This talk is devoted to computational methods for image segmentation, cartoon-texture separation and texture modeling, in a variational and partial differential equations approach. A multilayer curve evolution model will be presented for image segmentation that is well adapted to volumetric MRI brain data. Also, computational methods for modeling oscillations and image decomposition into cartoon and texture will be presented. Inspired by ideas of Y. Meyer and of D. Mumford- B. Gidas, images and in particular oscillatory patterns are now represented by more refined texture norms, such as dual norms or generalized functions. The difficulty arising in the minimization of such models will be addressed, and theoretical and experimental results will be presented.