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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.

65R10Integral transforms (numerical methods)
45K05Integro-partial differential equations
65R20Integral equations (numerical methods)
49Q20Variational problems in a geometric measure-theoretic setting
35K55Nonlinear parabolic equations
35R10Partial functional-differential equations
49J45Optimal control problems involving semicontinuity and convergence; relaxation
49L25Viscosity solutions (infinite-dimensional problems)
65M12Stability and convergence of numerical methods (IVP of PDE)
94A08Image processing (compression, reconstruction, etc.)
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