Characterizing first and second-order patches using geometry-limited diffusion

Abstract

I propose a diffusion process that operates on the jet-space of an image. This process uses variable conductance diffusion as an alternative to Ganssian scale in order to smooth differential measurements in a manner that preserves structures of interest. The process is presented within a general framework that suggests a wide range of possibilities for segmenting images on the basis of homogeneity of local shape. Previous work has shown how first-order geometry is used to locate ridges and valleys in greyscale objects. In this paper I use apply these principles to first and second-order geometry in order to find boundaries and skeletons of objects. Examples of first and second-order segmentations of medical images are given. This method appears to offer a r61iable and accurate means of segmenting images and is shown to preserve the orthogonal group properties of properly constructed geometric invariants.