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i9482: Improve documentation concerning norm functionality.

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Added forkfour Latex command to math js support.

Split cv::norm documentation between the cv::norm and its overload, to make things clearer

Corrected some typos and cleaned up grammar.

Result is clearer documentation for the norms.

Work pending...
This commit is contained in:
saskatchewancatch 2017-09-06 22:35:39 -06:00
parent 1caca2112b
commit b32685c714
4 changed files with 52 additions and 34 deletions
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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], 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], 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], 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], vecthree: ["\\begin{bmatrix} #1\\\\ #2\\\\ #3 \\end{bmatrix}", 3],
vecthreethree: ["\\begin{bmatrix} #1 & #2 & #3\\\\ #4 & #5 & #6\\\\ #7 & #8 & #9 \\end{bmatrix}", 9], vecthreethree: ["\\begin{bmatrix} #1 & #2 & #3\\\\ #4 & #5 & #6\\\\ #7 & #8 & #9 \\end{bmatrix}", 9],
hdotsfor: ["\\dots", 1], hdotsfor: ["\\dots", 1],

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

59
modules/core/include/opencv2/core.hpp
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@ -640,34 +640,44 @@ Scalar_ 's.
CV_EXPORTS_W void meanStdDev(InputArray src, OutputArray mean, OutputArray stddev, CV_EXPORTS_W void meanStdDev(InputArray src, OutputArray mean, OutputArray stddev,
InputArray mask=noArray()); InputArray mask=noArray());
/** @brief Calculates an absolute array norm, an absolute difference norm, or a /** @brief Calculates an absolute array norm.
relative difference norm.
The function cv::norm calculates an absolute norm of src1 (when there is no This version of cv::norm calculates the absolute norm of src1. The type of norm to calculate is specified using cv::NormTypes.
src2 ):
\f[norm = \forkthree{\|\texttt{src1}\|_{L_{\infty}} = \max _I | \texttt{src1} (I)|}{if \(\texttt{normType} = \texttt{NORM_INF}\) } \f[norm = \forkfour{\|\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_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] { \| \texttt{src1} \| _{L_2} = \sqrt{\sum_I \texttt{src1}(I)^2} }{if \(\texttt{normType} = \texttt{NORM_L2}\) }
{ \| \texttt{src1} \| _{L_2} ^{2} = \sum_I \texttt{src1}(I)^2} {if \(\texttt{normType} = \texttt{NORM_L2SQR}\)}\f]
If normType is not specified, NORM_L2 is used.
or an absolute or relative difference norm if src2 is there: 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 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$r(-1) = \begin{pmatrix} -1 \\ 2 \end{pmatrix}\f$
\f[norm = \forkthree{\frac{\|\texttt{src1}-\texttt{src2}\|_{L_{\infty}} }{\|\texttt{src2}\|_{L_{\infty}} }}{if \(\texttt{normType} = \texttt{NORM_RELATIVE | NORM_INF}\) } is calculated as follows
{ \frac{\|\texttt{src1}-\texttt{src2}\|_{L_1} }{\|\texttt{src2}\|_{L_1}} }{if \(\texttt{normType} = \texttt{NORM_RELATIVE | NORM_L1}\) } \f{align*}
{ \frac{\|\texttt{src1}-\texttt{src2}\|_{L_2} }{\|\texttt{src2}\|_{L_2}} }{if \(\texttt{normType} = \texttt{NORM_RELATIVE | NORM_L2}\) }\f] \| 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)
The function cv::norm returns the calculated norm. The function cv::norm returns the calculated norm.
When the mask parameter is specified and it is not empty, the norm is When the mask parameter is specified and it is not empty, the norm is
calculated only over the region specified by the mask. 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. the results for all channels are combined.
@param src1 first input array. @param src1 first input array.
@ -676,7 +686,24 @@ the results for all channels are combined.
*/ */
CV_EXPORTS_W double norm(InputArray src1, int normType = NORM_L2, InputArray mask = noArray()); 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.
\f[norm = \forkfour{\|\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 \(\texttt{normType} = \texttt{NORM_L2}\) }
{ \| \texttt{src1} - \texttt{src2} \| _{L_2} ^{2} = \sum_I (\texttt{src1}(I) - \texttt{src2}(I))^2 }{if \(\texttt{normType} = \texttt{NORM_L2SQR}\) }
\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]
@param src1 first input array. @param src1 first input array.
@param src2 second input array of the same size and the same type as src1. @param src2 second input array of the same size and the same type as src1.
@param normType type of the norm (cv::NormTypes). @param normType type of the norm (cv::NormTypes).

17
modules/core/include/opencv2/core/base.hpp
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@ -167,23 +167,6 @@ enum DecompTypes {
{ \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_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] { \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, enum NormTypes { NORM_INF = 1,
NORM_L1 = 2, NORM_L1 = 2,