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Evolution of characteristic functions of convex sets in the plane by the minimizing total variation flow

Alter, François; Caselles, Vincent; Chambolle, Antonin (2005), Evolution of characteristic functions of convex sets in the plane by the minimizing total variation flow, Interfaces and free boundaries, 7, 1, p. 29-53. http://dx.doi.org/10.4171/IFB/112

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Type
Article accepté pour publication ou publié
Date
2005
Journal name
Interfaces and free boundaries
Volume
7
Number
1
Publisher
European Mathematical Society
Pages
29-53
Publication identifier
Metadata
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Author(s)
Alter, François
Caselles, Vincent
Chambolle, Antonin cc
Abstract (EN)
In this paper we compute the explicit evolution of the Minimizing Total Variation flow when the initial condition is the characteristic function of a convex set in R2, or a finite number of them which are sufficiently separated. We shall also obtain some explicit solutions of the Total Variation formulation of the denoising problem in image processing. We illustrate these results with some experiments.
Subjects / Keywords
BV functions; total variation flow; convex set; denoising