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 Sintel, collected by Butler et al. in 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 highcontrast 3 × 3 patches from this video are well-modeled by a 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.We study the nonlinear statistics of a space of high-contrast 3 × 3 optical flow patches from the Sintel dataset using the topological machinery of [19] and [3]. We identify the topologies of dense subsets of this space using Vietoris-Rips complexes and persistent homology. The densest patches lie near a circle, the horizontal flow circle [1]. In a more refined analysis, we select out the optical flow patches Key words and phrases. Optical flow, computational topology, persistent homology, fiber bundle, zigzag persistence.
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