On the nonlinear analysis of optical flow
Keywords
Optical flow, persistent homology, high-contrast patches, Klein bottleAbstract
We utilize the methods of computational topology to the database of optical flow created by Roth and Black from range images, and demonstrate a qualitative topological analysis of spaces of $3 \times 3, 5 \times 5$ and $7 \times 7$ optical flow patches. We experimentally prove that there exist subspaces of the spaces of the three sizes high-contrast patches that are topologically equivalent to a circle and a three circles model, respectively. The Klein bottle is the quotient space described as the square $[0,1] \times [0,1]$ with sides identified by the relations $(0, y)\sim (1, y)$ for $y\in [0, 1]$ and $(x, 0) \sim (1-x, 1)$ for $ x\in [0, 1]$. For the space of $3 \times 3$ optical flow patches we found a subspace having the same homology as that of the Klein bottle. As the size of patches increases, the Klein bottle feature of the spaces of $5 \times 5$ and $7 \times 7$ optical flow patches gradually disappears.Published
2016-08-17
How to Cite
1.
XIA, Shengxiang and YIN, Yanmin. On the nonlinear analysis of optical flow. Topological Methods in Nonlinear Analysis. Online. 17 August 2016. Vol. 48, no. 2, pp. 661 - 676. [Accessed 24 April 2024].
Issue
Section
Articles
Stats
Number of views and downloads: 0
Number of citations: 0