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Decomposing the Laplacian

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1 Author(s)
Piech, M.A. ; Dept. of Math., State Univ. of New York, Buffalo, NY, USA

A correction is made and an elementary derivation is given of Clark's (ibid., vol.11, p.43-57, 1989) decomposition of the Laplacian Δ2f(x,y) into a second directional derivative in the gradient direction of f, and a product of gradient magnitude by curvature of the level curve through f(x,y)

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Pattern Analysis and Machine Intelligence, IEEE Transactions on  (Volume:12 ,  Issue: 8 )