The Application of Catastrophe Theory to Image Analysis

Abstract

In order to investigate the deep structure of Gaussian scale space images, one needs to understand the behaviour of critical points under the in flence of blurring. We show how the mathematical framework of catastrophe theory can be used to describe the various different types of annihilations and the creation of pairs of critical points and how this knowledge can be exploited in a scale space hierarchy tree for the purpose of pre-segmentation. We clarify the theory with an artificial image and a simulated MR image.