Riccardo March

Ancien Chercheur invité, IAC / CNR Roma, Italy

Contact :

Dernières publications dans le projet Ariana :

An approximation of the Mumford-Shah energy by a family of dicrete edge-preserving functionals. G. Aubert et L. Blanc-Féraud et R. March. Nonlinear Analysis, 64: pages 1908-1930, 2006. Mots-clés : Gamma Convergence, Elements finis, Segmentation. @ARTICLE{laure-na05, author = {Aubert, G. and Blanc-Féraud, L. and March, R.}, title = {An approximation of the Mumford-Shah energy by a family of dicrete edge-preserving functionals}, year = {2006}, journal = {Nonlinear Analysis}, volume = {64}, pages = {1908-1930}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/2006_laure-na05.pdf}, keyword = {Gamma Convergence, Elements finis, Segmentation} } Abstract : We show the Gamma-convergence of a family of discrete functionals to the Mumford and Shah image segmentation functional. The functionals of the family are constructed by modifying the elliptic approximating functionals proposed by Ambrosio and Tortorelli. The quadratic term of the energy related to the edges of the segmentation is replaced by a nonconvex functional. Gamma-convergence of discrete functionals with nonconvex perturbation for image classification. G. Aubert et L. Blanc-Féraud et R. March. SIAM Journal on Numerical Analysis, 42(3): pages 1128--1145, 2004. @ARTICLE{BLA04, author = {Aubert, G. and Blanc-Féraud, L. and March, R.}, title = {Gamma-convergence of discrete functionals with nonconvex perturbation for image classification}, year = {2004}, journal = {SIAM Journal on Numerical Analysis}, volume = {42}, number = {3}, pages = {1128--1145}, url = {http://epubs.siam.org/doi/abs/10.1137/S0036142902412336}, keyword = {} } Gamma-Convergence of Discrete Functionals with non Convex Perturbation for Image Classification. G. Aubert et L. Blanc-Féraud et R. March. Rapport de Recherche 4560, Inria, France, septembre 2002. Mots-clés : Gaussiennes generalisees, Classification, Regularisation. @TECHREPORT{4560, author = {Aubert, G. and Blanc-Féraud, L. and March, R.}, title = {Gamma-Convergence of Discrete Functionals with non Convex Perturbation for Image Classification}, year = {2002}, month = {septembre}, institution = {Inria}, type = {Research Report}, number = {4560}, address = {France}, url = {https://hal.inria.fr/inria-00072028}, pdf = {https://hal.inria.fr/file/index/docid/72028/filename/RR-4560.pdf}, ps = {https://hal.inria.fr/docs/00/07/20/28/PS/RR-4560.ps}, keyword = {Gaussiennes generalisees, Classification, Regularisation} } Résumé : Ce rapport contient la justification mathématique du modèle variationnel proposé en traitement d'image pour la classification supervisée. A partir des travaux effectués en mécanique des fluides pour les transitions de phase, nous avons développé un modèle de classification par minimisation d'une suite de fonctionnelles. Le résultat est une image de classes formée de régions homogènes séparées par des contours réguliers. Ce modèle diffère de ceux utilisés en mécanique des fluides car la perturbation utilisée n'est pas quadratique mais correspond à une fonction de régularisation d'image préservant les contours. La gamma-convergence de cette nouvelle suite de fonctionnelles est prouvée. 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.

Liste complète des publications dans le projet Ariana