Exact Solutions for Discrete Graphical Models: Multicuts and Reduction Techniques

Abstract

In the past years, discrete graphical models have become a major conceptual tool to model the structure of problems in image processing - example applications are image segmentation, image labeling, stereo vision, and tracking problems. It is therefore crucial to have techniques which are able to handle the occurring optimization problems and to deliver good solutions. Because of the hardness of these inference problems, so far mainly fast heuristic methods were used which yield approximate solutions. In this thesis we present exact methods for obtaining optimal solutions for the energy minimization problem of discrete graphical models; image segmentation serves as the main application. Since these problems are NP-hard in general, it is clear that in order to be able to handle problem sizes occurring in real-world applications one has to either (a) reduce the size of the problems or (b) restrict oneself to special problem classes. Concerning (a), we develop a combination of existing and new preprocessing steps which transform models into equivalent yet less complex ones. Concerning (b), we introduce the so-called multicut approach to image analysis: This is a generalization of the min s-t cut method which allows for solving models of a certain structure significantly faster than previously possible or even solving them to global optimality for the first time at all. On the whole, we present methods which solve NP-hard problems to proven optimality and which in some cases are as fast or even faster than approximative methods.