The Application of Catastrophe Theory to Image Analysis

摘要

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