Hyperbolic Numerics for Variational Approaches to Correspondence Problems

Authors:
Henning Zimmer;Michael Breuß;Joachim Weickert;Hans-Peter Seidel
Affiliations:
Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Saarland University, Saarbrücken, Germany 66041 and Max-Planck Institute for Informatics, Saarbrücken, Ger ...;Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Saarland University, Saarbrücken, Germany 66041;Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Saarland University, Saarbrücken, Germany 66041;Max-Planck Institute for Informatics, Saarbrücken, Germany 66123
Venue:
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Year:
2009

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Abstract

Variational approaches to correspondence problems such as stereo or optic flow have now been studied for more than 20 years. Nevertheless, only little attention has been paid to a subtle numerical approximation of derivatives. In the area of numerics for hyperbolic partial differential equations (HDEs) it is, however, well-known that such issues can be crucial for obtaining favourable results. In this paper we show that the use of hyperbolic numerics for variational approaches can lead to a significant quality gain in computational results. This improvement can be of the same order as obtained by introducing better models. Applying our novel scheme within existing variational models for stereo reconstruction and optic flow, we show that this approach can be beneficial for all variational approaches to correspondence problems.