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On the Nonlinear Statistics of Optical Flow

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Computational Topology in Image Context (CTIC 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11382))

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Abstract

In A naturalistic open source movie for optical flow evaluation, Butler et al. create a database of ground-truth optical flow from the computer-generated video Sintel. We study the high-contrast \(3\times 3\) patches from this video, and provide evidence that this dataset is well-modeled by a torus (a nonlinear 2-dimensional manifold). Our main tools are persistent homology and zigzag persistence, which are popular techniques from the field of computational topology. We show that the optical flow torus model is naturally equipped with the structure of a fiber bundle, which is furthermore related to the statistics of range images.

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Notes

  1. 1.

    A range image contains a distance at each pixel.

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Acknowledgements

We would like to thank Gunnar Carlsson, Bradley Nelson, Jose Perea, and Guillermo Sapiro for helpful conversations.

Author information

Authors and Affiliations

  1. Colorado State University, Fort Collins, CO, 80523, USA

    Henry Adams, Johnathan Bush, Brittany Carr, Lara Kassab & Joshua Mirth

Authors
  1. Henry Adams
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  2. Johnathan Bush
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  3. Brittany Carr
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  4. Lara Kassab
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  5. Joshua Mirth
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Corresponding author

Correspondence to Henry Adams .

Editor information

Editors and Affiliations

  1. Universidad de Málaga, Málaga, Spain

    Rebeca Marfil

  2. Universidad de Málaga, Málaga, Spain

    Mariletty Calderón

  3. University of Seville, Sevilla, Spain

    Fernando Díaz del Río

  4. University of Seville, Sevilla, Spain

    Pedro Real

  5. Universidad de Málaga, Málaga, Spain

    Antonio Bandera

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Adams, H., Bush, J., Carr, B., Kassab, L., Mirth, J. (2019). On the Nonlinear Statistics of Optical Flow. In: Marfil, R., Calderón, M., Díaz del Río, F., Real, P., Bandera, A. (eds) Computational Topology in Image Context. CTIC 2019. Lecture Notes in Computer Science(), vol 11382. Springer, Cham. https://doi.org/10.1007/978-3-030-10828-1_12

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  • DOI: https://doi.org/10.1007/978-3-030-10828-1_12

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