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Journal of Mathematical Imaging and Vision

, Volume 47, Issue 3, pp 179–209 | Cite as

A Variational Framework for Region-Based Segmentation Incorporating Physical Noise Models

  • Alex Sawatzky
  • Daniel Tenbrinck
  • Xiaoyi Jiang
  • Martin Burger
Article

Abstract

Image segmentation is one of the fundamental problems in computer vision and image processing. In the recent years mathematical models based on partial differential equations and variational methods have led to superior results in many applications, e.g., medical imaging. A majority of works on image segmentation implicitly assume the given image to be biased by additive Gaussian noise, for instance the popular Mumford-Shah model. Since this assumption is not suitable for a variety of problems, we propose a region-based variational segmentation framework to segment also images with non-Gaussian noise models. Motivated by applications in biomedical imaging, we discuss the cases of Poisson and multiplicative speckle noise intensively. Analytical results such as the existence of a solution are verified and we investigate the use of different regularization functionals to provide a-priori information regarding the expected solution. The performance of the proposed framework is illustrated by experimental results on synthetic and real data.

Keywords

Image segmentation Variational methods Maximum a-posteriori probability estimation Non-Gaussian noise models Multiplicative speckle noise Poisson noise Medical ultrasound imaging Positron emission tomography 

Notes

Acknowledgements

This study has been supported by the German Research Foundation DFG, SFB 656 MoBil (project B2, B3, C3), as well as DFG project BU 2327/1. The authors thank Jörg Stypmann (University Hospital of Münster) for providing medical ultrasound data. Furthermore, we thank Florian Büther and Klaus Schäfers (EIMI, WWU Münster) for providing PET data. The authors thank Tanja Teuber (TU Kaiserslautern) for useful hints on the speckle noise model.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Alex Sawatzky
    • 1
  • Daniel Tenbrinck
    • 2
  • Xiaoyi Jiang
    • 2
  • Martin Burger
    • 1
  1. 1.Institut für Numerische und Angewandte MathematikWestfälische Wilhelms-Universität MünsterMünsterGermany
  2. 2.Institut für InformatikWestfälische Wilhelms-Universität MünsterMünsterGermany

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