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Zbl 0746.65091
Catté, Francine; Lions, Pierre-Louis; Morel, Jean-Michel; Coll, Tomeu
Image selective smoothing and edge detection by nonlinear diffusion. (English)
[J] SIAM J. Numer. Anal. 29, No.1, 182-193 (1992). ISSN 0036-1429; ISSN 1095-7170/e

Authors propose a modification of the theory developed by {\it P. Perona} and {\it J. Malik} [Scale space and edge detection using anisotropic diffusion. Proc. IEEE Comput. Soc. Workshop on Computer Vision (1987) for edge detection and image restoration. This problem is closely related to solving the heat equation with the signal as initial condition. The paper first discusses in detail the theory mentioned above and proceeds then to describe the improvements and changes introduced by the authors. They discuss the consistency of their model, existence, uniqueness and an iterative solution. Finally the discretization of the solution is presented, along with some numerical results.
[E.Krause (Aachen)]

MSC 2000:: *65D17 Computer aided design (modeling of curves and surfaces)
76R50 Diffusion
94A08 Image processing
35K55 Nonlinear parabolic equations
68U10 Image processing
93D05 Lyapunov and other classical stabilities of control systems

Keywords: multiscale image analysis; nonlinear diffusion; stability; edge detection; image restoration; heat equation; consistency; iterative solution; numerical results

Cited in: Zbl 1131.35041 Zbl 1124.65096 Zbl 1033.35067 Zbl 1016.65069 Zbl 1013.65094 Zbl 0971.65085 Zbl 0971.65084 Zbl 0766.65117

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