Fast Parallel Algorithms for a Broad Class of Nonlinear Variational Diffusion Approaches

Abstract

Variational segmentation and nonlinear diffusion approaches have been very active research areas in the fields of image processing and computer vision during recent years. In the present paper, we review recent advances in the development of efficient numerical algorithms for these approaches. The performance of parallel implementations of these algorithms on general-purpose hardware is assessed. A mathematically clear connection between variational models and nonlinear diffusion filters is presented that allows to interpret one approach as an approximation of the other, and vice versa. Extending this continuous connection to the fully discrete setting enables us to derive many structural similarities between efficient numerical algorithms for both frameworks. These results provide a perspective for uniform implementations of nonlinear variational models and diffusion filters on parallel architectures.