Fast Algorithms for p-elastica Energy with the Application to Image Inpainting and Curve Reconstruction

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


In this paper, we propose fast and efficient algorithms for p-elastica energy (p = 1 or 2). Inspired by the recent algorithm for Euler’s elastica models in [16], the algorithm is extended to solve the problem related to p-elastica energy based on augmented Lagrangian method. The proposed algorithms are as efficient as the previous method in terms of low computational cost per iteration. We provide an algorithm which replaces fast Fourier transform (FFT) by a cheap arithmetic operation at each grid point. Numerical tests on image inpainting are provided to demonstrate the efficiency of the proposed algorithms. We also show examples of using the proposed algorithms in curve reconstruction from unorganized data set.


p-elastica energy Augmented Lagrangian method Euler’s elasitca Image inpainting Curve reconstruction Unorganized data set 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jooyoung Hahn
    • 1
  • Ginmo J. Chung
    • 2
  • Yu Wang
    • 2
  • Xue-Cheng Tai
    • 2
    • 3
  1. 1.Institute for Mathematics and Scientific ComputingUniversity of GrazAustria
  2. 2.Division of Mathematical Sciences, School of Physical Mathematical SciencesNanyang Technological UniversitySingapore
  3. 3.Mathematics InstituteUniversity of BergenNorway

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