On the Nonlinear Statistics of Optical Flow

  • Henry AdamsEmail author
  • Johnathan Bush
  • Brittany Carr
  • Lara Kassab
  • Joshua Mirth
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11382)


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.


Optical flow Computational topology Persistent homology Fiber bundle Zigzag persistence 



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


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Henry Adams
    • 1
    Email author
  • Johnathan Bush
    • 1
  • Brittany Carr
    • 1
  • Lara Kassab
    • 1
  • Joshua Mirth
    • 1
  1. 1.Colorado State UniversityFort CollinsUSA

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