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:
where z enumerates the compass direction kernels
and so on.
The edge direction is defined by the mask that produces the maximum edge magnitude.
Example images
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Boxfilter pavilion original.jpg
Original
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Kirschfilter maximum.jpg
Maximum gradient in the 8 directions
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Kirschfilter1.jpg
Image filtered with g1
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Kirschfilter2.jpg
Image filtered with g2
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Kirschfilter3.jpg
Image filtered with g3
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Kirschfilter4.jpg
Image filtered with g4
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Kirschfilter5.jpg
Image filtered with g5
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Kirschfilter6.jpg
Image filtered with g6
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Kirschfilter7.jpg
Image filtered with g7
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Kirschfilter8.jpg
Image filtered with g8
References
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