nD case). NULL is used if not required.
specified array region
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 .
[max], [min], [compare], [inRange], extractImageCOI, [mixChannels], [split], [Mat::reshape]
input single-channel array.
pointer to the returned minimum value; NULL is used if not required.
pointer to the returned maximum value; NULL is used if not required.
pointer to the returned minimum location (in 2D case); NULL is used if not required.
pointer to the returned maximum location (in 2D case); NULL is used if not required.
optional mask used to select a sub-array.
This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
input single-channel array.
pointer to the returned minimum value; NULL is used if not required.
pointer to the returned maximum value; NULL is used if not required.
pointer to the returned minimum location (in nD case); NULL is used if not required; Otherwise, it must point to an array of src.dims elements, the coordinates of the minimum element in each dimension are stored there sequentially.
pointer to the returned maximum location (in nD case). NULL is used if not required.
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 );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.
[split], [merge], [extractChannel], [insertChannel], [cvtColor]
input array or vector of matrices; all of the matrices must have the same size and the same depth.
number of matrices in src.
output array or vector of matrices; all the matrices must be allocated; their size and depth must be the same as in src[0].
number of matrices in dst.
array of index pairs specifying which channels are copied and where; fromTo[k2] is a 0-based index of the input channel in src, fromTo[k2+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 .
number of index pairs in fromTo.
This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
input array or vector of matrices; all of the matrices must have the same size and the same depth.
output array or vector of matrices; all the matrices must be allocated; their size and depth must be the same as in src[0].
array of index pairs specifying which channels are copied and where; fromTo[k2] is a 0-based index of the input channel in src, fromTo[k2+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 .
number of index pairs in fromTo.
This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
input array or vector of matrices; all of the matrices must have the same size and the same depth.
output array or vector of matrices; all the matrices must be allocated; their size and depth must be the same as in src[0].
array of index pairs specifying which channels are copied and where; fromTo[k2] is a 0-based index of the input channel in src, fromTo[k2+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 .
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).
first input array.
second input array of the same size and type as src1 .
output array of the same size and type as src1 .
operation flags; currently, the only supported flag is cv::DFT_ROWS, which indicates that each row of src1 and src2 is an independent 1D Fourier spectrum. If you do not want to use this flag, then simply add a 0 as value.
optional flag that conjugates the second input array before the multiplication (true) or not (false).
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'
[calcCovarMatrix], [gemm], [repeat], [reduce]
input single-channel matrix. Note that unlike gemm, the function can multiply not only floating-point matrices.
output square matrix.
Flag specifying the multiplication ordering. See the description below.
Optional delta matrix subtracted from src before the multiplication. When the matrix is empty ( delta=noArray() ), it is assumed to be zero, that is, nothing is subtracted. If it has the same size as src , it is simply subtracted. Otherwise, it is "repeated" (see repeat ) to cover the full src and then subtracted. Type of the delta matrix, when it is not empty, must be the same as the type of created output matrix. See the dtype parameter description below.
Optional scale factor for the matrix product.
Optional type of the output matrix. When it is negative, the output matrix will have the same type as src . Otherwise, it will be type=CV_MAT_DEPTH(dtype) that should be either CV_32F or CV_64F .
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 .
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.
[add], [subtract], [divide], [scaleAdd], [addWeighted], [accumulate], [accumulateProduct], [accumulateSquare], [Mat::convertTo]
first input array.
second input array of the same size and the same type as src1.
output array of the same size and type as src1.
optional scale factor.
optional depth of the output array
This version of [norm] calculates the absolute norm of src1. The type of norm to calculate is specified using [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) $.
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.
first input array.
type of the norm (see NormTypes).
optional operation mask; it must have the same size as src1 and CV_8UC1 type.
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 [NormTypes].
first input array.
second input array of the same size and the same type as src1.
type of the norm (see NormTypes).
optional operation mask; it must have the same size as src1 and CV_8UC1 type.
This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
first input array.
type of the norm (see NormTypes).
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);[norm], [Mat::convertTo], [SparseMat::convertTo]
input array.
output array of the same size as src .
norm value to normalize to or the lower range boundary in case of the range normalization.
upper range boundary in case of the range normalization; it is not used for the norm normalization.
normalization type (see cv::NormTypes).
when negative, the output array has the same type as src; otherwise, it has the same number of channels as src and the depth =CV_MAT_DEPTH(dtype).
optional operation mask.
This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
input array.
output array of the same size as src .
norm value to normalize to or the lower range boundary in case of the range normalization.
normalization type (see cv::NormTypes).
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.
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 .
[transform], [warpPerspective], [getPerspectiveTransform], [findHomography]
input two-channel or three-channel floating-point array; each element is a 2D/3D vector to be transformed.
output array of the same size and type as src.
3x3 or 4x4 floating-point transformation matrix.
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.
input floating-point array of x-coordinates of 2D vectors.
input array of y-coordinates of 2D vectors; it must have the same size and the same type as x.
output array of vector angles; it has the same size and same type as x .
when true, the function calculates the angle in degrees, otherwise, they are measured in radians.
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.
[cartToPolar], [magnitude], [phase], [exp], [log], [pow], [sqrt]
input floating-point array of magnitudes of 2D vectors; it can be an empty matrix (=Mat()), in this case, the function assumes that all the magnitudes are =1; if it is not empty, it must have the same size and type as angle.
input floating-point array of angles of 2D vectors.
output array of x-coordinates of 2D vectors; it has the same size and type as angle.
output array of y-coordinates of 2D vectors; it has the same size and type as angle.
when true, the input angles are measured in degrees, otherwise, they are measured in radians.
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.
[sqrt], [exp], [log], [cartToPolar], [polarToCart]
input array.
exponent of power.
output array of the same size and type as src.
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.rowsdst.colsiterFactor .
[RNG], [sort]
input/output numerical 1D array.
scale factor that determines the number of random swap operations (see the details below).
optional random number generator used for shuffling; if it is zero, theRNG () is used instead.
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.
[RNG], [randu]
output array of random numbers; the array must be pre-allocated and have 1 to 4 channels.
mean value (expectation) of the generated random numbers.
standard deviation of the generated random numbers; it can be either a vector (in which case a diagonal standard deviation matrix is assumed) or a square matrix.
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\\]
[RNG], [randn], [theRNG]
output array of random numbers; the array must be pre-allocated.
inclusive lower boundary of the generated random numbers.
exclusive upper boundary of the generated random numbers.
The function [reduce] reduces the matrix to a vector by treating the matrix rows/columns as a set of 1D vectors and performing the specified operation on the vectors until a single row/column is obtained. For example, the function can be used to compute horizontal and vertical projections of a raster image. In case of [REDUCE_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, REDUCE_SUM, CV_32F);
reduce(m, row_sum, 1, 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, REDUCE_SUM, CV_32F);
/*
col_sum_per_channel =
[9, 12]
\/[repeat]
input 2D matrix.
output vector. Its size and type is defined by dim and dtype parameters.
dimension index along which the matrix is reduced. 0 means that the matrix is reduced to a single row. 1 means that the matrix is reduced to a single column.
reduction operation that could be one of ReduceTypes
when negative, the output vector will have the same type as the input matrix, otherwise, its type will be CV_MAKE_TYPE(CV_MAT_DEPTH(dtype), src.channels()).
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].
[cv::reduce]
input array to replicate.
Flag to specify how many times the src is repeated along the vertical axis.
Flag to specify how many times the src is repeated along the horizontal axis.
output array of the same type as src.
This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
input array to replicate.
Flag to specify how many times the src is repeated along the vertical axis.
Flag to specify how many times the src is repeated along the horizontal axis.
[transpose] , [repeat] , [completeSymm], [flip], [RotateFlags]
input array.
output array of the same type as src. The size is the same with ROTATE_180, and the rows and cols are switched for ROTATE_90_CLOCKWISE and ROTATE_90_COUNTERCLOCKWISE.
an enum to specify how to rotate the array; see the enum RotateFlags
The function scaleAdd is one of the classical primitive linear algebra operations, known as DAXPY or
SAXPY in . 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);[add], [addWeighted], [subtract], [Mat::dot], [Mat::convertTo]
first input array.
scale factor for the first array.
second input array of the same size and type as src1.
output array of the same size and type as src1.
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]][Mat::zeros], [Mat::ones], [Mat::setTo], [Mat::operator=]
matrix to initialize (not necessarily square).
value to assign to diagonal elements.
The function [cv::setRNGSeed] sets state of default random number generator to custom value.
[RNG], [randu], [randn]
new state for default random number generator
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.
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.
[invert], [SVD], [eigen]
input matrix on the left-hand side of the system.
input matrix on the right-hand side of the system.
output solution.
solution (matrix inversion) method (DecompTypes)
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.
number of real roots. It can be 0, 1 or 2.
equation coefficients, an array of 3 or 4 elements.
output array of real roots that has 1 or 3 elements.
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\\]
array of polynomial coefficients.
output (complex) array of roots.
maximum number of iterations the algorithm does.
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.
[sortIdx], [randShuffle]
input single-channel array.
output array of the same size and type as src.
operation flags, a combination of SortFlags
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;
sortIdx(A, B, SORT_EVERY_ROW + SORT_ASCENDING);
// B will probably contain
// (because of equal elements in A some permutations are possible):
// [[1, 2, 0], [0, 2, 1], [0, 1, 2]][sort], [randShuffle]
input single-channel array.
output integer array of the same size as src.
operation flags that could be a combination of cv::SortFlags
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]
\/[merge], [mixChannels], [cvtColor]
input multi-channel array.
output array; the number of arrays must match src.channels(); the arrays themselves are reallocated, if needed.
This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
input multi-channel array.
output vector of arrays; the arrays themselves are reallocated, if needed.
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 .
input floating-point array.
output array of the same size and type as src.
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}
The reverse difference between a scalar and an array in the case ofSubRS:\[\texttt{dst}(I) =
\texttt{saturate} ( \texttt{src2} - \texttt{src1}(I) ) \quad \texttt{if mask}(I) \ne0\]`
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.
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.
[add], [addWeighted], [scaleAdd], [Mat::convertTo]
first input array or a scalar.
second input array or a scalar.
output array of the same size and the same number of channels as the input array.
optional operation mask; this is an 8-bit single channel array that specifies elements of the output array to be changed.
optional depth of the output array
The function [cv::sum] calculates and returns the sum of array elements, independently for each channel.
[countNonZero], [mean], [meanStdDev], [norm], [minMaxLoc], [reduce]
input array that must have from 1 to 4 channels.
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() .
[RNG], [randu], [randn]
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)\\]
input matrix.
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.
[perspectiveTransform], [getAffineTransform], [estimateAffine2D], [warpAffine], [warpPerspective]
input array that must have as many channels (1 to 4) as m.cols or m.cols-1.
output array of the same size and depth as src; it has as many channels as m.rows.
transformation 2x2 or 2x3 floating-point matrix.
The function [cv::transpose] transposes the matrix src : \\[\\texttt{dst} (i,j) = \\texttt{src}
(j,i)\\]
No complex conjugation is done in case of a complex matrix. It should be done separately if needed.
input array.
output array of the same type as src.
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(2)),
cv::Mat(1, 4, CV_8UC1, cv::Scalar(3)),};
cv::Mat out;
cv::vconcat( matArray, 3, out );
//out:
//[1, 1, 1, 1;
// 2, 2, 2, 2;
// 3, 3, 3, 3][cv::hconcat(const Mat*, size_t, OutputArray)],
[cv::hconcat(InputArrayOfArrays, OutputArray)] and
[cv::hconcat(InputArray, InputArray, OutputArray)]
input array or vector of matrices. all of the matrices must have the same number of cols and the same depth.
number of matrices in src.
output array. It has the same number of cols and depth as the src, and the sum of rows of the src.
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::Mat C;
cv::vconcat(A, B, C);
//C:
//[1, 7;
// 2, 8;
// 3, 9;
// 4, 10;
// 5, 11;
// 6, 12]first input array to be considered for vertical concatenation.
second input array to be considered for vertical concatenation.
output array. It has the same number of cols and depth as the src1 and src2, and the sum of rows of the src1 and src2.
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(2)),
cv::Mat(1, 4, CV_8UC1, cv::Scalar(3)),};
cv::Mat out;
cv::vconcat( matrices, out );
//out:
//[1, 1, 1, 1;
// 2, 2, 2, 2;
// 3, 3, 3, 3]input array or vector of matrices. all of the matrices must have the same number of cols and the same depth
output array. It has the same number of cols and depth as the src, and the sum of rows of the src. same depth.
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Various border types, image boundaries are denoted with
|[borderInterpolate], [copyMakeBorder]