Added example to the documentation for the NormTypes enum (L1, L2, INF)

diff --git a/modules/core/doc/pics/NormTypes_OneArray_1-2-INF.png b/modules/core/doc/pics/NormTypes_OneArray_1-2-INF.png
new file mode 100644 (file)
index 0000000..ec4304d
Binary files /dev/null and b/modules/core/doc/pics/NormTypes_OneArray_1-2-INF.png differ

diff --git a/modules/core/include/opencv2/core/base.hpp b/modules/core/include/opencv2/core/base.hpp
index 3ab0982..8fabf5f 100644 (file)
--- a/modules/core/include/opencv2/core/base.hpp
+++ b/modules/core/include/opencv2/core/base.hpp
@@ -164,7 +164,25 @@ enum DecompTypes {
 \f[norm =  \forkthree{\frac{\|\texttt{src1}-\texttt{src2}\|_{L_{\infty}}    }{\|\texttt{src2}\|_{L_{\infty}} }}{if  \(\texttt{normType} = \texttt{NORM_RELATIVE_INF}\) }
 { \frac{\|\texttt{src1}-\texttt{src2}\|_{L_1} }{\|\texttt{src2}\|_{L_1}} }{if  \(\texttt{normType} = \texttt{NORM_RELATIVE_L1}\) }
 { \frac{\|\texttt{src1}-\texttt{src2}\|_{L_2} }{\|\texttt{src2}\|_{L_2}} }{if  \(\texttt{normType} = \texttt{NORM_RELATIVE_L2}\) }\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,
                  NORM_L1        = 2,
                  NORM_L2        = 4,