The Kirsch operator or Kirsch compass kernel is a non-linear edge detector that finds the maximum edge strength in a few predetermined directions. It is named after the computer scientist Russell Kirsch.
The operator takes a single kernel mask and rotates it in 45 degree increments through all 8 compass directions: N, NW, W, SW, S, SE, E, and NE. The edge magnitude of the Kirsch operator is calculated as the maximum magnitude across all directions:
hn,m=maxz=1,...,8
| (z) | |
| \sum | |
| ij |
⋅ fn+i,m+j
where z enumerates the compass direction kernels g:
| g(1) |
=\begin{bmatrix}+5&+5&+5\\ -3&0&-3\\ -3&-3&-3\end{bmatrix},
| g(2) |
=\begin{bmatrix}+5&+5&-3\\ +5&0&-3\\ -3&-3&-3\end{bmatrix},
| g(3) |
=\begin{bmatrix}+5&-3&-3\\ +5&0&-3\\ +5&-3&-3\end{bmatrix},
| g(4) |
=\begin{bmatrix}-3&-3&-3\\ +5&0&-3\\ +5&+5&-3\end{bmatrix}
The edge direction is defined by the mask that produces the maximum edge magnitude.