Minimal partitions and image classification using a gradient-free perimeter approximation

Samuel Amstutz (1) , A.A. Novotny (2) , Nicolas van Goethem (3)

1 LANLG - Laboratoire d'Analyse non linéaire et Géométrie
2 LNCC / MCT - Laboratorio Nacional de Computação Cientifica [Rio de Janeiro]
3 CMAF - Centro de Matemática e Aplicações Fundamentais

In this paper we propose a new optimal partition algorithm and show applications to multilabel image classification problems. Possibly noisy and blurred greyscale and color images can be processed, with or without automatic update of the labels. Regularization is performed by a non standard approximation of the total interface length, which involves a system of uncoupled linear partial differential equations and shows $\Gamma$-converge properties in the set of characteristic functions. These good mathematical properties are recovered in the numerical convergence scheme.

Mots clés: Image classification; denoising; deblurring; optimal partitions; perimeter approximation

Domaines: Optimisation et contrôle [math.OC]

Samuel Amstutz, A.A. Novotny, Nicolas van Goethem. Minimal partitions and image classification using a gradient-free perimeter approximation. 2012. ⟨hal-00690011v2⟩