In this paper we study, in the framework of functions of bounded variation, a general variational problem arising in image recovery, introduced in [3]. We prove the existence and the uniqueness of a solution using low...
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In this paper we study, in the framework of functions of bounded variation, a general variational problem arising in image recovery, introduced in [3]. We prove the existence and the uniqueness of a solution using lower semicontinuity results for convex functionals of measures. We also give a new and fine characterization of the subdifferential of the functional, together with optimality conditions on the solution, using duality techniques of Temam for the theory of time-dependent minimal surfaces. We study the associated evolution equation in the context of nonlinear semigroup theory and we give an approximation result in continuous variables, using Gamma -convergence. Finally, we discretize the problems by finite differences schemes and we present several numerical results for signal and image reconstruction.
This paper describes a variational approach for estimating a discontinuous optical flow from a sequence of images. Defined as the apparent motion of the image brightness pattern, the optical flow is very important in ...
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This paper describes a variational approach for estimating a discontinuous optical flow from a sequence of images. Defined as the apparent motion of the image brightness pattern, the optical flow is very important in the computer vision community, where its accurate estimation is strongly needed. After a short overview of existing methods, we present a new variational method that we study in the space of bounded variations. We first present an integral representation of the optical flow problem which appears to be not lower semicontinuous. The relaxed functional is then calculated. We conclude by challenging questions about the possible numerical analysis of the abstract results.
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