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Inpainting of Cyclic Data Using First and Second Order Differences

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Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR 2015)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 8932))

Abstract

Cyclic data arise in various image and signal processing applications such as interferometric synthetic aperture radar, electroencephalogram data analysis, and color image restoration in HSV or LCh spaces. In this paper we introduce a variational inpainting model for cyclic data which utilizes our definition of absolute cyclic second order differences. Based on analytical expressions for the proximal mappings of these differences we propose a cyclic proximal point algorithm (CPPA) for minimizing the corresponding functional. We choose appropriate cycles to implement this algorithm in an efficient way. We further introduce a simple strategy to initialize the unknown inpainting region. Numerical results both for synthetic and real-world data demonstrate the performance of our algorithm.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Technische Universität Kaiserslautern, Kaiserslautern, Germany

    Ronny Bergmann

  2. Department of Mathematics, Technische Universität München and Fast Algorithms for Biomedical Imaging Group, Helmholtz-Zentrum München, München, Germany

    Andreas Weinmann

Authors
  1. Ronny Bergmann
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  2. Andreas Weinmann
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Bergen, 7800, Bergen, Norway

    Xue-Cheng Tai

  2. Department of Mathematics, University of California, Los Angeles, CA, USA

    Egil Bae

  3. The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, S.A.R.

    Tony F. Chan

  4. Telemark University College, Postboks 203, 3901, Porsgrunn, Norway

    Marius Lysaker

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Bergmann, R., Weinmann, A. (2015). Inpainting of Cyclic Data Using First and Second Order Differences. In: Tai, XC., Bae, E., Chan, T.F., Lysaker, M. (eds) Energy Minimization Methods in Computer Vision and Pattern Recognition. EMMCVPR 2015. Lecture Notes in Computer Science, vol 8932. Springer, Cham. https://doi.org/10.1007/978-3-319-14612-6_12

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  • DOI: https://doi.org/10.1007/978-3-319-14612-6_12

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-14611-9

  • Online ISBN: 978-3-319-14612-6

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