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Finite difference approximation of the Mumford‐Shah functional
Author(s) -
Gobbino Massimo
Publication year - 1998
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/(sici)1097-0312(199802)51:2<197::aid-cpa3>3.0.co;2-6
Subject(s) - pointwise , mathematics , discontinuity (linguistics) , pointwise convergence , convergence (economics) , enhanced data rates for gsm evolution , set (abstract data type) , mathematical analysis , pure mathematics , artificial intelligence , computer science , approx , economics , programming language , economic growth , operating system
Abstract We study the pointwise convergence and the Γ of a family of nonlocal functionals defined in \input amstex \loadmsbm $L^1_{\roman {loc}}(\Bbb R^n)$ to a local functional ${\cal F}(u)$ that depends on the gradient of u and on the set of discontinuity points of u . We apply this result to approximate a minimum problem introduced by Mumford and Shah to study edge detection in computer vision theory. © 1998 John Wiley & Sons, Inc.