opencv/doc/imgproc_object_detection.tex

%[TODO: from objdetect]
\section{Object Detection}

\ifCPy
\cvCPyFunc{MatchTemplate}
Compares a template against overlapped image regions.

\cvdefC{
void cvMatchTemplate( \par const CvArr* image,\par const CvArr* templ,\par CvArr* result,\par int method );
}\cvdefPy{MatchTemplate(image,templ,result,method)-> None}

\begin{description}
\cvarg{image}{Image where the search is running; should be 8-bit or 32-bit floating-point}
\cvarg{templ}{Searched template; must be not greater than the source image and the same data type as the image}
\cvarg{result}{A map of comparison results; single-channel 32-bit floating-point.
If \texttt{image} is $W \times H$ and
\texttt{templ} is $w \times h$ then \texttt{result} must be $(W-w+1) \times (H-h+1)$}
\cvarg{method}{Specifies the way the template must be compared with the image regions (see below)}
\end{description}

The function is similar to
\cvCPyCross{CalcBackProjectPatch}. It slides through \texttt{image}, compares the
overlapped patches of size $w \times h$ against \texttt{templ}
using the specified method and stores the comparison results to
\texttt{result}. Here are the formulas for the different comparison
methods one may use ($I$ denotes \texttt{image}, $T$ \texttt{template},
$R$ \texttt{result}). The summation is done over template and/or the
image patch: $x' = 0...w-1, y' = 0...h-1$

% \texttt{x'=0..w-1, y'=0..h-1}):

\begin{description}
\item[method=CV\_TM\_SQDIFF]
\[ R(x,y)=\sum_{x',y'} (T(x',y')-I(x+x',y+y'))^2 \]

\item[method=CV\_TM\_SQDIFF\_NORMED]
\[ R(x,y)=\frac
{\sum_{x',y'} (T(x',y')-I(x+x',y+y'))^2}
{\sqrt{\sum_{x',y'}T(x',y')^2 \cdot \sum_{x',y'} I(x+x',y+y')^2}}
\]

\item[method=CV\_TM\_CCORR]
\[ R(x,y)=\sum_{x',y'} (T(x',y') \cdot I(x+x',y+y')) \]

\item[method=CV\_TM\_CCORR\_NORMED]
\[ R(x,y)=\frac
{\sum_{x',y'} (T(x',y') \cdot I'(x+x',y+y'))}
{\sqrt{\sum_{x',y'}T(x',y')^2 \cdot \sum_{x',y'} I(x+x',y+y')^2}}
\]

\item[method=CV\_TM\_CCOEFF]
\[ R(x,y)=\sum_{x',y'} (T'(x',y') \cdot I(x+x',y+y')) \]

where
\[ 
\begin{array}{l}
T'(x',y')=T(x',y') - 1/(w \cdot h) \cdot \sum_{x'',y''} T(x'',y'')\\
I'(x+x',y+y')=I(x+x',y+y') - 1/(w \cdot h) \cdot \sum_{x'',y''} I(x+x'',y+y'')
\end{array}
\]

\item[method=CV\_TM\_CCOEFF\_NORMED]
\[ R(x,y)=\frac
{ \sum_{x',y'} (T'(x',y') \cdot I'(x+x',y+y')) }
{ \sqrt{\sum_{x',y'}T'(x',y')^2 \cdot \sum_{x',y'} I'(x+x',y+y')^2} }
\]
\end{description}

After the function finishes the comparison, the best matches can be found as global minimums (\texttt{CV\_TM\_SQDIFF}) or maximums (\texttt{CV\_TM\_CCORR} and \texttt{CV\_TM\_CCOEFF}) using the \cvCPyCross{MinMaxLoc} function. In the case of a color image, template summation in the numerator and each sum in the denominator is done over all of the channels (and separate mean values are used for each channel).

\fi

\ifCpp

\cvCppFunc{matchTemplate}
Compares a template against overlapped image regions.

\cvdefCpp{void matchTemplate( const Mat\& image, const Mat\& templ,\par
                    Mat\& result, int method );}
\begin{description}
\cvarg{image}{Image where the search is running; should be 8-bit or 32-bit floating-point}
\cvarg{templ}{Searched template; must be not greater than the source image and have the same data type}
\cvarg{result}{A map of comparison results; will be single-channel 32-bit floating-point.
If \texttt{image} is $W \times H$ and
\texttt{templ} is $w \times h$ then \texttt{result} will be $(W-w+1) \times (H-h+1)$}
\cvarg{method}{Specifies the comparison method (see below)}
\end{description}

The function slides through \texttt{image}, compares the
overlapped patches of size $w \times h$ against \texttt{templ}
using the specified method and stores the comparison results to
\texttt{result}. Here are the formulas for the available comparison
methods ($I$ denotes \texttt{image}, $T$ \texttt{template},
$R$ \texttt{result}). The summation is done over template and/or the
image patch: $x' = 0...w-1, y' = 0...h-1$

% \texttt{x'=0..w-1, y'=0..h-1}):

\begin{description}
\item[method=CV\_TM\_SQDIFF]
\[ R(x,y)=\sum_{x',y'} (T(x',y')-I(x+x',y+y'))^2 \]

\item[method=CV\_TM\_SQDIFF\_NORMED]
\[ R(x,y)=\frac
{\sum_{x',y'} (T(x',y')-I(x+x',y+y'))^2}
{\sqrt{\sum_{x',y'}T(x',y')^2 \cdot \sum_{x',y'} I(x+x',y+y')^2}}
\]

\item[method=CV\_TM\_CCORR]
\[ R(x,y)=\sum_{x',y'} (T(x',y') \cdot I(x+x',y+y')) \]

\item[method=CV\_TM\_CCORR\_NORMED]
\[ R(x,y)=\frac
{\sum_{x',y'} (T(x',y') \cdot I'(x+x',y+y'))}
{\sqrt{\sum_{x',y'}T(x',y')^2 \cdot \sum_{x',y'} I(x+x',y+y')^2}}
\]

\item[method=CV\_TM\_CCOEFF]
\[ R(x,y)=\sum_{x',y'} (T'(x',y') \cdot I(x+x',y+y')) \]

where
\[ 
\begin{array}{l}
T'(x',y')=T(x',y') - 1/(w \cdot h) \cdot \sum_{x'',y''} T(x'',y'')\\
I'(x+x',y+y')=I(x+x',y+y') - 1/(w \cdot h) \cdot \sum_{x'',y''} I(x+x'',y+y'')
\end{array}
\]

\item[method=CV\_TM\_CCOEFF\_NORMED]
\[ R(x,y)=\frac
{ \sum_{x',y'} (T'(x',y') \cdot I'(x+x',y+y')) }
{ \sqrt{\sum_{x',y'}T'(x',y')^2 \cdot \sum_{x',y'} I'(x+x',y+y')^2} }
\]
\end{description}

After the function finishes the comparison, the best matches can be found as global minimums (when \texttt{CV\_TM\_SQDIFF} was used) or maximums (when \texttt{CV\_TM\_CCORR} or \texttt{CV\_TM\_CCOEFF} was used) using the \cvCppCross{minMaxLoc} function. In the case of a color image, template summation in the numerator and each sum in the denominator is done over all of the channels (and separate mean values are used for each channel). That is, the function can take a color template and a color image; the result will still be a single-channel image, which is easier to analyze.

\fi