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Kirsch operator

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Kirsch operator

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 A. Kirsch.

Mathematical description

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:

h n , m = m a x z = 1 , … , 8 ∑ i = − 1 1 ∑ j = − 1 1 g i j ( z ) ⋅ f n + i , m + j

where z enumerates the compass direction kernels g:

g ( 1 ) = [ + 5 + 5 + 5 − 3 0 − 3 − 3 − 3 − 3 ] ,   g ( 2 ) = [ + 5 + 5 − 3 + 5 0 − 3 − 3 − 3 − 3 ] ,   g ( 3 ) = [ + 5 − 3 − 3 + 5 0 − 3 + 5 − 3 − 3 ] ,   g ( 4 ) = [ − 3 − 3 − 3 + 5 0 − 3 + 5 + 5 − 3 ] and so on.

The edge direction is defined by the mask that produces the maximum edge magnitude.

References

Kirsch operator Wikipedia
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