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Deep Eikonal Solvers

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Scale Space and Variational Methods in Computer Vision (SSVM 2019)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 11603))

Abstract

A deep learning approach to numerically approximate the solution to the Eikonal equation is introduced. The proposed method is built on the fast marching scheme which comprises of two components: a local numerical solver and an update scheme. We replace the formulaic local numerical solver with a trained neural network to provide highly accurate estimates of local distances for a variety of different geometries and sampling conditions. Our learning approach generalizes not only to flat Euclidean domains but also to curved surfaces enabled by the incorporation of certain invariant features in the neural network architecture. We show a considerable gain in performance, validated by smaller errors and higher orders of accuracy for the numerical solutions of the Eikonal equation computed on different surfaces. The proposed approach leverages the approximation power of neural networks to enhance the performance of numerical algorithms, thereby, connecting the somewhat disparate themes of numerical geometry and learning.

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Authors and Affiliations

  1. Technion - Israel Institute of Technology, Haifa, Israel

    Moshe Lichtenstein, Gautam Pai & Ron Kimmel

Authors
  1. Moshe Lichtenstein
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  2. Gautam Pai
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  3. Ron Kimmel
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Corresponding author

Correspondence to Moshe Lichtenstein .

Editor information

Editors and Affiliations

  1. University of Lübeck, Lübeck, Germany

    Jan Lellmann

  2. University of Erlangen-Nuremberg (FAU), Erlangen, Germany

    Martin Burger

  3. University of Lübeck, Lübeck, Germany

    Jan Modersitzki

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Lichtenstein, M., Pai, G., Kimmel, R. (2019). Deep Eikonal Solvers. In: Lellmann, J., Burger, M., Modersitzki, J. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2019. Lecture Notes in Computer Science(), vol 11603. Springer, Cham. https://doi.org/10.1007/978-3-030-22368-7_4

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  • DOI: https://doi.org/10.1007/978-3-030-22368-7_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-22367-0

  • Online ISBN: 978-3-030-22368-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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