PUMA
Istituto di Scienza e Tecnologie dell'Informazione     
March R. Variational problems arising in early vision : approximation by gamma-convergence. Internal note IEI-B4-55, 1990.
 
 
Abstract
(English)
Visual reconstruction problems tend to be mathematically ill-posed. They can be reformulated as well-posed variational problems using regularization theory. A generalization of the standard regularization method to visual reconstruction with discontinuities leads to variational problems which include the discontinuity contours in their unknowns. The minimization of the corresponding functionals is a difficult problem. This paper suggests the use of the Γ-convergence theory to approximate the functional to be minimized by elliptic functionals, which are more tractable. A Γ-convergence theorem which is of relevance to vision applications is discussed, and the results of computer experiments with both synthetic and real images are shown.
Subject Early vision
Discontinuity detection
Variational convergence


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