Nonlinear anisotropic diffusion filtering for multiscale edge enhancement

Abstract

Nonlinear anisotropic diffusion filtering is a procedure based on nonlinearevolution partial differential equations which seeks to improve imagesqualitatively by removing noise while preserving details and even enhancingedges. However, well known implementations are sensitive to parameterswhich are necessarily tuned to sharpen a narrow range of edge slopes;otherwise, edges are either blurred or staircased. In this work, nonlinearanisotropic diffusion filters have been developed which sharpen edges over awide range of slope scales and which reduce noise conservatively withdissipation purely along feature boundaries. Specifically, the range ofsharpened edge slopes is widened as backward diffusion normal to level setsis balanced with forward diffusion tangent to level sets. Also, noise isreduced by selectively altering the balance toward diminishing normalbackward diffusion and particularly toward total variation filtering. Thetheoretical motivation for the proposed filters is presented together withcomputational results comparing them with other nonlinear anisotropicdiffusion filters on both synthetic images and magnetic resonance images.