Abstract
A numerical approach to the problem: minF λ(E), whereF λ(E)=P(E,R n)+λ|Ω/E|, is considered. The functionalF λ is approximated, using techniques of Γ-convergence, with a sequence of functionals that are successively discretized by finite differences. A relation between the index of the approximating sequence and the meshsize of the domain is found.
Riassunto
Viene presentato un approccio numerico del problema: minF λ(E), doveF λ(E)=P(E,R n)+λ|Ω/E|. Il funzionaleF λ viene approssimato, usando tecniche di Γ-convergenza, con una successione di funzionali, successivamente discretizzati con differenze finite. Viene trovata una relazione tra l'indice della successione approssimante e il passo del reticolo del dominio.
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Bellettini, G. A numerical approach to a minimum problem with applications in image segmentation. Ann. Univ. Ferrara 36, 99–111 (1990). https://doi.org/10.1007/BF02837210
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DOI: https://doi.org/10.1007/BF02837210