Monotonically decreasing eigenvalue for edge-sharpening diffusion

Abstract

Anisotropic diffusion is classified by the eigenvalue of the Hessian matrix associated with the diffusivity function into two categories: one incapable of edge-sharpening and the other capable of selective edge sharpening. A third class is proposed: the eigenvalue starts with a small value and decreases monotonically with image gradient magnitude so that the stronger the edge is, the more it is sharpened. Two such examples are given and one is found to consistently produce the best PSNR at all simulated noise levels.