Exploring Non-linear Difusion: The Difusion Echo

Abstract

The Gaussian serves as Green’s function for the linear diffusion equation and as a source for intuitive understanding of the linear difusion process. In general, non-linear difusion equations have no known closed formsolu tions and thereby no equally simple description. This article introduces a simple, intuitive description of these processes in terms of the Difusion Echo. The Difusion Echo offers intuitive visualisations for non-linear difusion processes.

In addition, the Difusion Echo has potential for o?ering simple formulations for grouping problems. Furthermore, the Difusion Echo can be considered a deep structure summary and thereby offers an alternative to multi-scale linking and ?ooding techniques.