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Image selective smoothing and edge detection by nonlinear diffusion. (English) Zbl 0746.65091
Authors propose a modification of the theory developed by P. Perona and 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.
Reviewer: E.Krause (Aachen)

65D17 Computer-aided design (modeling of curves and surfaces)
76R50 Diffusion
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
35K55 Nonlinear parabolic equations
68U10 Computing methodologies for image processing
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
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