Variance filter

The variance filter is a non-linear edge detector used in image processing .

An analytical description is possible as follows:

${\displaystyle h_{nm}=S_{nm}^{2}={\frac {1}{(2M+1)^{2}}}\ \sum _{i=-M}^{+M}\sum _{j=-M}^{+M}(f_{n+i,m+j}-{\bar {f}}_{nm})^{2}}$

where denotes the gray value mean of the current environment. ${\displaystyle {\bar {f}}_{nm}}$