Kirsch-Operator
Encyclopedia
The Kirsch-operator is a non-linear
Nonlinearity
In mathematics, a nonlinear system is one that does not satisfy the superposition principle, or one whose output is not directly proportional to its input; a linear system fulfills these conditions. In other words, a nonlinear system is any problem where the variable to be solved for cannot be...

 edge detector
Edge detection
Edge detection is a fundamental tool in image processing and computer vision, particularly in the areas of feature detection and feature extraction, which aim at identifying points in a digital image at which the image brightness changes sharply or, more formally, has discontinuities...

that finds the maximum edge strength in a few predetermined directions.

Mathematical description

The operator is calculated as follows for directions with 45° difference:

where the direction kernels and so on.
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