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Gamma-convergence of discrete functionals with non convex perturbation for image classification

Gilles Aubert 1 Laure Blanc-Féraud Riccardo March
1 ARIANA - Inverse problems in earth monitoring
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - SIS - Signal, Images et Systèmes
Abstract : The purpose of this report is to show the theoretical soundness of a variation- al method proposed in image processing for supervised classification. Based on works developed for phase transitions in fluid mechanics, the classification is obtained by minimizing a sequence of functionals. The method provides an image composed of homogeneous regions with regular boundaries, a region being defined as a set of pixels belonging to the same class. In this paper, we show the gamma-convergence of the sequence of functionals which differ from the ones proposed in fluid mechanics in the sense that the perturbation term is not quadratic but has a finite asymptote at infinity, corresponding to an edge preserving regularization term in image processing.
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Submitted on : Tuesday, May 23, 2006 - 7:36:15 PM
Last modification on : Thursday, February 3, 2022 - 11:17:09 AM
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  • HAL Id : inria-00072028, version 1

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Gilles Aubert, Laure Blanc-Féraud, Riccardo March. Gamma-convergence of discrete functionals with non convex perturbation for image classification. RR-4560, INRIA. 2002. ⟨inria-00072028⟩

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