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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 629–642Cite as

Adaptive Discretizations for Non-smooth Variational Vision

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

Abstract

Variational problems in vision are solved numerically on the pixel lattice because it provides the simplest computational grid to discretize the input images, even though a uniform grid seldom matches the complexity of the solution. To adapt the complexity of the discretization to the solution, it is necessary to adopt finite-element techniques that match the resolution of piecewise polynomial bases to the resolving power of the variational model, but such techniques have been overlooked for nonsmooth variational models. To address this issue, we investigate the pros and cons of finite-element discretizations for nonsmooth variational problems in vision, their multiresolution properties, and the optimization algorithms to solve them. Our 2 and 3D experiments in image segmentation, optical flow, stereo, and depth fusion reveal the conditions where finite-element can outperform finite-difference discretizations by achieving significant computational savings with a minor loss of accuracy.

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Acknowledgements

This research was partially funded by SNSF grant P300P2-161038, NSF grant 442511-SS-22001 and AFOSR grant FA9550-15-1-0229.

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Authors and Affiliations

  1. UCLA Vision Lab, Los Angeles, USA

    Virginia Estellers & Stefano Soatto

Authors
  1. Virginia Estellers
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  2. Stefano Soatto
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Corresponding author

Correspondence to Virginia Estellers .

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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Estellers, V., Soatto, S. (2017). Adaptive Discretizations for Non-smooth Variational Vision. 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_50

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  • DOI: https://doi.org/10.1007/978-3-319-58771-4_50

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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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