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=== Canny ===
{{main|Canny edge detector}}
[[John Canny]] considered the mathematical problem of deriving an optimal smoothing filter, given the criteria of detection, localization and minimizing multiple responses to a single edge.<ref>J. Canny (1986) "[http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.420.3300&rep=rep1&type=pdf A computational approach to edge detection]", IEEE Transactions on Pattern Analysis and Machine Intelligence, vol 8, pages 679–714.</ref> He showed that the optimal filter, given these assumptions, is a sum of four exponential terms. He also showed that this filter can be well approximated by first-order derivatives of Gaussians.
Canny also introduced the notion of non-maximum suppression, which means that, given the presmoothing filters, edge points are defined as points where the gradient magnitude assumes a local maximum in the gradient direction.
Looking for the zero crossing of the 2nd derivative along the gradient direction was first proposed by [[Haralick]].<ref>
R. Haralick, (1984) "[http://haralick-org.torahcode.us/journals/04767475.pdf Digital step edges from zero crossing of second directional derivatives]", IEEE Transactions on Pattern Analysis and Machine Intelligence, 6(1):58–68.
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It took less than two decades to find a modern geometric variational meaning for that operator, that links it to the [[Marr–Hildreth algorithm|Marr–Hildreth]] (zero crossing of the Laplacian) edge detector.
That observation was presented by [[Ron Kimmel]] and [[Alfred Bruckstein]].<ref>{{Cite web |url=https://www.cs.technion.ac.il/~ron/PAPERS/laplacian_ijcv2003.pdf |title=R. Kimmel and A.M. Bruckstein (2003) "On regularized Laplacian zero crossings and other optimal edge integrators", ''International Journal of Computer Vision'', 53(3) pages 225–243. |access-date=2019-09-15 |archive-date=2021-03-08 |archive-url=https://web.archive.org/web/20210308012954/https://www.cs.technion.ac.il/~ron/PAPERS/laplacian_ijcv2003.pdf |url-status=dead }}</ref>
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