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A Fast Augmented Lagrangian Method for Euler’s Elastica Model

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Scale Space and Variational Methods in Computer Vision (SSVM 2011)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 6667))

Abstract

In this paper, a fast algorithm for Euler’s elastica functional is proposed, in which the Euler’s elastica functional is reformulated as a constrained minimization problem. Combining the augmented Lagrangian method and operator splitting techniques, the resulting saddle-point problem is solved by a serial of sub-problems. To tackle the nonlinear constraints arising in the model, a novel fixed-point-based approach is proposed so that all the sub-problems either are linear problems or have closed form solutions. Numerical examples are provided to demonstrate the performance of the proposed method.

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Author information

Authors and Affiliations

  1. Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore

    Yuping Duan & Xue-Cheng Tai

  2. Computer Science Department, Technion, Haifa, 32000, Israel

    Yu Wang

  3. Department of Mathematics, University of Bergen, Johannes Brunsgate 12, 5007, Bergen, Norway

    Xue-Cheng Tai

  4. Institute for Mathematics and Scientific Computing, University of Graz, Austria

    Jooyoung Hahn

Authors
  1. Yuping Duan
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  2. Yu Wang
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  3. Xue-Cheng Tai
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  4. Jooyoung Hahn
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Editor information

Editors and Affiliations

  1. Computer Science Department, Technion — Israel Institute of Technology, 718 Taub Building Technion, 32000, Haifa, Israel

    Alfred M. Bruckstein

  2. Department of Biomedical Engineering, Biomedical Image Analysis and Interpretation, Eindhoven University of Technology, Den Dolech 2 – WH 2.101, 5600 MB, Eindhoven, The Netherlands

    Bart M. ter Haar Romeny

  3. Faculaty of Engineering, School of Electrical Engineering, Tel Aviv University, Ramat Aviv, 69978, Israel

    Alexander M. Bronstein

  4. Institute of Computationa Science, Faculty of Informatics SI-109, Università della Svizzera Italiana, Via Giuseppe Buffi 13, 6904, Lugano, Switzerland

    Michael M. Bronstein

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© 2012 Springer-Verlag Berlin Heidelberg

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Duan, Y., Wang, Y., Tai, XC., Hahn, J. (2012). A Fast Augmented Lagrangian Method for Euler’s Elastica Model. In: Bruckstein, A.M., ter Haar Romeny, B.M., Bronstein, A.M., Bronstein, M.M. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2011. Lecture Notes in Computer Science, vol 6667. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24785-9_13

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  • DOI: https://doi.org/10.1007/978-3-642-24785-9_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24784-2

  • Online ISBN: 978-3-642-24785-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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