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Finite difference approximation of the Mumford-Shah functional

✍ Scribed by Massimo Gobbino

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
333 KB
Volume
51
Category
Article
ISSN
0010-3640

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✦ Synopsis

We study the pointwise convergence and the Ξ“-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.

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