Models and numerical methods in nonlinear diffusion equations for 2D/3D image and image sequence analysis

Scaled-space and image enhancement techniques based on Partial Differential Equations (PDEs) have proved to be powerful methods in the processing of two-dimensional (2D) and three-dimensional (3D) images and image sequences. In the nonlinear setting this filter class allows to integrate a-priori knowledge into evolution. The aim of this review is to discuss three new models we have recently presented [15, 9, 8] and two representative geometry driven diffusion models, namely the regularized Perona-Malik anisotropic diffusion equation [13, 3], and the nonlinear degenerate diffusion equation of the mean curvature flow type [2]. Results of the application of the models to the filtering of image and image sequences taken from real problems are presented.