Geodesic
Evolution of characteristic functions of convex sets in the plane by the minimizing total variation flow
François Alter1 ; Vicent Caselles2 ; Antonin Chambolle3 orcid
1CMLA-ENS, Cachan, France
2Universitat Pompeu-Fabra, Barcelona, Spain
3Ecole Polytechnique, Palaiseau, France
Interfaces and free boundaries, Tome 7 (2005) no. 1, pp. 29-53

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DOI

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.
DOI : 10.4171/ifb/112
Classification : 35-XX, 65-XX, 76-XX, 92-XX
Mots-clés : BV functions, total variation flow, convex set, denoising

François Alter  1   ; Vicent Caselles  2   ; Antonin Chambolle  3

1 CMLA-ENS, Cachan, France
2 Universitat Pompeu-Fabra, Barcelona, Spain
3 Ecole Polytechnique, Palaiseau, France 
François Alter; Vicent Caselles; Antonin Chambolle. Evolution of characteristic functions of convex sets in the plane by the minimizing total variation flow. Interfaces and free boundaries, Tome 7 (2005) no. 1, pp. 29-53. doi: 10.4171/ifb/112
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