Enhancement of Textured Images Using Complex Diffusion Incorporating Schrodinger's Potential

The complex diffusion process, recently introduced in image processing and computer vision by combining the linear diffusion equation and the `free-particle' Schrodinger equation, is further generalized by incorporating the Schrodinger potential. We show that this generalized complex diffusion equation is inherently endowed with processing properties Suitable for dealing with textures in a naturally coupled manner. The schrödinger potential is self adopting to the specific properties of an image at hand in that it implements an image specific wavelet shrinkage algorithm. Results indicate that the generalized complex diffusion processing scheme not only preserves textures better than demonstrated by previously reported results, but can even enhance textures by adjusting the coefficient that determines that magnitude of the potential, relative to the potentialless complex diffusion. This is in a way analogous to the enhancement of edges by the Forward-and-Backward diffusion process.