Nonlinear anisotropic diffusion filtering for multiscale edge enhancement

Nonlinear anisotropic diffusion filtering is a procedure based on nonlinear evolution partial differential equations which seeks to improve images qualitatively by removing noise while preserving details and even enhancing edges. However, well known implementations are sensitive to parameters which are necessarily tuned to sharpen a narrow range of edge slopes; otherwise, edges are either blurred or staircased. In this work, nonlinear anisotropic diffusion filters have been developed which sharpen edges over a wide range of slope scales and which reduce noise conservatively with dissipation purely along feature boundaries. Specifically, the range of sharpened edge slopes is widened as backward diffusion normal to level sets is balanced with forward diffusion tangent to level sets. Also, noise is reduced by selectively altering the balance toward diminishing normal backward diffusion and particularly toward total variation filtering. The theoretical motivation for the proposed filters is presented together with computational results comparing them with other nonlinear anisotropic diffusion filters on both synthetic images and magnetic resonance images.