Calculus of Variations and Geometric Measure Theory

G. Aubert - L. Blanc-Feraud - R. March

$\Gamma$-convergence of discrete functionals with nonconvex perturbation for image classification

created by march on 20 Dec 2004


Published Paper

Inserted: 20 dec 2004

Journal: SIAM J. Numer. Anal.
Volume: 42
Number: 3
Pages: 1128-1145
Year: 2004


The purpose of this paper is to show the theoretical soundness of a variational 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.