Multiscale segmentation with vector-valued nonlinear diffusions on arbitrary graphs.

We propose a novel family of nonlinear diffusion equations and apply it to the problem of segmentation of multivalued images. We show that this family can be viewed as an extension of stabilized inverse diffusion equations (SIDEs) which were proposed for restoration, enhancement, and segmentation of scalar-valued signals and images in [39]. Our new diffusion equations can process vector-valued images defined on arbitrary graphs which makes them well suited for segmentation. In addition, we introduce novel ways of utilizing the shape information luring the diffusion process. We demonstrate the effectiveness of our methods on a large number of segmentation tasks.