Visual reconstruction with discontinuities using variational methods

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 ?-convergence theory to approximate the functional to be minimized by elliptic functionals, which are more tractable. A ?-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.