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arXiv · 1812.00875

A torus model for optical flow

Henry Adams·Johnathan Bush·Brittany Carr·Lara Kassab·Joshua Mirth
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Abstract

We propose a torus model for high-contrast patches of optical flow. Our model is derived from a database of ground-truth optical flow from the computer-generated video \emph{Sintel}, collected by Butler et al.\ in \emph{A naturalistic open source movie for optical flow evaluation}. Using persistent homology and zigzag persistence, popular tools from the field of computational topology, we show that the high-contrast $3\times 3$ patches from this video are well-modeled by a \emph{torus}, a nonlinear 2-dimensional manifold. Furthermore, we show that the optical flow torus model is naturally equipped with the structure of a fiber bundle, related to the statistics of range image patches.

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Henry Adams, Johnathan Bush, Brittany Carr, Lara Kassab, Joshua Mirth. 2018-11-09. A torus model for optical flow. https://doi.org/10.1016/j.patrec.2019.11.029

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