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International Conference on Scale Space and Variational Methods in Computer Vision

SSVM 2017: Scale Space and Variational Methods in Computer Vision pp 283–294Cite as

Nonlinear Flows for Displacement Correction and Applications in Tomography

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Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10302))

Abstract

In this paper we derive nonlinear evolution equations associated with a class of non-convex energy functionals which can be used for correcting displacement errors in imaging data. We show a preliminary convergence result of a relaxed convexification of the non-convex optimization problem. Some properties on the behavior of the solutions of these filtering flows are studied by numerical analysis. At the end, we provide examples for correcting angular perturbations in tomographical data.

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Acknowledgements

The authors thank the reviewers for some helpful comments. The work of OS has been supported by the Austrian Science Fund (FWF): Geometry and Simulation, project S11704 (Variational methods for imaging on manifolds), and Interdisciplinary Coupled Physics Imaging, project P26687-N25.

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Authors and Affiliations

  1. Computational Science Center, University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Wien, Austria

    Guozhi Dong & Otmar Scherzer

  2. Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenbergerstrasse 69, 4040, Linz, Austria

    Otmar Scherzer

Authors
  1. Guozhi Dong
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  2. Otmar Scherzer
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Corresponding author

Correspondence to Guozhi Dong .

Editor information

Editors and Affiliations

  1. University of Copenhagen , Copenhagen, Denmark

    François Lauze

  2. Technical University of Denmark , Kongens Lyngby, Denmark

    Yiqiu Dong

  3. Technical University of Denmark , Kongens Lyngby, Denmark

    Anders Bjorholm Dahl

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Dong, G., Scherzer, O. (2017). Nonlinear Flows for Displacement Correction and Applications in Tomography. In: Lauze, F., Dong, Y., Dahl, A. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2017. Lecture Notes in Computer Science(), vol 10302. Springer, Cham. https://doi.org/10.1007/978-3-319-58771-4_23

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  • DOI: https://doi.org/10.1007/978-3-319-58771-4_23

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-58770-7

  • Online ISBN: 978-3-319-58771-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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