Geometrie Flows for Image Processing

Abstract

Based on modern invariant theory and symmetry groups, a high- level way of defining invariant geometric flows for a given Lie group is first described in this work. We then analyze in more detail different subgroups of the projective group, which are of special interest for computer vision. We classify the corresponding invariant flows and show that the geometric heat flow is the simplest possible one. Results on invariant geometric flows of surfaces are presented in this paper as well. We then show how the planar curve flow obtained for the affine group can be used for geometric smoothing of planar shapes and edge preserving enhancement of MRI. We conclude the paper with the presentation of other applications of geometric flows in image processing, which include segmentation, anisotropic diffusion of color images, and contrast normalization.