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Article Dans Une Revue Applicable Analysis Année : 2005

Optimal partitions, regularized solutions, and application to image classification

Gilles Aubert
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Résumé

This article is concerned with the problem of finding a regular and homogeneous partition of a Lipschitz open set Omega of R^2. This type of problem occurs in image classification which consists in assigning a label (that is a class or a phase) to each pixel of an observed image. Such a problem can numerically be solved by using a level set formulation. But this approach generally relies on heuristic arguments. We intend here to give a theoretical justification in the two phases case. In the first part of the paper, we prove that the partition problem we consider admits a solution. And in the second part, we justify the numerical approach which is usually done to compute a solution.
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Dates et versions

hal-00202002 , version 1 (03-01-2008)

Identifiants

  • HAL Id : hal-00202002 , version 1

Citer

Gilles Aubert, Jean-François Aujol. Optimal partitions, regularized solutions, and application to image classification. Applicable Analysis, 2005, 84 (1), p. 15-35. ⟨hal-00202002⟩
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