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Image selective smoothing and edge detection by nonlinear diffusion. II. (English) Zbl 0766.65117
[For part I, see ibid. 29, No. 1, 182–193 (1992; Zbl 0746.65091).]
The authors study a class of nonlinear parabolic integro-differential equations for image processing. The diffusion term is modelled in such a way, that the dependent variable diffuses in the direction orthogonal to its gradient but not in all directions. Thereby the dependent variable can be made smooth near an “edge”, with a minimal smoothing of the edge.
A stable algorithm is then proposed for image restoration. It is based on the “mean curvature motion” equation. Application of the solution is persuasively demonstrated for several cases.
Reviewer: E.Krause (Aachen)

MSC:
65R10 Numerical methods for integral transforms
45K05 Integro-partial differential equations
65R20 Numerical methods for integral equations
49Q20 Variational problems in a geometric measure-theoretic setting
35K55 Nonlinear parabolic equations
35R10 Partial functional-differential equations
49J45 Methods involving semicontinuity and convergence; relaxation
49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
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