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 3×3 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.
Cite
@article{arxiv.1812.00875,
title = {A torus model for optical flow},
author = {Henry Adams and Johnathan Bush and Brittany Carr and Lara Kassab and Joshua Mirth},
journal= {arXiv preprint arXiv:1812.00875},
year = {2020}
}