Complex Difusion Processes for Image Filtering

Abstract

A framework that naturally uni?es smoothing and enhancement processes is presented. We generalize the linear and nonlinear scale spaces in the complex domain, by combining the difusion equation with the simpli?ed Schrödinger equation. A fundamental solution for the linear case is developed. Preliminary analysis of the complex difusion shows that the generalized difusion has properties of both forward and inverse difusion. An important observation, supported theoretically and numerically, is that the imaginary part can be regarded as an edge detector (smoothed second derivative), after rescaling by time, when the complex difusion coefficient approaches the real axis. Based on this observation, a nonlinear complex process for ramp preserving denoising is developed.