Istituto di Scienza e Tecnologie dell'Informazione     
March R. Visual reconstruction with discontinuities using variational methods. Internal note IEI-B4-04, 1990.
Visual reconstruction problems tend to be mathematically ill-posed. They can be reformulated as well-posed variational problems using regolarization theory. A generalization of the standard regolarization method to visual reconstruction with discontinuities leads to variational problems which include the discontinuity contours in their unknows. 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 a computer experiment with synthetic images are shown.
Subject Early vision
Discontinuity detection
Variational convergence

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