We study the pointwise convergence and the Gamma-convergence of a family of nonlocal functionals defined in L^1_loc(R^n) to a local functional 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.
Finite difference approximation of the Mumford-Shah functional
GOBBINO, MASSIMO
1998-01-01
Abstract
We study the pointwise convergence and the Gamma-convergence of a family of nonlocal functionals defined in L^1_loc(R^n) to a local functional 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.File in questo prodotto:
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