On the nonlinear analysis of optical flow
On the nonlinear analysis of optical flow
复制标题
DOI：
10.12775/tmna.2016.054
复制
发表时间：
2016-08
影响因子：
0.7
通讯作者：
Shengxiang Xia;Yanmin Yin
中科院分区：
文献类型：
--
作者：
Shengxiang Xia;Yanmin Yin
利用计算拓扑学的方法，对Roth和Black建立的距离像光流场数据库进行了定性的拓扑分析，给出了3 × 3、5 × 5和7 × 7光流场斑空间的定性拓扑分析.我们实验证明，存在的空间的三个大小的高对比度补丁，分别是一个圆和三个圆模型的拓扑等价的子空间。克莱因瓶是一个商空间，它被描述为平方$[0，1] \times [0，1]$，其边由关系$（0，y）\sim（1，y）$（对于$y\in [0，1]$）和$（x，0）\sim（1-x，1）$（对于$ x\in [0，1]$）确定。对于$3 \times 3$光流补丁的空间，我们发现了一个子空间具有相同的同源的克莱因瓶。随着斑块尺寸的增大，$5 \times 5$和$7 \times 7$光流斑块空间的Klein瓶特征逐渐消失.
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.