Γ-convergence of discrete functionals with nonconvex perturbation for image classification

被引:9
作者
Aubert, G [1 ]
Blanc-Féraud, L
March, R
机构
[1] Univ Nice, CNRS, UMR 6621, Lab JA Dieudonne, F-06108 Nice 2, France
[2] UNSA, CNRS, Projet Ariana, Lab I3S, F-06902 Sophia Antipolis, France
[3] INRIA Sophia Antipolis, F-06902 Sophia Antipolis, France
[4] CNR, ISt Applicaz Calcolo, I-00161 Rome, Italy
关键词
Gamma-convergence; finite elements; image processing; phase transitions;
D O I
10.1137/S0036142902412336
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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.
引用
收藏
页码:1128 / 1145
页数:18
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