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An Optimal Control Approach to Find Sparse Data for Laplace Interpolation

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Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR 2013)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 8081))

Abstract

Finding optimal data for inpainting is a key problem in the context of partial differential equation-based image compression. We present a new model for optimising the data used for the reconstruction by the underlying homogeneous diffusion process. Our approach is based on an optimal control framework with a strictly convex cost functional containing an L 1 term to enforce sparsity of the data and non-convex constraints. We propose a numerical approach that solves a series of convex optimisation problems with linear constraints. Our numerical examples show that it outperforms existing methods with respect to quality and computation time.

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Author information

Authors and Affiliations

  1. Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Saarland University, Campus E1.7, 66041, Saarbrücken, Germany

    Laurent Hoeltgen, Simon Setzer & Joachim Weickert

Authors
  1. Laurent Hoeltgen
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  2. Simon Setzer
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  3. Joachim Weickert
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Editor information

Editors and Affiliations

  1. Centre for Mathematical Sciences, Lund University, Sweden

    Anders Heyden , Fredrik Kahl , Carl Olsson  & Magnus Oskarsson , ,  & 

  2. Dept. of Mathematics, University of Bergen, Johaness Brunsgate 12, 5007, Bergen, Norway

    Xue-Cheng Tai

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Hoeltgen, L., Setzer, S., Weickert, J. (2013). An Optimal Control Approach to Find Sparse Data for Laplace Interpolation. In: Heyden, A., Kahl, F., Olsson, C., Oskarsson, M., Tai, XC. (eds) Energy Minimization Methods in Computer Vision and Pattern Recognition. EMMCVPR 2013. Lecture Notes in Computer Science, vol 8081. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40395-8_12

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  • DOI: https://doi.org/10.1007/978-3-642-40395-8_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40394-1

  • Online ISBN: 978-3-642-40395-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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