Diffusion-Based Image Segmentation Methods

Abstract

Image segmentation is an important task in image analysis and computer vision. A difficult problem in image segmentation is to decide whether two image points belong to one or to two image segments. The decision to this question can be based on measuring the distance between the points. Measuring this distance is the main topic of the thesis. We especially focus on the techniques that are based on the spectral decomposition and on the diffusion processes since they may be regarded as sophisticated and promising. In this work, however, we firstly show that they are not always good in the given context. This claim is supported by the theoretical considerations as well as by the extensive computational simulations. On the basis of these observations, we continue with the proposition of several new distance measures that try to remedy the problems that have been discovered. The new methods can be divided into two groups. The first group contains three methods that are based on the diffusion processes and are inspired by the diffusion distance. The second group consists of only one method that combines the resistance and the geodesic distance. We describe the new methods from the theoretical point of view; the results of testing are presented as well. The results show that the methods have certain good properties and may be useful in image segmentation.