Statistical analysis of discontinuous phenomena with potts functionals [Elektronische Ressource] / vorgelegt von Angela Kempe

Statistical Analysis of DiscontinuousPhenomena with Potts FunctionalsDISSERTATIONzur Erlangung des akademischen Gradeseines Doktors der Naturwissenschaftendes Fachbereichs Mathematikder Ludwig-Maximilians-Universit˜at Munc˜ henvorgelegt vonAngela Kempe30. Januar 20041. Berichtertstatter: Prof. Dr. G. Winkler2. Berichterstatter: Prof. Dr. P. L. DaviesTag der mundlic˜ hen Prufung:˜ 25. Juni 2004Fur˜ meine OmaPrefaceThis thesis was carried out under the supervision of Prof. Dr. Gerhard Win-kler. From 01.01.2000 to 31.12.2002 it was funded by the GSF-National Re-search Center for Environment and Health, Neuherberg, and from 01.01.03to 31.01.2004 by the Graduate Program Applied Algorithmic Mathematicsof the Deutsche Forschungsgemeinschaft at the Munich University of Tech-nology.ThesimulationswererealizedonthesoftwarepackageAntsInFieldsdevel-oped byF. Friedrich (2003). It was also used for most of the illustrations.I thank the members of the GSF-Institute of Biomathematics and Biome-try for their support. I am particularly indebted to Gerhard Winkler, OlafWittich, Volkmar Liebscher, and Felix Friedrich for their sedulous help andencouragement. Many thanks to my friends and my mother.Munich, January 2004 Angela KempeiContentsPreface iZusammenfassung viiIntroduction 1I Analysis of Potts Functionalsand their Minimizers 51 Segmentations and Potts Functionals 91.1 Potts Functionals . . . . . . . . . . . . . . . . . . . . . . . . . 91.