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 | Integral transforms (numerical methods) |

45K05 | Integro-partial differential equations |

65R20 | Integral equations (numerical methods) |

49Q20 | Variational problems in a geometric measure-theoretic setting |

35K55 | Nonlinear parabolic equations |

35R10 | Partial functional-differential equations |

49J45 | Optimal control problems involving semicontinuity and convergence; relaxation |

49L25 | Viscosity solutions (infinite-dimensional problems) |

65M12 | Stability and convergence of numerical methods (IVP of PDE) |

94A08 | Image processing (compression, reconstruction, etc.) |