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Merge pull request #9574 from saskatchewancatch:i9482

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pull/9454/merge
Vadim Pisarevsky 7 years ago
parent 8c7f19850f c9d3c0f206
commit f1aa180a40
4 changed files with 87 additions and 61 deletions
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  1. 1
      doc/mymath.js
  2. 9
      doc/mymath.sty
  3. 57
      modules/core/include/opencv2/core.hpp
  4. 81
      modules/core/include/opencv2/core/base.hpp

1
doc/mymath.js
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@ -6,6 +6,7 @@ MathJax.Hub.Config(
matTT: [ "\\[ \\left|\\begin{array}{ccc} #1 & #2 & #3\\\\ #4 & #5 & #6\\\\ #7 & #8 & #9 \\end{array}\\right| \\]", 9],
fork: ["\\left\\{ \\begin{array}{l l} #1 & \\mbox{#2}\\\\ #3 & \\mbox{#4}\\\\ \\end{array} \\right.", 4],
forkthree: ["\\left\\{ \\begin{array}{l l} #1 & \\mbox{#2}\\\\ #3 & \\mbox{#4}\\\\ #5 & \\mbox{#6}\\\\ \\end{array} \\right.", 6],
forkfour: ["\\left\\{ \\begin{array}{l l} #1 & \\mbox{#2}\\\\ #3 & \\mbox{#4}\\\\ #5 & \\mbox{#6}\\\\ #7 & \\mbox{#8}\\\\ \\end{array} \\right.", 8],
vecthree: ["\\begin{bmatrix} #1\\\\ #2\\\\ #3 \\end{bmatrix}", 3],
vecthreethree: ["\\begin{bmatrix} #1 & #2 & #3\\\\ #4 & #5 & #6\\\\ #7 & #8 & #9 \\end{bmatrix}", 9],
hdotsfor: ["\\dots", 1],

9
doc/mymath.sty
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@ -28,7 +28,14 @@
#3 & \mbox{#4}\\
#5 & \mbox{#6}\\
\end{array} \right.}
\newcommand{\forkthree}[8]{
\left\{
\begin{array}{l l}
#1 & \mbox{#2}\\
#3 & \mbox{#4}\\
#5 & \mbox{#6}\\
#7 & \mbox{#8}\\
\end{array} \right.}
\newcommand{\vecthree}[3]{
\begin{bmatrix}
#1\\

57
modules/core/include/opencv2/core.hpp
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@ -640,43 +640,50 @@ Scalar_ 's.
CV_EXPORTS_W void meanStdDev(InputArray src, OutputArray mean, OutputArray stddev,
InputArray mask=noArray());
/** @brief Calculates an absolute array norm, an absolute difference norm, or a
relative difference norm.
The function cv::norm calculates an absolute norm of src1 (when there is no
src2 ):
\f[norm = \forkthree{\|\texttt{src1}\|_{L_{\infty}} = \max _I | \texttt{src1} (I)|}{if \(\texttt{normType} = \texttt{NORM_INF}\) }
{ \| \texttt{src1} \| _{L_1} = \sum _I | \texttt{src1} (I)|}{if \(\texttt{normType} = \texttt{NORM_L1}\) }
{ \| \texttt{src1} \| _{L_2} = \sqrt{\sum_I \texttt{src1}(I)^2} }{if \(\texttt{normType} = \texttt{NORM_L2}\) }\f]
or an absolute or relative difference norm if src2 is there:
\f[norm = \forkthree{\|\texttt{src1}-\texttt{src2}\|_{L_{\infty}} = \max _I | \texttt{src1} (I) - \texttt{src2} (I)|}{if \(\texttt{normType} = \texttt{NORM_INF}\) }
{ \| \texttt{src1} - \texttt{src2} \| _{L_1} = \sum _I | \texttt{src1} (I) - \texttt{src2} (I)|}{if \(\texttt{normType} = \texttt{NORM_L1}\) }
{ \| \texttt{src1} - \texttt{src2} \| _{L_2} = \sqrt{\sum_I (\texttt{src1}(I) - \texttt{src2}(I))^2} }{if \(\texttt{normType} = \texttt{NORM_L2}\) }\f]
or
\f[norm = \forkthree{\frac{\|\texttt{src1}-\texttt{src2}\|_{L_{\infty}} }{\|\texttt{src2}\|_{L_{\infty}} }}{if \(\texttt{normType} = \texttt{NORM_RELATIVE | NORM_INF}\) }
{ \frac{\|\texttt{src1}-\texttt{src2}\|_{L_1} }{\|\texttt{src2}\|_{L_1}} }{if \(\texttt{normType} = \texttt{NORM_RELATIVE | NORM_L1}\) }
{ \frac{\|\texttt{src1}-\texttt{src2}\|_{L_2} }{\|\texttt{src2}\|_{L_2}} }{if \(\texttt{normType} = \texttt{NORM_RELATIVE | NORM_L2}\) }\f]
The function cv::norm returns the calculated norm.
/** @brief Calculates the absolute norm of an array.
This version of cv::norm calculates the absolute norm of src1. The type of norm to calculate is specified using cv::NormTypes.
As example for one array consider the function \f$r(x)= \begin{pmatrix} x \\ 1-x \end{pmatrix}, x \in [-1;1]\f$.
The \f$ L_{1}, L_{2} \f$ and \f$ L_{\infty} \f$ norm for the sample value \f$r(-1) = \begin{pmatrix} -1 \\ 2 \end{pmatrix}\f$
is calculated as follows
\f{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
\f}
and for \f$r(0.5) = \begin{pmatrix} 0.5 \\ 0.5 \end{pmatrix}\f$ the calculation is
\f{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.
\f}
The following graphic shows all values for the three norm functions \f$\| r(x) \|_{L_1}, \| r(x) \|_{L_2}\f$ and \f$\| r(x) \|_{L_\infty}\f$.
It is notable that the \f$ L_{1} \f$ norm forms the upper and the \f$ L_{\infty} \f$ norm forms the lower border for the example function \f$ r(x) \f$.
![Graphs for the different norm functions from the above example](pics/NormTypes_OneArray_1-2-INF.png)
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.
A multi-channel input arrays are treated as a single-channel, that is,
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.
@param src1 first input array.
@param normType type of the norm (see cv::NormTypes).
@param mask optional operation mask; it must have the same size as src1 and CV_8UC1 type.
*/
CV_EXPORTS_W double norm(InputArray src1, int normType = NORM_L2, InputArray mask = noArray());
/** @overload
/** @brief Calculates an absolute difference norm or a relative difference norm.
This version of cv::norm calculates the absolute difference norm
or the relative difference norm of arrays src1 and src2.
The type of norm to calculate is specified using cv::NormTypes.
@param src1 first input array.
@param src2 second input array of the same size and the same type as src1.
@param normType type of the norm (cv::NormTypes).

81
modules/core/include/opencv2/core/base.hpp
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@ -152,46 +152,57 @@ enum DecompTypes {
};
/** norm types
- For one array:
\f[norm = \forkthree{\|\texttt{src1}\|_{L_{\infty}} = \max _I | \texttt{src1} (I)|}{if \(\texttt{normType} = \texttt{NORM_INF}\) }
{ \| \texttt{src1} \| _{L_1} = \sum _I | \texttt{src1} (I)|}{if \(\texttt{normType} = \texttt{NORM_L1}\) }
{ \| \texttt{src1} \| _{L_2} = \sqrt{\sum_I \texttt{src1}(I)^2} }{if \(\texttt{normType} = \texttt{NORM_L2}\) }\f]
- Absolute norm for two arrays
\f[norm = \forkthree{\|\texttt{src1}-\texttt{src2}\|_{L_{\infty}} = \max _I | \texttt{src1} (I) - \texttt{src2} (I)|}{if \(\texttt{normType} = \texttt{NORM_INF}\) }
{ \| \texttt{src1} - \texttt{src2} \| _{L_1} = \sum _I | \texttt{src1} (I) - \texttt{src2} (I)|}{if \(\texttt{normType} = \texttt{NORM_L1}\) }
{ \| \texttt{src1} - \texttt{src2} \| _{L_2} = \sqrt{\sum_I (\texttt{src1}(I) - \texttt{src2}(I))^2} }{if \(\texttt{normType} = \texttt{NORM_L2}\) }\f]
- Relative norm for two arrays
\f[norm = \forkthree{\frac{\|\texttt{src1}-\texttt{src2}\|_{L_{\infty}} }{\|\texttt{src2}\|_{L_{\infty}} }}{if \(\texttt{normType} = \texttt{NORM_RELATIVE | NORM_INF}\) }
{ \frac{\|\texttt{src1}-\texttt{src2}\|_{L_1} }{\|\texttt{src2}\|_{L_1}} }{if \(\texttt{normType} = \texttt{NORM_RELATIVE | NORM_L1}\) }
{ \frac{\|\texttt{src1}-\texttt{src2}\|_{L_2} }{\|\texttt{src2}\|_{L_2}} }{if \(\texttt{normType} = \texttt{NORM_RELATIVE | NORM_L2}\) }\f]
As example for one array consider the function \f$r(x)= \begin{pmatrix} x \\ 1-x \end{pmatrix}, x \in [-1;1]\f$.
The \f$ L_{1}, L_{2} \f$ and \f$ L_{\infty} \f$ norm for the sample value \f$r(-1) = \begin{pmatrix} -1 \\ 2 \end{pmatrix}\f$
is calculated as follows
\f{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
\f}
and for \f$r(0.5) = \begin{pmatrix} 0.5 \\ 0.5 \end{pmatrix}\f$ the calculation is
\f{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.
\f}
The following graphic shows all values for the three norm functions \f$\| r(x) \|_{L_1}, \| r(x) \|_{L_2}\f$ and \f$\| r(x) \|_{L_\infty}\f$.
It is notable that the \f$ L_{1} \f$ norm forms the upper and the \f$ L_{\infty} \f$ norm forms the lower border for the example function \f$ r(x) \f$.
![Graphs for the different norm functions from the above example](pics/NormTypes_OneArray_1-2-INF.png)
*/
enum NormTypes { NORM_INF = 1,
src1 and src2 denote input arrays.
*/
enum NormTypes {
/**
\f[
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 \(\texttt{normType} = \texttt{NORM_RELATIVE | NORM_INF}\) }
\f]
*/
NORM_INF = 1,
/**
\f[
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 \(\texttt{normType} = \texttt{NORM_RELATIVE | NORM_L1}\) }
\f]*/
NORM_L1 = 2,
/**
\f[
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 \(\texttt{normType} = \texttt{NORM_RELATIVE | NORM_L2}\) }
\f]
*/
NORM_L2 = 4,
/**
\f[
norm = \forkthree
{ \| \texttt{src1} \| _{L_2} ^{2} = \sum_I \texttt{src1}(I)^2} {if \(\texttt{normType} = \texttt{NORM_L2SQR}\)}
{ \| \texttt{src1} - \texttt{src2} \| _{L_2} ^{2} = \sum_I (\texttt{src1}(I) - \texttt{src2}(I))^2 }{if \(\texttt{normType} = \texttt{NORM_L2SQR}\) }
{ \left(\frac{\|\texttt{src1}-\texttt{src2}\|_{L_2} }{\|\texttt{src2}\|_{L_2}}\right)^2 }{if \(\texttt{normType} = \texttt{NORM_RELATIVE | NORM_L2}\) }
\f]
*/
NORM_L2SQR = 5,
/**
In the case of one input array, calculates the Hamming distance of the array from zero,
In the case of two input arrays, calculates the Hamming distance between the arrays.
*/
NORM_HAMMING = 6,
/**
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_HAMMING2 = 7,
NORM_TYPE_MASK = 7,
NORM_TYPE_MASK = 7, //!< bit-mask which can be used to separate norm type from norm flags
NORM_RELATIVE = 8, //!< flag
NORM_MINMAX = 32 //!< flag
};

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