Segmentation of Stochastic Images using ... - Jacobs University

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Acknowledgement I would like to thank my advisor Prof. Dr. Tobias Preusser for the guidance during my PhD studies and for giving me the opportunity to work in the rapidly growing field of stochastic modeling. Furthermore, Prof. Preusser’s connection to Fraunhofer MEVIS enabled me to work in an inspiring environment of people working on image processing problems. Furthermore, I would like to thank Prof. Dr. Marcel Oliver and Prof. Dr. Joachim Weickert for being members of my dissertation committee. Special thanks go to the Jacobs University Bremen for the financial support during my PhD studies. Without the tuition waiver for the complete time of my PhD studies and the scholarship during the first two years, I would not be able to finish my studies successfully. Furthermore, special thanks go to Fraunhofer MEVIS for the student assistance contract during the first two years of my PhD studies and the possibility to use the infrastructure of the institute for my studies. I am grateful to all my colleagues at the "Modeling and Simulation" group at Fraunhofer MEVIS. Especially, I would like to thank Sabrina Haase, Hanne Tiesler, and Dr. Ole Schwen for reading and commenting on a draft of this thesis. I am also thankful to the QuocMesh collective from the work group of Prof. Dr. Martin Rumpf at the Institute of Numerical Simulation of the Rheinische Friedrich-Wilhelms-Universität Bonn. All implementations of the methods from this thesis are done in QuocMesh and without this excellent finite element library this would be much more work. Especially, I would like to thank Dr. Ole Schwen for answering all my questions concerning QuocMesh. I am also grateful to Prof. Dr. Robert M. Kirby from the University of Utah in Salt Lake City, USA, for the possibility to stay two weeks at the Scientific Computing and Imaging Institute in Salt Lake City. Furthermore, I would like to thank Prof. Kirby and Prof. Joshi for the fruitful discussions during my stay in Salt Lake City. iii
Page 1: Segmentation of Stochastic Images u
Page 7 and 8: Contents Acknowledgement Abstract N
Page 9: Notation u image function ⊗ tenso
Page 12 and 13: Chapter 1 Introduction Figure 1.2:
Page 14 and 15: Chapter 1 Introduction Ambrosio-Tor
Page 17 and 18: Chapter 2 Image Segmentation and Li
Page 19 and 20: 2.2 Random Walker Segmentation Defi
Page 21 and 22: 2.2 Random Walker Segmentation Figu
Page 23 and 24: 2.3 Mumford-Shah and Ambrosio-Torto
Page 25 and 26: 2.3 Mumford-Shah and Ambrosio-Torto
Page 27 and 28: 2.4 Level Sets for Image Segmentati
Page 29 and 30: 2.4 Level Sets for Image Segmentati
Page 31 and 32: 2.5 Why is Classical Image Processi
Page 33 and 34: 2.6 Work Related to the Stochastic
Page 35 and 36: Chapter 3 SPDEs and Polynomial Chao
Page 37 and 38: 3.2 Stochastic Partial Differential
Page 39 and 40: 3.3 Polynomial Chaos Expansions Fig
Page 41 and 42: 3.3 Polynomial Chaos Expansions The
Page 43 and 44: 3.3 Polynomial Chaos Expansions H 1
Page 45 and 46: 3.4 Relation to Interval Arithmetic
Page 47 and 48: Chapter 4 Discretization of SPDEs T
Page 49 and 50: 4.3 Stochastic Finite Elements meth
Page 51 and 52: 4.4 Generalized Spectral Decomposit
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4.4 Generalized Spectral Decomposit
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4.5 Adaptive Grids Figure 4.3: Refi
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Chapter 5 Stochastic Images As desc
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5.2 Generation of Stochastic Images
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5.2 Generation of Stochastic Images
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5.4 Visualization of Stochastic Ima
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5.4 Visualization of Stochastic Ima
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Chapter 6 Segmentation of Stochasti
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Chapter 7 Stochastic Level Sets Lev
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7.1 Derivation of a Stochastic Leve
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7.2 Discretization of the Stochasti
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7.4 Numerical Experiments cosine in
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7.4 Numerical Experiments Figure 7.
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7.5 Segmentation of Stochastic Imag
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Chapter 8 Segmentation of Classical
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8.1 Random Walker Segmentation with
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8.2 Ambrosio-Tortorelli Segmentatio
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8.2 Ambrosio-Tortorelli Segmentatio
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8.4 Geodesic Active Contours with S
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Chapter 9 Summary, Discussion, and
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9.3 Outlook and Future Work of leve
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List of Figures 3.2 Sparsity struct
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List of Figures 6.16 Comparison of
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List of Tables 3.1 The first ten on
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vaporization state, and the coagula
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Bibliography [29] V. Caselles, F. C
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Bibliography [62] J. Gubner. Probab
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Bibliography [97] M. Matsumoto and
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Bibliography [129] T. Preusser and
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