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The Kirsch-operator is a non-linear edge detector 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. Example images Original Maximum gradient in the 8 directions Image filtered with g1 Image filtered with g2 Image filtered with g3 Image filtered with g4 Image filtered with g5 Image filtered with g6 Image filtered with g7 Image filtered with g8 References Kirsch, R. (1971). "Computer determination of the constituent structure of biological images". Computers and Biomedical Research 4: 315-328. doi:10.1016/0010-4809(71)90034-6. http://www.sciencedirect.com/science/article/pii/0010480971900346.