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Decomposing the Laplacian
August 1990 (vol. 12 no. 8)
pp. 830-831

Correction is made and an elementary derivation is given of Clark's decomposition of the Laplacian Delta /sup 2/f(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).

[1] J. J. Clark, "Authenticating edges produced by zero-crossing algorithms,"IEEE Trans. Pattern Anal. Machine Intell., vol. 11, pp. 43- 57, 1989.
[2] R. M. Haralick, "Digital step edges from zero crossing of second directional derivatives,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-6, pp. 58-68, 1984.
[3] G. B. Thomas, Jr. and R. L. Finney,Calculus and Analytic Geometry, 7th ed. Reading, MA: Addison-Wesley, 1988.

Index Terms:
Laplacian; decomposition; second directional derivative; calculus
M.A. Piech, "Decomposing the Laplacian," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 12, no. 8, pp. 830-831, Aug. 1990, doi:10.1109/34.57673
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