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Zbl 0766.65117
Alvarez, Luis; Lions, Pierre-Louis; Morel, Jean-Michel
(Alvarez León, Luis)
Image selective smoothing and edge detection by nonlinear diffusion. II. (English)
[J] SIAM J. Numer. Anal. 29, No. 3, 845-866 (1992). ISSN 0036-1429; ISSN 1095-7170/e

[For part I, see ibid. 29, No. 1, 182--193 (1992; Zbl 0746.65091).]\par 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.\par 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.
[E.Krause (Aachen)]

MSC 2000:: *65R10 Integral transforms (numerical methods)
45K05 Integro-partial differential equations
65R20 Integral equations (numerical methods)
49Q20 Variational problems in geometric measure-theoretic setting
35K55 Nonlinear parabolic equations
35R10 Difference-partial differential equations
49J45 Optimal control problems inv. semicontinuity and convergence
49L25 Viscosity solutions
65M12 Stability and convergence of numerical methods (IVP of PDE)
94A08 Image processing

Keywords: image smoothing; diffusion equation; mean curvature motion equation; nonlinear parabolic integro-differential equations; image processing; image restoration

Citations: Zbl 0746.65091

Cited in: Zbl 1138.68631 Zbl 1131.35041 Zbl 0817.65017

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