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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.


MSC:
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.)