A Fast Augmented Lagrangian Method for Euler’s Elastica Model

  • Yuping Duan
  • Yu Wang
  • Xue-Cheng Tai
  • Jooyoung Hahn
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6667)


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.


Closed Form Solution Image Denoising Augmented Lagrangian Method Constrain Minimization Problem Augmented Lagrangian Algorithm 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Yuping Duan
    • 1
  • Yu Wang
    • 2
  • Xue-Cheng Tai
    • 1
    • 3
  • Jooyoung Hahn
    • 4
  1. 1.Division of Mathematical Sciences, School of Physical and Mathematical SciencesNanyang Technological UniversitySingapore
  2. 2.Computer Science DepartmentTechnionHaifaIsrael
  3. 3.Department of MathematicsUniversity of BergenBergenNorway
  4. 4.Institute for Mathematics and Scientific ComputingUniversity of GrazAustria

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