Global minimizers of the Mumford-Shah function
نویسندگان
چکیده
منابع مشابه
Endpoint Regularity of 2d Mumford-shah Minimizers
We prove an ε-regularity theorem at the endpoint of connected arcs for 2-dimensional Mumford-Shah minimizers. In particular we show that, if in a given ball Br(x) the jump set of a given MumfordShah minimizer is sufficiently close, in the Hausdorff distance, to a radius of Br(x), then in a smaller ball the jump set is a connected arc which terminates at some interior point y0 and it is C 1,α up...
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We prove higher integrability for the gradient of local minimizers of the Mumford-Shah energy functional, providing a positive answer to a conjecture of De Giorgi [5].
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We study global Mumford-Shah minimizers in R , introduced by Bonnet as blow-up limits of Mumford-Shah minimizers. We prove a new monotonicity formula for the energy of u when the singular set K is contained in a smooth enough cone. We then use this monotonicity to prove that for any reduced global minimizer (u,K) in R, if K is contained in a half-plane and touching its edge, then it is the half...
متن کاملOn the homogeneity of global minimizers for the Mumford-Shah functional when K is a smooth cone
We show that if (u,K) is a global minimizer for the Mumford-Shah functional in R , and if K is a smooth enough cone, then (modulo constants) u is a homogenous function of degree 1 2 . We deduce some applications in R as for instance that an angular sector cannot be the singular set of a global minimizer, that if K is a half-plane then u is the corresponding cracktip function of two variables, o...
متن کاملHIGHER INTEGRABILITY OF THE GRADIENT FOR MINIMIZERS OF THE 2d MUMFORD-SHAH ENERGY
We prove the existence of an exponent p > 2 with the property that the approximate gradient of any local minimizer of the 2-dimensional Mumford-Shah energy belongs to Lploc.
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ژورنال
عنوان ژورنال: Current Developments in Mathematics
سال: 1997
ISSN: 1089-6384,2164-4829
DOI: 10.4310/cdm.1997.v1997.n1.a13