On the existence of solutions to a problem in multidimensional segmentation
type: Item
instance of: scholarly article
title: On the existence of solutions to a problem in multidimensional segmentation
zbMATH Open document ID: 0729.49003
DOI: 10.1016/S0294-1449(16)30271-2
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 1991-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/78249
review text: The authors give an existence result for a minimum problem related to image segmentation in computer vision. In the framework of the calculus of variations this minimum problem pertains to the class of ``Minimal boundary problems with free discontinuity'' recently studied by De Giorgi-Carriero and Leaci. The main result is the following: Let \(n\geq 2\), M open \(\subset R^ n\), \(0<\lambda <+\infty\), \(1\leq p<+\infty\), \(g\in L^ p(M)\cap L^{\infty}(M)\). Then there exists at least one pair (K,u) minimizing \[ F(K,u)=\lambda \int_{M\setminus K}| u-g|^ p dx+H^{n-1}(K\cap M), \] with k closed \(\subset R^ n\), \(u\in C'(M\setminus K)\) such that \(\nabla u\equiv 0\) in \(M\setminus K\).
Mathematics Subject Classification ID: 49J10
Mathematics Subject Classification ID: 49N70
Mathematics Subject Classification ID: 49N75
zbMATH DE Number: 4205225
zbMATH Keywords: image segmentation in computer vision
zbMATH Keywords: Minimal boundary problems with free discontinuity
author: Giuseppe Congedo
author: Italo Tamanini
reviewed by: Rosanna Schianchi
MaRDI profile type: Publication
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OpenAlex ID: W159255535
description: scientific article; zbMATH DE number 4205225