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

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... ions. 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 -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 -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 -hard problems to proven optimality and which in some cases are as fast or even faster than approximative methods. I got to know him as a supportive and reliable person, taking care of the students under his guidance. My second supervisor, Prof. Christoph Schnörr, introduced me to the field of image analysis in general and graphical models in particular. I am thankful to him for offering a complementing perspective from the viewpoint of application. I owe special gratitude to Jörg Kappes for his help throughout the past years -he always had an open door for me and was willingly sharing his experience. Thorsten Bonato and Stefan Wiesberg helped me to get Thorsten's max cut code running with my instances. The evaluation of the superpixel algorithms was done in collaboration with Borislav Antic. Stefan Lörwald provided support with the new version of PORTA. Thanks to all of you! Being in between two research groups, I had a lot of people helping me with administrative tasks. Our secretaries Catherine Proux-Wieland, Anke Sopka, Karin Tenschert, Barbara Werner, and Evelyn Wilhelm were taming the bureaucratic beasts to make life easier. Thanks to our system administrators who were responsible for keeping our machines running: