Riccardo March

Former Visitor, IAC / CNR Roma, Italy

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Last publications in Ariana Research Group :

An approximation of the Mumford-Shah energy by a family of dicrete edge-preserving functionals. G. Aubert and L. Blanc-Féraud and R. March. Nonlinear Analysis, 64: pages 1908-1930, 2006. Keywords : Gamma Convergence, Finite Element, 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, Finite Element, 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 and L. Blanc-Féraud and 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 and L. Blanc-Féraud and R. March. Research Report 4560, Inria, France, September 2002. Keywords : Generalised Gaussians, Classification, Regularization. @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 = {September}, 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 = {Generalised Gaussians, Classification, Regularization} } 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.

All publications in Ariana Research Group