Calculates an absolute value of each matrix element.
MatExpr abs
(const Mat& m)¶
MatExpr abs
(const MatExpr& e)¶Parameters: |
|
---|
abs
is a meta-function that is expanded to one of absdiff()
or convertScaleAbs()
forms:
C = abs(A-B)
is equivalent toabsdiff(A, B, C)
C = abs(A)
is equivalent toabsdiff(A, Scalar::all(0), C)
C = Mat_<Vec<uchar,n> >(abs(A*alpha + beta))
is equivalent toconvertScaleAbs(A, C, alpha, beta)
The output matrix has the same size and the same type as the input one except for the last case, where C
is depth=CV_8U
.
See also
Calculates the per-element absolute difference between two arrays or between an array and a scalar.
void absdiff
(InputArray src1, InputArray src2, OutputArray dst)¶
cv2.
absdiff
(src1, src2[, dst]) → dst¶
void cvAbsDiff
(const CvArr* src1, const CvArr* src2, CvArr* dst)¶
void cvAbsDiffS
(const CvArr* src, CvArr* dst, CvScalar value)¶
cv.
AbsDiff
(src1, src2, dst) → None¶
cv.
AbsDiffS
(src, dst, value) → None¶Parameters: |
|
---|
The function absdiff
calculates:
Absolute difference between two arrays when they have the same size and type:
Absolute difference between an array and a scalar when the second array is constructed from
Scalar
or has as many elements as the number of channels insrc1
: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 insrc2
: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.
See also
Calculates the per-element sum of two arrays or an array and a scalar.
void add
(InputArray src1, InputArray src2, OutputArray dst, InputArray mask=noArray(), int dtype=-1)¶
cv2.
add
(src1, src2[, dst[, mask[, dtype]]]) → dst¶
void cvAdd
(const CvArr* src1, const CvArr* src2, CvArr* dst, const CvArr* mask=NULL)¶
void cvAddS
(const CvArr* src, CvScalar value, CvArr* dst, const CvArr* mask=NULL)¶
cv.
Add
(src1, src2, dst, mask=None) → None¶
cv.
AddS
(src, value, dst, mask=None) → None¶Parameters: |
|
---|
The function add
calculates:
Sum of two arrays when both input arrays have the same size and the same number of channels:
Sum of an array and a scalar when
src2
is constructed fromScalar
or has the same number of elements assrc1.channels()
:Sum of a scalar and an array when
src1
is constructed fromScalar
or has the same number of elements assrc2.channels()
:where
I
is a multi-dimensional index of array elements. In case of multi-channel arrays, each channel is processed independently.
The first function in the list above can be replaced with matrix expressions:
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.
See also
subtract()
,
addWeighted()
,
scaleAdd()
,
Mat::convertTo()
,
Matrix Expressions
Calculates the weighted sum of two arrays.
void addWeighted
(InputArray src1, double alpha, InputArray src2, double beta, double gamma, OutputArray dst, int dtype=-1)¶
cv2.
addWeighted
(src1, alpha, src2, beta, gamma[, dst[, dtype]]) → dst¶
void cvAddWeighted
(const CvArr* src1, double alpha, const CvArr* src2, double beta, double gamma, CvArr* dst)¶
cv.
AddWeighted
(src1, alpha, src2, beta, gamma, dst) → None¶Parameters: |
|
---|
The function addWeighted
calculates the weighted sum of two arrays as follows:
where I
is a multi-dimensional index of array elements. In case of multi-channel arrays, each channel is processed independently.
The function can be replaced with a matrix expression:
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.
See also
add()
,
subtract()
,
scaleAdd()
,
Mat::convertTo()
,
Matrix Expressions
Calculates the per-element bit-wise conjunction of two arrays or an array and a scalar.
void bitwise_and
(InputArray src1, InputArray src2, OutputArray dst, InputArray mask=noArray())¶
cv2.
bitwise_and
(src1, src2[, dst[, mask]]) → dst¶
void cvAnd
(const CvArr* src1, const CvArr* src2, CvArr* dst, const CvArr* mask=NULL)¶
void cvAndS
(const CvArr* src, CvScalar value, CvArr* dst, const CvArr* mask=NULL)¶
cv.
And
(src1, src2, dst, mask=None) → None¶
cv.
AndS
(src, value, dst, mask=None) → None¶Parameters: |
|
---|
The function calculates the per-element bit-wise logical conjunction for:
Two arrays when
src1
andsrc2
have the same size:An array and a scalar when
src2
is constructed fromScalar
or has the same number of elements assrc1.channels()
:A scalar and an array when
src1
is constructed fromScalar
or has the same number of elements assrc2.channels()
:
In case of floating-point arrays, their machine-specific bit representations (usually IEEE754-compliant) are used for the operation. In case of multi-channel arrays, each channel is processed independently. In the second and third cases above, the scalar is first converted to the array type.
Inverts every bit of an array.
void bitwise_not
(InputArray src, OutputArray dst, InputArray mask=noArray())¶
cv2.
bitwise_not
(src[, dst[, mask]]) → dst¶
void cvNot
(const CvArr* src, CvArr* dst)¶
cv.
Not
(src, dst) → None¶Parameters: |
|
---|
The function calculates per-element bit-wise inversion of the input array:
In case of a floating-point input array, its machine-specific bit representation (usually IEEE754-compliant) is used for the operation. In case of multi-channel arrays, each channel is processed independently.
Calculates the per-element bit-wise disjunction of two arrays or an array and a scalar.
void bitwise_or
(InputArray src1, InputArray src2, OutputArray dst, InputArray mask=noArray())¶
cv2.
bitwise_or
(src1, src2[, dst[, mask]]) → dst¶
void cvOr
(const CvArr* src1, const CvArr* src2, CvArr* dst, const CvArr* mask=NULL)¶
void cvOrS
(const CvArr* src, CvScalar value, CvArr* dst, const CvArr* mask=NULL)¶
cv.
Or
(src1, src2, dst, mask=None) → None¶
cv.
OrS
(src, value, dst, mask=None) → None¶Parameters: |
|
---|
The function calculates the per-element bit-wise logical disjunction for:
Two arrays when
src1
andsrc2
have the same size:An array and a scalar when
src2
is constructed fromScalar
or has the same number of elements assrc1.channels()
:A scalar and an array when
src1
is constructed fromScalar
or has the same number of elements assrc2.channels()
:
In case of floating-point arrays, their machine-specific bit representations (usually IEEE754-compliant) are used for the operation. In case of multi-channel arrays, each channel is processed independently. In the second and third cases above, the scalar is first converted to the array type.
Calculates the per-element bit-wise “exclusive or” operation on two arrays or an array and a scalar.
void bitwise_xor
(InputArray src1, InputArray src2, OutputArray dst, InputArray mask=noArray())¶
cv2.
bitwise_xor
(src1, src2[, dst[, mask]]) → dst¶
void cvXor
(const CvArr* src1, const CvArr* src2, CvArr* dst, const CvArr* mask=NULL)¶
void cvXorS
(const CvArr* src, CvScalar value, CvArr* dst, const CvArr* mask=NULL)¶
cv.
Xor
(src1, src2, dst, mask=None) → None¶
cv.
XorS
(src, value, dst, mask=None) → None¶Parameters: |
|
---|
The function calculates the per-element bit-wise logical “exclusive-or” operation for:
Two arrays when
src1
andsrc2
have the same size:An array and a scalar when
src2
is constructed fromScalar
or has the same number of elements assrc1.channels()
:A scalar and an array when
src1
is constructed fromScalar
or has the same number of elements assrc2.channels()
:
In case of floating-point arrays, their machine-specific bit representations (usually IEEE754-compliant) are used for the operation. In case of multi-channel arrays, each channel is processed independently. In the 2nd and 3rd cases above, the scalar is first converted to the array type.
Calculates the covariance matrix of a set of vectors.
void calcCovarMatrix
(const Mat* samples, int nsamples, Mat& covar, Mat& mean, int flags, int ctype=CV_64F)¶
void calcCovarMatrix
(InputArray samples, OutputArray covar, OutputArray mean, int flags, int ctype=CV_64F)¶
cv2.
calcCovarMatrix
(samples, flags[, covar[, mean[, ctype]]]) → covar, mean¶
void cvCalcCovarMatrix
(const CvArr** vects, int count, CvArr* cov_mat, CvArr* avg, int flags)¶
cv.
CalcCovarMatrix
(vects, covMat, avg, flags) → None¶Parameters: |
|
---|
The functions calcCovarMatrix
calculate the covariance matrix and, optionally, the mean vector of the set of input vectors.
See also
Calculates the magnitude and angle of 2D vectors.
void cartToPolar
(InputArray x, InputArray y, OutputArray magnitude, OutputArray angle, bool angleInDegrees=false)¶
cv2.
cartToPolar
(x, y[, magnitude[, angle[, angleInDegrees]]]) → magnitude, angle¶
void cvCartToPolar
(const CvArr* x, const CvArr* y, CvArr* magnitude, CvArr* angle=NULL, int angle_in_degrees=0 )¶
cv.
CartToPolar
(x, y, magnitude, angle=None, angleInDegrees=0) → None¶Parameters: |
|
---|
The function cartToPolar
calculates either the magnitude, angle, or both for every 2D vector (x(I),y(I)):
The angles are calculated with accuracy about 0.3 degrees. For the point (0,0), the angle is set to 0.
Checks every element of an input array for invalid values.
bool checkRange
(InputArray a, bool quiet=true, Point* pos=0, double minVal=-DBL_MAX, double maxVal=DBL_MAX )¶
cv2.
checkRange
(a[, quiet[, minVal[, maxVal]]]) → retval, pos¶Parameters: |
|
---|
The functions checkRange
check that every array element is neither NaN nor
infinite. When minVal < -DBL_MAX
and maxVal < DBL_MAX
, the functions also check that each value is between minVal
and maxVal
. In case of multi-channel arrays, each channel is processed independently.
If some values are out of range, position of the first outlier is stored in pos
(when
pos != NULL
). Then, the functions either return false (when quiet=true
) or throw an exception.
Performs the per-element comparison of two arrays or an array and scalar value.
void compare
(InputArray src1, InputArray src2, OutputArray dst, int cmpop)¶
cv2.
compare
(src1, src2, cmpop[, dst]) → dst¶
void cvCmp
(const CvArr* src1, const CvArr* src2, CvArr* dst, int cmp_op)¶
cv.
Cmp
(src1, src2, dst, cmpOp) → None¶
void cvCmpS
(const CvArr* src, double value, CvArr* dst, int cmp_op)¶
cv.
CmpS
(src, value, dst, cmpOp) → None¶Parameters: |
|
---|
The function compares:
Elements of two arrays when
src1
andsrc2
have the same size:Elements of
src1
with a scalarsrc2
whensrc2
is constructed fromScalar
or has a single element:
src1
with elements ofsrc2
whensrc1
is constructed fromScalar
or has a single element:
When the comparison result is true, the corresponding element of output array is set to 255. The comparison operations can be replaced with the equivalent matrix expressions:
Mat dst1 = src1 >= src2;
Mat dst2 = src1 < 8;
...
See also
Copies the lower or the upper half of a square matrix to another half.
void completeSymm
(InputOutputArray mtx, bool lowerToUpper=false)¶
cv2.
completeSymm
(mtx[, lowerToUpper]) → None¶Parameters: |
|
---|
The function completeSymm
copies the lower half of a square matrix to its another half. The matrix diagonal remains unchanged:
- for if
lowerToUpper=false
- for if
lowerToUpper=true
See also
Scales, calculates absolute values, and converts the result to 8-bit.
void convertScaleAbs
(InputArray src, OutputArray dst, double alpha=1, double beta=0)¶
cv2.
convertScaleAbs
(src[, dst[, alpha[, beta]]]) → dst¶
void cvConvertScaleAbs
(const CvArr* src, CvArr* dst, double scale=1, double shift=0)¶
cv.
ConvertScaleAbs
(src, dst, scale=1.0, shift=0.0) → None¶Parameters: |
|
---|
On each element of the input array, the function convertScaleAbs
performs three operations sequentially: scaling, taking an absolute value, conversion to an unsigned 8-bit type:
In case of multi-channel arrays, the function processes each channel independently. When the output is not 8-bit, the operation can be emulated by calling the Mat::convertTo
method (or by using matrix expressions) and then by calculating an absolute value of the result. For example:
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
See also
Counts non-zero array elements.
int countNonZero
(InputArray src)¶
cv2.
countNonZero
(src) → retval¶
int cvCountNonZero
(const CvArr* arr)¶
cv.
CountNonZero
(arr) → int¶Parameters: | src – single-channel array. |
---|
The function returns the number of non-zero elements in src
:
See also
mean()
,
meanStdDev()
,
norm()
,
minMaxLoc()
,
calcCovarMatrix()
Converts CvMat
, IplImage
, or CvMatND
to Mat
.
Mat cvarrToMat
(const CvArr* arr, bool copyData=false, bool allowND=true, int coiMode=0 )¶Parameters: |
|
---|
The function cvarrToMat
converts CvMat
, IplImage
, or CvMatND
header to
Mat
header, and optionally duplicates the underlying data. The constructed header is returned by the function.
When copyData=false
, the conversion is done really fast (in O(1) time) and the newly created matrix header will have refcount=0
, which means that no reference counting is done for the matrix data. In this case, you have to preserve the data until the new header is destructed. Otherwise, when copyData=true
, the new buffer is allocated and managed as if you created a new matrix from scratch and copied the data there. That is, cvarrToMat(arr, true)
is equivalent to cvarrToMat(arr, false).clone()
(assuming that COI is not set). The function provides a uniform way of supporting
CvArr
paradigm in the code that is migrated to use new-style data structures internally. The reverse transformation, from
Mat
to
CvMat
or
IplImage
can be done by a simple assignment:
CvMat* A = cvCreateMat(10, 10, CV_32F);
cvSetIdentity(A);
IplImage A1; cvGetImage(A, &A1);
Mat B = cvarrToMat(A);
Mat B1 = cvarrToMat(&A1);
IplImage C = B;
CvMat C1 = B1;
// now A, A1, B, B1, C and C1 are different headers
// for the same 10x10 floating-point array.
// note that you will need to use "&"
// to pass C & C1 to OpenCV functions, for example:
printf("%g\n", cvNorm(&C1, 0, CV_L2));
Normally, the function is used to convert an old-style 2D array (
CvMat
or
IplImage
) to Mat
. However, the function can also take
CvMatND
as an input and create
Mat()
for it, if it is possible. And, for CvMatND A
, it is possible if and only if A.dim[i].size*A.dim.step[i] == A.dim.step[i-1]
for all or for all but one i, 0 < i < A.dims
. That is, the matrix data should be continuous or it should be representable as a sequence of continuous matrices. By using this function in this way, you can process
CvMatND
using an arbitrary element-wise function.
The last parameter, coiMode
, specifies how to deal with an image with COI set. By default, it is 0 and the function reports an error when an image with COI comes in. And coiMode=1
means that no error is signalled. You have to check COI presence and handle it manually. The modern structures, such as
Mat
and
MatND
do not support COI natively. To process an individual channel of a new-style array, you need either to organize a loop over the array (for example, using matrix iterators) where the channel of interest will be processed, or extract the COI using
mixChannels()
(for new-style arrays) or
extractImageCOI()
(for old-style arrays), process this individual channel, and insert it back to the output array if needed (using
mixChannels()
or
insertImageCOI()
, respectively).
See also
cvGetImage()
,
cvGetMat()
,
extractImageCOI()
,
insertImageCOI()
,
mixChannels()
Performs a forward or inverse discrete Cosine transform of 1D or 2D array.
void dct
(InputArray src, OutputArray dst, int flags=0)¶
cv2.
dct
(src[, dst[, flags]]) → dst¶
void cvDCT
(const CvArr* src, CvArr* dst, int flags)¶
cv.
DCT
(src, dst, flags) → None¶Parameters: |
|
---|
The function dct
performs a forward or inverse discrete Cosine transform (DCT) of a 1D or 2D floating-point array:
Forward Cosine transform of a 1D vector of N
elements:
where
and
, for j > 0.
Inverse Cosine transform of a 1D vector of N
elements:
(since is an orthogonal matrix, )
Forward 2D Cosine transform of M x N
matrix:
Inverse 2D Cosine transform of M x N
matrix:
The function chooses the mode of operation by looking at the flags and size of the input array:
(flags & DCT_INVERSE) == 0
, the function does a forward 1D or 2D transform. Otherwise, it is an inverse 1D or 2D transform.(flags & DCT_ROWS) != 0
, the function performs a 1D transform of each row.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);
See also
Performs a forward or inverse Discrete Fourier transform of a 1D or 2D floating-point array.
void dft
(InputArray src, OutputArray dst, int flags=0, int nonzeroRows=0)¶
cv2.
dft
(src[, dst[, flags[, nonzeroRows]]]) → dst¶
void cvDFT
(const CvArr* src, CvArr* dst, int flags, int nonzero_rows=0 )¶
cv.
DFT
(src, dst, flags, nonzeroRows=0) → None¶Parameters: |
|
---|
The function performs one of the following:
Forward the Fourier transform of a 1D vector of N
elements:
where and
Inverse the Fourier transform of a 1D vector of N
elements:
where
Forward the 2D Fourier transform of a M x N
matrix:
Inverse the 2D Fourier transform of a M x N
matrix:
In case of real (single-channel) data, the output spectrum of the forward Fourier transform or input spectrum of the inverse Fourier transform can be represented in a packed format called CCS (complex-conjugate-symmetrical). It was borrowed from IPL (Intel* Image Processing Library). Here is how 2D CCS spectrum looks:
In case of 1D transform of a real vector, the output looks like the first row of the matrix above.
So, the function chooses an operation mode depending on the flags and size of the input array:
If
DFT_ROWS
is set or the input array has a single row or single column, the function performs a 1D forward or inverse transform of each row of a matrix whenDFT_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 theDFT_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
orDFT_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 flagsDFT_INVERSE
andDFT_ROWS
.When
DFT_INVERSE
is set and the input array is real, or it is complex butDFT_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 flagsDFT_INVERSE
andDFT_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:
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.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.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()
.
See also
dct()
, getOptimalDFTSize()
, mulSpectrums()
, filter2D()
, matchTemplate()
, flip()
, cartToPolar()
, magnitude()
, phase()
Note
Performs per-element division of two arrays or a scalar by an array.
void divide
(InputArray src1, InputArray src2, OutputArray dst, double scale=1, int dtype=-1)¶
void divide
(double scale, InputArray src2, OutputArray dst, int dtype=-1)¶
cv2.
divide
(src1, src2[, dst[, scale[, dtype]]]) → dst¶
cv2.
divide
(scale, src2[, dst[, dtype]]) → dst
void cvDiv
(const CvArr* src1, const CvArr* src2, CvArr* dst, double scale=1)¶
cv.
Div
(src1, src2, dst, scale=1) → None¶Parameters: |
|
---|
The functions divide
divide one array by another:
or a scalar by an array when there is no src1
:
When src2(I)
is zero, dst(I)
will also be zero. Different channels of multi-channel arrays are processed independently.
Note
Saturation is not applied when the output array has the depth CV_32S
. You may even get result of an incorrect sign in the case of overflow.
See also
Returns the determinant of a square floating-point matrix.
double determinant
(InputArray mtx)¶
cv2.
determinant
(mtx) → retval¶
double cvDet
(const CvArr* mat)¶
cv.
Det
(mat) → float¶Parameters: |
|
---|
The function determinant
calculates and returns the determinant of the specified matrix. For small matrices ( mtx.cols=mtx.rows<=3
),
the direct method is used. For larger matrices, the function uses LU factorization with partial pivoting.
For symmetric positively-determined matrices, it is also possible to use eigen()
decomposition to calculate the determinant.
See also
Calculates eigenvalues and eigenvectors of a symmetric matrix.
bool eigen
(InputArray src, OutputArray eigenvalues, int lowindex=-1, int highindex=-1)¶
bool eigen
(InputArray src, OutputArray eigenvalues, OutputArray eigenvectors, int lowindex=-1, int highindex=-1)¶
cv2.
eigen
(src, computeEigenvectors[, eigenvalues[, eigenvectors]]) → retval, eigenvalues, eigenvectors¶
void cvEigenVV
(CvArr* mat, CvArr* evects, CvArr* evals, double eps=0, int lowindex=-1, int highindex=-1 )¶
cv.
EigenVV
(mat, evects, evals, eps, lowindex=-1, highindex=-1) → None¶Parameters: |
|
---|
The functions eigen
calculate just eigenvalues, or eigenvalues and eigenvectors of the symmetric matrix src
:
src*eigenvectors.row(i).t() = eigenvalues.at<srcType>(i)*eigenvectors.row(i).t()
Note
in the new and the old interfaces different ordering of eigenvalues and eigenvectors parameters is used.
See also
Calculates the exponent of every array element.
void exp
(InputArray src, OutputArray dst)¶
cv2.
exp
(src[, dst]) → dst¶
void cvExp
(const CvArr* src, CvArr* dst)¶
cv.
Exp
(src, dst) → None¶Parameters: |
|
---|
The function exp
calculates the exponent of every element of the input array:
The maximum relative error is about 7e-6
for single-precision input and less than 1e-10
for double-precision input. Currently, the function converts denormalized values to zeros on output. Special values (NaN, Inf) are not handled.
See also
log()
, cartToPolar()
, polarToCart()
, phase()
, pow()
, sqrt()
, magnitude()
Extracts the selected image channel.
void extractImageCOI
(const CvArr* arr, OutputArray coiimg, int coi=-1 )¶Parameters: |
|
---|
The function extractImageCOI
is used to extract an image COI from an old-style array and put the result to the new-style C++ matrix. As usual, the output matrix is reallocated using Mat::create
if needed.
To extract a channel from a new-style matrix, use
mixChannels()
or
split()
.
See also
mixChannels()
, split()
, merge()
, cvarrToMat()
, cvSetImageCOI()
, cvGetImageCOI()
Copies the selected image channel from a new-style C++ matrix to the old-style C array.
void insertImageCOI
(InputArray coiimg, CvArr* arr, int coi=-1 )¶Parameters: |
|
---|
The function insertImageCOI
is used to extract an image COI from a new-style C++ matrix and put the result to the old-style array.
The sample below illustrates how to use the function:
Mat temp(240, 320, CV_8UC1, Scalar(255));
IplImage* img = cvCreateImage(cvSize(320,240), IPL_DEPTH_8U, 3);
insertImageCOI(temp, img, 1); //insert to the first channel
cvNamedWindow("window",1);
cvShowImage("window", img); //you should see green image, because channel number 1 is green (BGR)
cvWaitKey(0);
cvDestroyAllWindows();
cvReleaseImage(&img);
To insert a channel to a new-style matrix, use
merge()
.
See also
mixChannels()
, split()
, merge()
, cvarrToMat()
, cvSetImageCOI()
, cvGetImageCOI()
Flips a 2D array around vertical, horizontal, or both axes.
void flip
(InputArray src, OutputArray dst, int flipCode)¶
cv2.
flip
(src, flipCode[, dst]) → dst¶
void cvFlip
(const CvArr* src, CvArr* dst=NULL, int flip_mode=0 )¶
cv.
Flip
(src, dst=None, flipMode=0) → None¶Parameters: |
|
---|
The function flip
flips the array in one of three different ways (row and column indices are 0-based):
The example scenarios of using the function are the following:
- Vertical flipping of the image (
flipCode == 0
) to switch between top-left and bottom-left image origin. This is a typical operation in video processing on Microsoft Windows* OS.- Horizontal flipping of the image with the subsequent horizontal shift and absolute difference calculation to check for a vertical-axis symmetry (
flipCode > 0
).- Simultaneous horizontal and vertical flipping of the image with the subsequent shift and absolute difference calculation to check for a central symmetry (
flipCode < 0
).- Reversing the order of point arrays (
flipCode > 0
orflipCode == 0
).
See also
Performs generalized matrix multiplication.
void gemm
(InputArray src1, InputArray src2, double alpha, InputArray src3, double beta, OutputArray dst, int flags=0 )¶
cv2.
gemm
(src1, src2, alpha, src3, beta[, dst[, flags]]) → dst¶
void cvGEMM
(const CvArr* src1, const CvArr* src2, double alpha, const CvArr* src3, double beta, CvArr* dst, int tABC=0)¶
cv.
GEMM
(src1, src2, alpha, src3, beta, dst, tABC=0) → None¶Parameters: |
|
---|
The function performs generalized matrix multiplication similar to the gemm
functions in BLAS level 3. For example, gemm(src1, src2, alpha, src3, beta, dst, GEMM_1_T + GEMM_3_T)
corresponds to
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();
See also
Returns a conversion function for a single pixel.
ConvertData getConvertElem
(int fromType, int toType)¶
ConvertScaleData getConvertScaleElem
(int fromType, int toType)¶Parameters: |
|
---|
The functions getConvertElem
and getConvertScaleElem
return pointers to the functions for converting individual pixels from one type to another. While the main function purpose is to convert single pixels (actually, for converting sparse matrices from one type to another), you can use them to convert the whole row of a dense matrix or the whole matrix at once, by setting cn = matrix.cols*matrix.rows*matrix.channels()
if the matrix data is continuous.
ConvertData
and ConvertScaleData
are defined as:
typedef void (*ConvertData)(const void* from, void* to, int cn)
typedef void (*ConvertScaleData)(const void* from, void* to,
int cn, double alpha, double beta)
See also
Returns the optimal DFT size for a given vector size.
int getOptimalDFTSize
(int vecsize)¶
cv2.
getOptimalDFTSize
(vecsize) → retval¶
int cvGetOptimalDFTSize
(int size0)¶
cv.
GetOptimalDFTSize
(size0) → int¶Parameters: | vecsize – vector size. |
---|
DFT performance is not a monotonic function of a vector size. Therefore, when you calculate convolution of two arrays or perform the spectral analysis of an array, it usually makes sense to pad the input data with zeros to get a bit larger array that can be transformed much faster than the original one. Arrays whose size is a power-of-two (2, 4, 8, 16, 32, ...) are the fastest to process. Though, the arrays whose size is a product of 2’s, 3’s, and 5’s (for example, 300 = 5*5*3*2*2) are also processed quite efficiently.
The function getOptimalDFTSize
returns the minimum number N
that is greater than or equal to vecsize
so that the DFT of a vector of size N
can be processed efficiently. In the current implementation N
= 2 p * 3 q * 5 r for some integer p
, q
, r
.
The function returns a negative number if vecsize
is too large (very close to INT_MAX
).
While the function cannot be used directly to estimate the optimal vector size for DCT transform (since the current DCT implementation supports only even-size vectors), it can be easily processed as getOptimalDFTSize((vecsize+1)/2)*2
.
See also
dft()
, dct()
, idft()
, idct()
, mulSpectrums()
Calculates the inverse Discrete Cosine Transform of a 1D or 2D array.
void idct
(InputArray src, OutputArray dst, int flags=0)¶
cv2.
idct
(src[, dst[, flags]]) → dst¶Parameters: |
|
---|
idct(src, dst, flags)
is equivalent to dct(src, dst, flags | DCT_INVERSE)
.
See also
Calculates the inverse Discrete Fourier Transform of a 1D or 2D array.
void idft
(InputArray src, OutputArray dst, int flags=0, int nonzeroRows=0)¶
cv2.
idft
(src[, dst[, flags[, nonzeroRows]]]) → dst¶Parameters: |
---|
idft(src, dst, flags)
is equivalent to dft(src, dst, flags | DFT_INVERSE)
.
See dft()
for details.
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
Checks if array elements lie between the elements of two other arrays.
void inRange
(InputArray src, InputArray lowerb, InputArray upperb, OutputArray dst)¶
cv2.
inRange
(src, lowerb, upperb[, dst]) → dst¶
void cvInRange
(const CvArr* src, const CvArr* lower, const CvArr* upper, CvArr* dst)¶
void cvInRangeS
(const CvArr* src, CvScalar lower, CvScalar upper, CvArr* dst)¶
cv.
InRange
(src, lower, upper, dst) → None¶
cv.
InRangeS
(src, lower, upper, dst) → None¶Parameters: |
|
---|
The function checks the range as follows:
For every element of a single-channel input array:
For two-channel arrays:
and so forth.
That is, dst
(I) is set to 255 (all 1
-bits) if src
(I) is within the specified 1D, 2D, 3D, ... box and 0 otherwise.
When the lower and/or upper boundary parameters are scalars, the indexes (I)
at lowerb
and upperb
in the above formulas should be omitted.
Finds the inverse or pseudo-inverse of a matrix.
double invert
(InputArray src, OutputArray dst, int flags=DECOMP_LU)¶
cv2.
invert
(src[, dst[, flags]]) → retval, dst¶
double cvInvert
(const CvArr* src, CvArr* dst, int method=CV_LU )¶
cv.
Invert
(src, dst, method=CV_LU) → float¶Parameters: |
|
---|
The function invert
inverts the matrix src
and stores the result in dst
.
When the matrix src
is singular or non-square, the function calculates the pseudo-inverse matrix (the dst
matrix) so that norm(src*dst - I)
is minimal, where I is an identity matrix.
In case of the DECOMP_LU
method, the function returns non-zero value if the inverse has been successfully calculated and 0 if src
is singular.
In case of the DECOMP_SVD
method, the function returns the inverse condition number of src
(the ratio of the smallest singular value to the largest singular value) and 0 if src
is singular. The SVD method calculates a pseudo-inverse matrix if src
is singular.
Similarly to DECOMP_LU
, the method DECOMP_CHOLESKY
works only with non-singular square matrices that should also be symmetrical and positively defined. In this case, the function stores the inverted matrix in dst
and returns non-zero. Otherwise, it returns 0.
Calculates the natural logarithm of every array element.
void log
(InputArray src, OutputArray dst)¶
cv2.
log
(src[, dst]) → dst¶
void cvLog
(const CvArr* src, CvArr* dst)¶
cv.
Log
(src, dst) → None¶Parameters: |
|
---|
The function log
calculates the natural logarithm of the absolute value of every element of the input array:
where C
is a large negative number (about -700 in the current implementation).
The maximum relative error is about 7e-6
for single-precision input and less than 1e-10
for double-precision input. Special values (NaN, Inf) are not handled.
See also
exp()
,
cartToPolar()
,
polarToCart()
,
phase()
,
pow()
,
sqrt()
,
magnitude()
Performs a look-up table transform of an array.
void LUT
(InputArray src, InputArray lut, OutputArray dst, int interpolation=0 )¶
cv2.
LUT
(src, lut[, dst[, interpolation]]) → dst¶
void cvLUT
(const CvArr* src, CvArr* dst, const CvArr* lut)¶
cv.
LUT
(src, dst, lut) → None¶Parameters: |
|
---|
The function LUT
fills the output array with values from the look-up table. Indices of the entries are taken from the input array. That is, the function processes each element of src
as follows:
where
See also
Calculates the magnitude of 2D vectors.
void magnitude
(InputArray x, InputArray y, OutputArray magnitude)¶
cv2.
magnitude
(x, y[, magnitude]) → magnitude¶Parameters: |
|
---|
The function magnitude
calculates the magnitude of 2D vectors formed from the corresponding elements of x
and y
arrays:
See also
Calculates the Mahalanobis distance between two vectors.
double Mahalanobis
(InputArray v1, InputArray v2, InputArray icovar)¶
cv2.
Mahalanobis
(v1, v2, icovar) → retval¶
double cvMahalanobis
(const CvArr* vec1, const CvArr* vec2, const CvArr* mat)¶
cv.
Mahalonobis
(vec1, vec2, mat) → None¶Parameters: |
|
---|
The function Mahalanobis
calculates and returns the weighted distance between two vectors:
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).
Calculates per-element maximum of two arrays or an array and a scalar.
MatExpr max
(const Mat& a, const Mat& b)¶
MatExpr max
(const Mat& a, double s)¶
MatExpr max
(double s, const Mat& a)¶
void max
(InputArray src1, InputArray src2, OutputArray dst)¶
void max
(const Mat& src1, const Mat& src2, Mat& dst)¶
void max
(const Mat& src1, double src2, Mat& dst)¶
cv2.
max
(src1, src2[, dst]) → dst¶
void cvMax
(const CvArr* src1, const CvArr* src2, CvArr* dst)¶
void cvMaxS
(const CvArr* src, double value, CvArr* dst)¶
cv.
Max
(src1, src2, dst) → None¶
cv.
MaxS
(src, value, dst) → None¶Parameters: |
|
---|
The functions max
calculate the per-element maximum of two arrays:
or array and a scalar:
In the second variant, when the input array is multi-channel, each channel is compared with value
independently.
The first 3 variants of the function listed above are actually a part of Matrix Expressions . They return an expression object that can be further either transformed/ assigned to a matrix, or passed to a function, and so on.
See also
min()
,
compare()
,
inRange()
,
minMaxLoc()
,
Matrix Expressions
Calculates an average (mean) of array elements.
Scalar mean
(InputArray src, InputArray mask=noArray())¶
cv2.
mean
(src[, mask]) → retval¶
CvScalar cvAvg
(const CvArr* arr, const CvArr* mask=NULL )¶
cv.
Avg
(arr, mask=None) → scalar¶Parameters: |
|
---|
The function mean
calculates the mean value M
of array elements, independently for each channel, and return it:
When all the mask elements are 0’s, the functions return Scalar::all(0)
.
See also
Calculates a mean and standard deviation of array elements.
void meanStdDev
(InputArray src, OutputArray mean, OutputArray stddev, InputArray mask=noArray())¶
cv2.
meanStdDev
(src[, mean[, stddev[, mask]]]) → mean, stddev¶
void cvAvgSdv
(const CvArr* arr, CvScalar* mean, CvScalar* std_dev, const CvArr* mask=NULL )¶
cv.
AvgSdv
(arr, mask=None) -> (mean, stdDev)¶Parameters: |
|
---|
The function meanStdDev
calculates the mean and the standard deviation M
of array elements independently for each channel and returns it via the output parameters:
When all the mask elements are 0’s, the functions return mean=stddev=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()
.
See also
countNonZero()
,
mean()
,
norm()
,
minMaxLoc()
,
calcCovarMatrix()
Creates one multichannel array out of several single-channel ones.
void merge
(const Mat* mv, size_t count, OutputArray dst)¶
void merge
(InputArrayOfArrays mv, OutputArray dst)¶
cv2.
merge
(mv[, dst]) → dst¶
void cvMerge
(const CvArr* src0, const CvArr* src1, const CvArr* src2, const CvArr* src3, CvArr* dst)¶
cv.
Merge
(src0, src1, src2, src3, dst) → None¶Parameters: |
|
---|
The functions merge
merge 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
split()
does the reverse operation. If you need to shuffle channels in some other advanced way, use
mixChannels()
.
See also
Calculates per-element minimum of two arrays or an array and a scalar.
MatExpr min
(const Mat& a, const Mat& b)¶
MatExpr min
(const Mat& a, double s)¶
MatExpr min
(double s, const Mat& a)¶
void min
(InputArray src1, InputArray src2, OutputArray dst)¶
void min
(const Mat& src1, const Mat& src2, Mat& dst)¶
void min
(const Mat& src1, double src2, Mat& dst)¶
cv2.
min
(src1, src2[, dst]) → dst¶
void cvMin
(const CvArr* src1, const CvArr* src2, CvArr* dst)¶
void cvMinS
(const CvArr* src, double value, CvArr* dst)¶
cv.
Min
(src1, src2, dst) → None¶
cv.
MinS
(src, value, dst) → None¶Parameters: |
|
---|
The functions min
calculate the per-element minimum of two arrays:
or array and a scalar:
In the second variant, when the input array is multi-channel, each channel is compared with value
independently.
The first three variants of the function listed above are actually a part of Matrix Expressions . They return the expression object that can be further either transformed/assigned to a matrix, or passed to a function, and so on.
See also
max()
,
compare()
,
inRange()
,
minMaxLoc()
,
Matrix Expressions
Finds the global minimum and maximum in an array
void minMaxIdx
(InputArray src, double* minVal, double* maxVal, int* minIdx=0, int* maxIdx=0, InputArray mask=noArray())¶Parameters: |
|
---|
The function minMaxIdx
finds the minimum and maximum element values and their positions. The extremums are searched across the whole array or, if mask
is not an empty array, in the specified array region.
The function does not work with multi-channel arrays. If you need to find minimum or maximum elements across all the channels, use
Mat::reshape()
first to reinterpret the array as single-channel. Or you may extract the particular channel using either
extractImageCOI()
, or
mixChannels()
, or
split()
.
In case of a sparse matrix, the minimum is found among non-zero elements only.
Finds the global minimum and maximum in an array.
void minMaxLoc
(InputArray src, double* minVal, double* maxVal=0, Point* minLoc=0, Point* maxLoc=0, InputArray mask=noArray())¶
void minMaxLoc
(const SparseMat& a, double* minVal, double* maxVal, int* minIdx=0, int* maxIdx=0 )¶
cv2.
minMaxLoc
(src[, mask]) → minVal, maxVal, minLoc, maxLoc¶
void cvMinMaxLoc
(const CvArr* arr, double* min_val, double* max_val, CvPoint* min_loc=NULL, CvPoint* max_loc=NULL, const CvArr* mask=NULL )¶
cv.
MinMaxLoc
(arr, mask=None)-> (minVal, maxVal, minLoc, maxLoc)¶Parameters: |
|
---|
The functions minMaxLoc
find the minimum and maximum element values and their positions. The extremums are searched across the whole array or,
if mask
is not an empty array, in the specified array region.
The functions do not work with multi-channel arrays. If you need to find minimum or maximum elements across all the channels, use
Mat::reshape()
first to reinterpret the array as single-channel. Or you may extract the particular channel using either
extractImageCOI()
, or
mixChannels()
, or
split()
.
See also
max()
,
min()
,
compare()
,
inRange()
,
extractImageCOI()
,
mixChannels()
,
split()
,
Mat::reshape()
Copies specified channels from input arrays to the specified channels of output arrays.
void mixChannels
(const Mat* src, size_t nsrcs, Mat* dst, size_t ndsts, const int* fromTo, size_t npairs)¶
void mixChannels
(const vector<Mat>& src, vector<Mat>& dst, const int* fromTo, size_t npairs)¶
cv2.
mixChannels
(src, dst, fromTo) → None¶
void cvMixChannels
(const CvArr** src, int src_count, CvArr** dst, int dst_count, const int* from_to, int pair_count)¶
cv.
MixChannels
(src, dst, fromTo) → None¶Parameters: |
|
---|
The functions mixChannels
provide an advanced mechanism for shuffling image channels.
split()
and
merge()
and some forms of
cvtColor()
are partial cases of mixChannels
.
In the example below, the code splits a 4-channel RGBA image into a 3-channel BGR (with R and B channels swapped) and a separate alpha-channel image:
Mat rgba( 100, 100, CV_8UC4, Scalar(1,2,3,4) );
Mat bgr( rgba.rows, rgba.cols, CV_8UC3 );
Mat alpha( rgba.rows, rgba.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 };
// rgba[0] -> bgr[2], rgba[1] -> bgr[1],
// rgba[2] -> bgr[0], rgba[3] -> alpha[0]
int from_to[] = { 0,2, 1,1, 2,0, 3,3 };
mixChannels( &rgba, 1, out, 2, from_to, 4 );
Note
Unlike many other new-style C++ functions in OpenCV (see the introduction section and Mat::create()
), mixChannels
requires the output arrays to be pre-allocated before calling the function.
See also
Performs the per-element multiplication of two Fourier spectrums.
void mulSpectrums
(InputArray a, InputArray b, OutputArray c, int flags, bool conjB=false )¶
cv2.
mulSpectrums
(a, b, flags[, c[, conjB]]) → c¶
void cvMulSpectrums
(const CvArr* src1, const CvArr* src2, CvArr* dst, int flags)¶
cv.
MulSpectrums
(src1, src2, dst, flags) → None¶Parameters: |
|
---|
The function mulSpectrums
performs the per-element multiplication of the two CCS-packed or complex matrices that are results of a real or complex Fourier transform.
The function, together with
dft()
and
idft()
, may be used to calculate convolution (pass conjB=false
) or correlation (pass conjB=true
) of two arrays rapidly. When the arrays are complex, they are simply multiplied (per element) with an optional conjugation of the second-array elements. When the arrays are real, they are assumed to be CCS-packed (see
dft()
for details).
Calculates the per-element scaled product of two arrays.
void multiply
(InputArray src1, InputArray src2, OutputArray dst, double scale=1, int dtype=-1 )¶
cv2.
multiply
(src1, src2[, dst[, scale[, dtype]]]) → dst¶
void cvMul
(const CvArr* src1, const CvArr* src2, CvArr* dst, double scale=1)¶
cv.
Mul
(src1, src2, dst, scale=1) → None¶Parameters: |
|
---|
The function multiply
calculates the per-element product of two arrays:
There is also a
Matrix Expressions -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.
Calculates the product of a matrix and its transposition.
void mulTransposed
(InputArray src, OutputArray dst, bool aTa, InputArray delta=noArray(), double scale=1, int dtype=-1 )¶
cv2.
mulTransposed
(src, aTa[, dst[, delta[, scale[, dtype]]]]) → dst¶
void cvMulTransposed
(const CvArr* src, CvArr* dst, int order, const CvArr* delta=NULL, double scale=1. )¶
cv.
MulTransposed
(src, dst, order, delta=None, scale=1.0) → None¶Parameters: |
|
---|
The function mulTransposed
calculates the product of src
and its transposition:
if aTa=true
, and
otherwise. The function is used to calculate the covariance matrix. With zero delta, it can be used as a faster substitute for general matrix product A*B
when B=A'
See also
Calculates an absolute array norm, an absolute difference norm, or a relative difference norm.
double norm
(InputArray src1, int normType=NORM_L2, InputArray mask=noArray())¶
double norm
(InputArray src1, InputArray src2, int normType=NORM_L2, InputArray mask=noArray() )¶
double norm
(const SparseMat& src, int normType)¶
cv2.
norm
(src1[, normType[, mask]]) → retval¶
cv2.
norm
(src1, src2[, normType[, mask]]) → retval
double cvNorm
(const CvArr* arr1, const CvArr* arr2=NULL, int norm_type=CV_L2, const CvArr* mask=NULL )¶
cv.
Norm
(arr1, arr2, normType=CV_L2, mask=None) → float¶Parameters: |
|
---|
The functions norm
calculate an absolute norm of src1
(when there is no src2
):
or an absolute or relative difference norm if src2
is there:
or
The functions norm
return the calculated norm.
When the mask
parameter is specified and it is not empty, the norm is calculated only over the region specified by the mask.
A multi-channel input arrays are treated as a single-channel, that is, the results for all channels are combined.
Normalizes the norm or value range of an array.
void normalize
(InputArray src, OutputArray dst, double alpha=1, double beta=0, int norm_type=NORM_L2, int dtype=-1, InputArray mask=noArray() )¶
void normalize
(const SparseMat& src, SparseMat& dst, double alpha, int normType)¶
cv2.
normalize
(src[, dst[, alpha[, beta[, norm_type[, dtype[, mask]]]]]]) → dst¶Parameters: |
|
---|
The functions normalize
scale and shift the input array elements so that
(where p=Inf, 1 or 2) when normType=NORM_INF
, NORM_L1
, or NORM_L2
, respectively; or so that
when normType=NORM_MINMAX
(for dense arrays only).
The optional mask specifies a sub-array to be normalized. This means that the norm or min-n-max are calculated over the sub-array, and then this sub-array is modified to be normalized. If you want to only use the mask to calculate the norm or min-max but modify the whole array, you can use
norm()
and
Mat::convertTo()
.
In case of sparse matrices, only the non-zero values are analyzed and transformed. Because of this, the range transformation for sparse matrices is not allowed since it can shift the zero level.
See also
PCA
¶Principal Component Analysis class.
The class is used to calculate a special basis for a set of vectors. The basis will consist of eigenvectors of the covariance matrix calculated from the input set of vectors. The class PCA
can also transform vectors to/from the new coordinate space defined by the basis. Usually, in this new coordinate system, each vector from the original set (and any linear combination of such vectors) can be quite accurately approximated by taking its first few components, corresponding to the eigenvectors of the largest eigenvalues of the covariance matrix. Geometrically it means that you calculate a projection of the vector to a subspace formed by a few eigenvectors corresponding to the dominant eigenvalues of the covariance matrix. And usually such a projection is very close to the original vector. So, you can represent the original vector from a high-dimensional space with a much shorter vector consisting of the projected vector’s coordinates in the subspace. Such a transformation is also known as Karhunen-Loeve Transform, or KLT. See
http://en.wikipedia.org/wiki/Principal_component_analysis .
The sample below is the function that takes two matrices. The first function stores a set of vectors (a row per vector) that is used to calculate PCA. The second function stores another “test” set of vectors (a row per vector). First, these vectors are compressed with PCA, then reconstructed back, and then the reconstruction error norm is computed and printed for each vector.
PCA compressPCA(InputArray pcaset, int maxComponents,
const Mat& testset, OutputArray compressed)
{
PCA pca(pcaset, // pass the data
Mat(), // there is no pre-computed mean vector,
// so let the PCA engine to compute it
CV_PCA_DATA_AS_ROW, // indicate that the vectors
// are stored as matrix rows
// (use CV_PCA_DATA_AS_COL if the vectors are
// the matrix columns)
maxComponents // specify how many principal components to retain
);
// if there is no test data, just return the computed basis, ready-to-use
if( !testset.data )
return pca;
CV_Assert( testset.cols == pcaset.cols );
compressed.create(testset.rows, maxComponents, testset.type());
Mat reconstructed;
for( int i = 0; i < testset.rows; i++ )
{
Mat vec = testset.row(i), coeffs = compressed.row(i);
// compress the vector, the result will be stored
// in the i-th row of the output matrix
pca.project(vec, coeffs);
// and then reconstruct it
pca.backProject(coeffs, reconstructed);
// and measure the error
printf("%d. diff = %g\n", i, norm(vec, reconstructed, NORM_L2));
}
return pca;
}
See also
Note
PCA constructors
PCA::
PCA
()¶
PCA::
PCA
(InputArray data, InputArray mean, int flags, int maxComponents=0)¶
PCA::
PCA
(InputArray data, InputArray mean, int flags, double retainedVariance)¶Parameters: |
|
---|
The default constructor initializes an empty PCA structure. The other constructors initialize the structure and call
PCA::operator()
.
Performs Principal Component Analysis of the supplied dataset.
PCA& PCA::
operator()
(InputArray data, InputArray mean, int flags, int maxComponents=0)¶
PCA& PCA::
computeVar
(InputArray data, InputArray mean, int flags, double retainedVariance)¶
cv2.
PCACompute
(data[, mean[, eigenvectors[, maxComponents]]]) → mean, eigenvectors¶
cv2.
PCAComputeVar
(data, retainedVariance[, mean[, eigenvectors]]) → mean, eigenvectors¶Parameters: |
|
---|
The operator performs PCA of the supplied dataset. It is safe to reuse the same PCA structure for multiple datasets. That is, if the structure has been previously used with another dataset, the existing internal data is reclaimed and the new eigenvalues
, eigenvectors
, and mean
are allocated and computed.
The computed eigenvalues are sorted from the largest to the smallest and the corresponding eigenvectors are stored as PCA::eigenvectors
rows.
Projects vector(s) to the principal component subspace.
Mat PCA::
project
(InputArray vec) const
¶
void PCA::
project
(InputArray vec, OutputArray result) const
¶
cv2.
PCAProject
(data, mean, eigenvectors[, result]) → result¶Parameters: |
|
---|
The methods project one or more vectors to the principal component subspace, where each vector projection is represented by coefficients in the principal component basis. The first form of the method returns the matrix that the second form writes to the result. So the first form can be used as a part of expression while the second form can be more efficient in a processing loop.
Reconstructs vectors from their PC projections.
Mat PCA::
backProject
(InputArray vec) const
¶
void PCA::
backProject
(InputArray vec, OutputArray result) const
¶
cv2.
PCABackProject
(data, mean, eigenvectors[, result]) → result¶Parameters: |
|
---|
The methods are inverse operations to
PCA::project()
. They take PC coordinates of projected vectors and reconstruct the original vectors. Unless all the principal components have been retained, the reconstructed vectors are different from the originals. But typically, the difference is small if the number of components is large enough (but still much smaller than the original vector dimensionality). As a result, PCA is used.
Performs the perspective matrix transformation of vectors.
void perspectiveTransform
(InputArray src, OutputArray dst, InputArray m)¶
cv2.
perspectiveTransform
(src, m[, dst]) → dst¶
void cvPerspectiveTransform
(const CvArr* src, CvArr* dst, const CvMat* mat)¶
cv.
PerspectiveTransform
(src, dst, mat) → None¶Parameters: |
|
---|
The function perspectiveTransform
transforms every element of src
by treating it as a 2D or 3D vector, in the following way:
where
and
Here a 3D vector transformation is shown. In case of a 2D vector transformation, the z
component is omitted.
Note
The function transforms a sparse set of 2D or 3D vectors. If you want to transform an image using perspective transformation, use warpPerspective()
. If you have an inverse problem, that is, you want to compute the most probable perspective transformation out of several pairs of corresponding points, you can use getPerspectiveTransform()
or findHomography()
.
Calculates the rotation angle of 2D vectors.
void phase
(InputArray x, InputArray y, OutputArray angle, bool angleInDegrees=false)¶
cv2.
phase
(x, y[, angle[, angleInDegrees]]) → angle¶Parameters: |
|
---|
The function phase
calculates the rotation angle of each 2D vector that is formed from the corresponding elements of x
and y
:
The angle estimation accuracy is about 0.3 degrees. When x(I)=y(I)=0
, the corresponding angle(I)
is set to 0.
Calculates x and y coordinates of 2D vectors from their magnitude and angle.
void polarToCart
(InputArray magnitude, InputArray angle, OutputArray x, OutputArray y, bool angleInDegrees=false)¶
cv2.
polarToCart
(magnitude, angle[, x[, y[, angleInDegrees]]]) → x, y¶
void cvPolarToCart
(const CvArr* magnitude, const CvArr* angle, CvArr* x, CvArr* y, int angle_in_degrees=0 )¶
cv.
PolarToCart
(magnitude, angle, x, y, angleInDegrees=0) → None¶Parameters: |
|
---|
The function polarToCart
calculates the Cartesian coordinates of each 2D vector represented by the corresponding elements of magnitude
and angle
:
The relative accuracy of the estimated coordinates is about 1e-6
.
See also
cartToPolar()
,
magnitude()
,
phase()
,
exp()
,
log()
,
pow()
,
sqrt()
Raises every array element to a power.
void pow
(InputArray src, double power, OutputArray dst)¶
cv2.
pow
(src, power[, dst]) → dst¶
void cvPow
(const CvArr* src, CvArr* dst, double power)¶
cv.
Pow
(src, dst, power) → None¶Parameters: |
|
---|
The function pow
raises every element of the input array to power
:
So, for a non-integer power exponent, the absolute values of input array elements are used. However, it is possible to get true values for negative values using some extra operations. In the example below, computing the 5th root of array src
shows:
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.
See also
RNG
¶Random number generator. It encapsulates the state (currently, a 64-bit integer) and has methods to return scalar random values and to fill arrays with random values. Currently it supports uniform and Gaussian (normal) distributions. The generator uses Multiply-With-Carry algorithm, introduced by G. Marsaglia ( http://en.wikipedia.org/wiki/Multiply-with-carry ). Gaussian-distribution random numbers are generated using the Ziggurat algorithm ( http://en.wikipedia.org/wiki/Ziggurat_algorithm ), introduced by G. Marsaglia and W. W. Tsang.
The constructors
RNG::
RNG
()¶
RNG::
RNG
(uint64 state)¶Parameters: |
|
---|
These are the RNG constructors. The first form sets the state to some pre-defined value, equal to 2**32-1
in the current implementation. The second form sets the state to the specified value. If you passed state=0
, the constructor uses the above default value instead to avoid the singular random number sequence, consisting of all zeros.
Returns the next random number.
unsigned int RNG::
next
()¶The method updates the state using the MWC algorithm and returns the next 32-bit random number.
Returns the next random number of the specified type.
RNG::
operator
uchar()¶
RNG::
operator
schar()¶
RNG::
operator
ushort()¶
RNG::
operator
short int()¶
RNG::
operator
int()¶
RNG::
operator
unsigned int()¶
RNG::
operator
float()¶
RNG::
operator
double()¶Each of the methods updates the state using the MWC algorithm and returns the next random number of the specified type. In case of integer types, the returned number is from the available value range for the specified type. In case of floating-point types, the returned value is from [0,1)
range.
Returns the next random number.
unsigned int RNG::
operator()
()¶
unsigned int RNG::
operator()
(unsigned int N)¶Parameters: |
|
---|
The methods transform the state using the MWC algorithm and return the next random number. The first form is equivalent to
RNG::next()
. The second form returns the random number modulo N
, which means that the result is in the range [0, N)
.
Returns the next random number sampled from the uniform distribution.
int RNG::
uniform
(int a, int b)¶
float RNG::
uniform
(float a, float b)¶
double RNG::
uniform
(double a, double b)¶Parameters: |
|
---|
The methods transform the state using the MWC algorithm and return the next uniformly-distributed random number of the specified type, deduced from the input parameter type, from the range [a, b)
. There is a nuance illustrated by the following sample:
RNG rng;
// always produces 0
double a = rng.uniform(0, 1);
// produces double from [0, 1)
double a1 = rng.uniform((double)0, (double)1);
// produces float from [0, 1)
double b = rng.uniform(0.f, 1.f);
// produces double from [0, 1)
double c = rng.uniform(0., 1.);
// may cause compiler error because of ambiguity:
// RNG::uniform(0, (int)0.999999)? or RNG::uniform((double)0, 0.99999)?
double d = rng.uniform(0, 0.999999);
The compiler does not take into account the type of the variable to which you assign the result of RNG::uniform
. The only thing that matters to the compiler is the type of a
and b
parameters. So, if you want a floating-point random number, but the range boundaries are integer numbers, either put dots in the end, if they are constants, or use explicit type cast operators, as in the a1
initialization above.
Returns the next random number sampled from the Gaussian distribution.
double RNG::
gaussian
(double sigma)¶Parameters: |
|
---|
The method transforms the state using the MWC algorithm and returns the next random number from the Gaussian distribution N(0,sigma)
. That is, the mean value of the returned random numbers is zero and the standard deviation is the specified sigma
.
Fills arrays with random numbers.
void RNG::
fill
(InputOutputArray mat, int distType, InputArray a, InputArray b, bool saturateRange=false )¶Parameters: |
|
---|
Each of the methods fills the matrix with the random values from the specified distribution. As the new numbers are generated, the RNG state is updated accordingly. In case of multiple-channel images, every channel is filled independently, which means that RNG cannot generate samples from the multi-dimensional Gaussian distribution with non-diagonal covariance matrix directly. To do that, the method generates samples from multi-dimensional standard Gaussian distribution with zero mean and identity covariation matrix, and then transforms them using transform()
to get samples from the specified Gaussian distribution.
Generates a single uniformly-distributed random number or an array of random numbers.
template<typename _Tp> _Tp randu
()¶
void randu
(InputOutputArray dst, InputArray low, InputArray high)¶
cv2.
randu
(dst, low, high) → None¶Parameters: |
|
---|
The template functions randu
generate and return the next uniformly-distributed random value of the specified type. randu<int>()
is an equivalent to (int)theRNG();
, and so on. See
RNG
description.
The second non-template variant of the function fills the matrix dst
with uniformly-distributed random numbers from the specified range:
Fills the array with normally distributed random numbers.
void randn
(InputOutputArray dst, InputArray mean, InputArray stddev)¶
cv2.
randn
(dst, mean, stddev) → None¶Parameters: |
|
---|
The function randn
fills the matrix dst
with normally distributed random numbers with the specified mean vector and the standard deviation matrix. The generated random numbers are clipped to fit the value range of the output array data type.
Shuffles the array elements randomly.
void randShuffle
(InputOutputArray dst, double iterFactor=1., RNG* rng=0 )¶
cv2.
randShuffle
(dst[, iterFactor]) → None¶Parameters: |
|
---|
The function randShuffle
shuffles the specified 1D array by randomly choosing pairs of elements and swapping them. The number of such swap operations will be dst.rows*dst.cols*iterFactor
.
Reduces a matrix to a vector.
void reduce
(InputArray src, OutputArray dst, int dim, int rtype, int dtype=-1 )¶
cv2.
reduce
(src, dim, rtype[, dst[, dtype]]) → dst¶
void cvReduce
(const CvArr* src, CvArr* dst, int dim=-1, int op=CV_REDUCE_SUM)¶
cv.
Reduce
(src, dst, dim=-1, op=CV_REDUCE_SUM) → None¶Parameters: |
|
---|
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 CV_REDUCE_SUM
and CV_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.
See also
Fills the output array with repeated copies of the input array.
void repeat
(InputArray src, int ny, int nx, OutputArray dst)¶
Mat repeat
(const Mat& src, int ny, int nx)¶
cv2.
repeat
(src, ny, nx[, dst]) → dst¶
void cvRepeat
(const CvArr* src, CvArr* dst)¶
cv.
Repeat
(src, dst) → None¶Parameters: |
|
---|
The functions
repeat()
duplicate the input array one or more times along each of the two axes:
The second variant of the function is more convenient to use with Matrix Expressions .
See also
Calculates the sum of a scaled array and another array.
void scaleAdd
(InputArray src1, double alpha, InputArray src2, OutputArray dst)¶
cv2.
scaleAdd
(src1, alpha, src2[, dst]) → dst¶
void cvScaleAdd
(const CvArr* src1, CvScalar scale, const CvArr* src2, CvArr* dst)¶
cv.
ScaleAdd
(src1, scale, src2, dst) → None¶Parameters: |
|
---|
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:
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);
See also
add()
,
addWeighted()
,
subtract()
,
Mat::dot()
,
Mat::convertTo()
,
Matrix Expressions
Initializes a scaled identity matrix.
void setIdentity
(InputOutputArray mtx, const Scalar& s=Scalar(1) )¶
cv2.
setIdentity
(mtx[, s]) → None¶
void cvSetIdentity
(CvArr* mat, CvScalar value=cvRealScalar(1))¶
cv.
SetIdentity
(mat, value=1) → None¶Parameters: |
|
---|
The function
setIdentity()
initializes a scaled identity matrix:
The function can also be emulated using the matrix initializers and the matrix expressions:
Mat A = Mat::eye(4, 3, CV_32F)*5;
// A will be set to [[5, 0, 0], [0, 5, 0], [0, 0, 5], [0, 0, 0]]
Solves one or more linear systems or least-squares problems.
bool solve
(InputArray src1, InputArray src2, OutputArray dst, int flags=DECOMP_LU)¶
cv2.
solve
(src1, src2[, dst[, flags]]) → retval, dst¶
int cvSolve
(const CvArr* src1, const CvArr* src2, CvArr* dst, int method=CV_LU)¶
cv.
Solve
(A, B, X, method=CV_LU) → None¶Parameters: |
|
---|
The function solve
solves a linear system or least-squares problem (the latter is possible with SVD or QR methods, or by specifying the flag DECOMP_NORMAL
):
If DECOMP_LU
or DECOMP_CHOLESKY
method is used, the function returns 1 if src1
(or
) is non-singular. Otherwise, it returns 0. In the latter case, dst
is not valid. Other methods find a pseudo-solution in case of a singular left-hand side part.
Note
If you want to find a unity-norm solution of an under-defined singular system , the function solve
will not do the work. Use SVD::solveZ()
instead.
Finds the real roots of a cubic equation.
int solveCubic
(InputArray coeffs, OutputArray roots)¶
cv2.
solveCubic
(coeffs[, roots]) → retval, roots¶
int cvSolveCubic
(const CvMat* coeffs, CvMat* roots)¶
cv.
SolveCubic
(coeffs, roots) → None¶Parameters: |
|
---|
The function solveCubic
finds the real roots of a cubic equation:
coeffs
is a 4-element vector:coeffs
is a 3-element vector:The roots are stored in the roots
array.
Finds the real or complex roots of a polynomial equation.
double solvePoly
(InputArray coeffs, OutputArray roots, int maxIters=300 )¶
cv2.
solvePoly
(coeffs[, roots[, maxIters]]) → retval, roots¶Parameters: |
|
---|
The function solvePoly
finds real and complex roots of a polynomial equation:
Sorts each row or each column of a matrix.
void sort
(InputArray src, OutputArray dst, int flags)¶
cv2.
sort
(src, flags[, dst]) → dst¶Parameters: |
|
---|
The function sort
sorts each matrix row or each matrix column in ascending or descending order. So you should pass two operation flags to get desired behaviour. If you want to sort matrix rows or columns lexicographically, you can use STL std::sort
generic function with the proper comparison predicate.
See also
Sorts each row or each column of a matrix.
void sortIdx
(InputArray src, OutputArray dst, int flags)¶
cv2.
sortIdx
(src, flags[, dst]) → dst¶Parameters: |
|
---|
The function sortIdx
sorts each matrix row or each matrix column in the ascending or descending order. So you should pass two operation flags to get desired behaviour. Instead of reordering the elements themselves, it stores the indices of sorted elements in the output array. For example:
Mat A = Mat::eye(3,3,CV_32F), B;
sortIdx(A, B, CV_SORT_EVERY_ROW + CV_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]]
See also
Divides a multi-channel array into several single-channel arrays.
void split
(const Mat& src, Mat* mvbegin)¶
void split
(InputArray m, OutputArrayOfArrays mv)¶
cv2.
split
(m[, mv]) → mv¶
void cvSplit
(const CvArr* src, CvArr* dst0, CvArr* dst1, CvArr* dst2, CvArr* dst3)¶
cv.
Split
(src, dst0, dst1, dst2, dst3) → None¶Parameters: |
|
---|
The functions split
split a multi-channel array into separate single-channel arrays:
If you need to extract a single channel or do some other sophisticated channel permutation, use
mixChannels()
.
See also
Calculates a square root of array elements.
void sqrt
(InputArray src, OutputArray dst)¶
cv2.
sqrt
(src[, dst]) → dst¶
float cvSqrt
(float value)¶
cv.
Sqrt
(value) → float¶Parameters: |
|
---|
The functions sqrt
calculate a square root of each input array element. In case of multi-channel arrays, each channel is processed independently. The accuracy is approximately the same as of the built-in std::sqrt
.
See also
Calculates the per-element difference between two arrays or array and a scalar.
void subtract
(InputArray src1, InputArray src2, OutputArray dst, InputArray mask=noArray(), int dtype=-1)¶
cv2.
subtract
(src1, src2[, dst[, mask[, dtype]]]) → dst¶
void cvSub
(const CvArr* src1, const CvArr* src2, CvArr* dst, const CvArr* mask=NULL)¶
void cvSubRS
(const CvArr* src, CvScalar value, CvArr* dst, const CvArr* mask=NULL )¶
void cvSubS
(const CvArr* src, CvScalar value, CvArr* dst, const CvArr* mask=NULL )¶
cv.
Sub
(src1, src2, dst, mask=None) → None¶
cv.
SubRS
(src, value, dst, mask=None) → None¶
cv.
SubS
(src, value, dst, mask=None) → None¶Parameters: |
|
---|
The function subtract
calculates:
Difference between two arrays, when both input arrays have the same size and the same number of channels:
Difference between an array and a scalar, when
src2
is constructed fromScalar
or has the same number of elements assrc1.channels()
:Difference between a scalar and an array, when
src1
is constructed fromScalar
or has the same number of elements assrc2.channels()
:The reverse difference between a scalar and an array in the case of
SubRS
:
where I
is a multi-dimensional index of array elements. In case of multi-channel arrays, each channel is processed independently.
The first function in the list above can be replaced with matrix expressions:
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.
See also
add()
,
addWeighted()
,
scaleAdd()
,
Mat::convertTo()
,
Matrix Expressions
SVD
¶Class for computing Singular Value Decomposition of a floating-point matrix. The Singular Value Decomposition is used to solve least-square problems, under-determined linear systems, invert matrices, compute condition numbers, and so on.
For a faster operation, you can pass flags=SVD::MODIFY_A|...
to modify the decomposed matrix when it is not necessary to preserve it. If you want to compute a condition number of a matrix or an absolute value of its determinant, you do not need u
and vt
. You can pass flags=SVD::NO_UV|...
. Another flag FULL_UV
indicates that full-size u
and vt
must be computed, which is not necessary most of the time.
See also
The constructors.
SVD::
SVD
()¶
SVD::
SVD
(InputArray src, int flags=0 )¶Parameters: |
|
---|
The first constructor initializes an empty SVD
structure. The second constructor initializes an empty SVD
structure and then calls
SVD::operator()
.
Performs SVD of a matrix.
SVD& SVD::
operator()
(InputArray src, int flags=0 )¶Parameters: |
|
---|
The operator performs the singular value decomposition of the supplied matrix. The u
,``vt`` , and the vector of singular values w
are stored in the structure. The same SVD
structure can be reused many times with different matrices. Each time, if needed, the previous u
,``vt`` , and w
are reclaimed and the new matrices are created, which is all handled by
Mat::create()
.
Performs SVD of a matrix
static void SVD::
compute
(InputArray src, OutputArray w, OutputArray u, OutputArray vt, int flags=0 )¶
static void SVD::
compute
(InputArray src, OutputArray w, int flags=0 )¶
cv2.
SVDecomp
(src[, w[, u[, vt[, flags]]]]) → w, u, vt¶
void cvSVD
(CvArr* A, CvArr* W, CvArr* U=NULL, CvArr* V=NULL, int flags=0 )¶
cv.
SVD
(A, W, U=None, V=None, flags=0) → None¶Parameters: |
|
---|
The methods/functions perform SVD of matrix. Unlike SVD::SVD
constructor and SVD::operator()
, they store the results to the user-provided matrices.
Mat A, w, u, vt;
SVD::compute(A, w, u, vt);
Solves an under-determined singular linear system.
static void SVD::
solveZ
(InputArray src, OutputArray dst)¶Parameters: |
|
---|
The method finds a unit-length solution x
of a singular linear system
A*x = 0
. Depending on the rank of A
, there can be no solutions, a single solution or an infinite number of solutions. In general, the algorithm solves the following problem:
Performs a singular value back substitution.
void SVD::
backSubst
(InputArray rhs, OutputArray dst) const
¶
static void SVD::
backSubst
(InputArray w, InputArray u, InputArray vt, InputArray rhs, OutputArray dst)¶
cv2.
SVBackSubst
(w, u, vt, rhs[, dst]) → dst¶
void cvSVBkSb
(const CvArr* W, const CvArr* U, const CvArr* V, const CvArr* B, CvArr* X, int flags)¶
cv.
SVBkSb
(W, U, V, B, X, flags) → None¶Parameters: |
|
---|
The method calculates a back substitution for the specified right-hand side:
Using this technique you can either get a very accurate solution of the convenient linear system, or the best (in the least-squares terms) pseudo-solution of an overdetermined linear system.
Note
Explicit SVD with the further back substitution only makes sense if you need to solve many linear systems with the same left-hand side (for example, src
). If all you need is to solve a single system (possibly with multiple rhs
immediately available), simply call solve()
add pass DECOMP_SVD
there. It does absolutely the same thing.
Calculates the sum of array elements.
Scalar sum
(InputArray src)¶
cv2.
sumElems
(src) → retval¶
CvScalar cvSum
(const CvArr* arr)¶
cv.
Sum
(arr) → scalar¶Parameters: | arr – input array that must have from 1 to 4 channels. |
---|
The functions sum
calculate and return the sum of array elements, independently for each channel.
See also
countNonZero()
,
mean()
,
meanStdDev()
,
norm()
,
minMaxLoc()
,
reduce()
Returns the default random number generator.
RNG& theRNG
()¶The function theRNG
returns the default random number generator. For each thread, there is a separate random number generator, so you can use the function safely in multi-thread environments. If you just need to get a single random number using this generator or initialize an array, you can use
randu()
or
randn()
instead. But if you are going to generate many random numbers inside a loop, it is much faster to use this function to retrieve the generator and then use RNG::operator _Tp()
.
Returns the trace of a matrix.
Scalar trace
(InputArray mtx)¶
cv2.
trace
(mtx) → retval¶
CvScalar cvTrace
(const CvArr* mat)¶
cv.
Trace
(mat) → scalar¶Parameters: | mat – input matrix. |
---|
The function trace
returns the sum of the diagonal elements of the matrix mtx
.
Performs the matrix transformation of every array element.
void transform
(InputArray src, OutputArray dst, InputArray m)¶
cv2.
transform
(src, m[, dst]) → dst¶
void cvTransform
(const CvArr* src, CvArr* dst, const CvMat* transmat, const CvMat* shiftvec=NULL )¶
cv.
Transform
(src, dst, transmat, shiftvec=None) → None¶Parameters: |
|
---|
The function transform
performs the matrix transformation of every element of the array src
and stores the results in dst
:
(when m.cols=src.channels()
), or
(when m.cols=src.channels()+1
)
Every element of the N
-channel array src
is interpreted as N
-element vector that is transformed using
the M x N
or M x (N+1)
matrix m
to M
-element vector - the corresponding element of the output array dst
.
The function may be used for geometrical transformation of
N
-dimensional
points, arbitrary linear color space transformation (such as various kinds of RGB to YUV transforms), shuffling the image channels, and so forth.
Transposes a matrix.
void transpose
(InputArray src, OutputArray dst)¶
cv2.
transpose
(src[, dst]) → dst¶
void cvTranspose
(const CvArr* src, CvArr* dst)¶
cv.
Transpose
(src, dst) → None¶Parameters: |
|
---|
The function transpose()
transposes the matrix src
:
Note
No complex conjugation is done in case of a complex matrix. It it should be done separately if needed.