Total Variation Minimization for Scalar/Vector Regularization

In this chapter we present regularization by using Total Variation (TV) minimization based on a level set approach. After introducing the problem of regularization and citing related work, we introduce our main tool, the Fast Level Sets Transform (FLST). This algorithm decomposes an image in a tree of shapes which gives us a non-redundant and complete representation of the image. This representation, associated to some theoretical facts about functions of bounded variation, leads us to a TV minimization algorithm based on level sets. We conclude by comparing this approach to other implementation and/or other models and show applications to regularization of gray scale and color images, as well as optical flow.ou