Variational Models for Image Segmentation, Image Restoration and Texture Modeling

This talk is devoted to several variational problems arising in image analysis. The first part of the talk is devoted to image segmentation using a new multilayer level set approach. Several nested level lines of the same level set function are used to partition images into different components.

The second part of the talk is devoted to the decomposition of a given image or function f into two components u (cartoon) and v (texture). The component u represents the main geometric features of the image f, and it is modeled in the classical way by a function of bounded variation. The component v corresponds to oscillatory patterns and it is modeled by generalized functions in dual spaces. Such spaces have small norms for oscillatory functions and provide more refined texture norms than the L^p norms. The main difficulty is how to analyze and to solve such models in practice. Theoretical and computational results will be discussed, together with experimental results that validate the proposed models.

This is joint work with G. Chung, T. Le and L. Lieu.