The goal of this paper is to propose a unified framework for nonlinear refinement of optical flow. The first model is a two-phase refinement process where an initial estimate obtained in the first phase is subsequently refined in the second phase using additional constraints. We study the mathematical well-posedness of this formulation using an evolutionary-PDE approach. The second model is a single-phase improvement process involving an anisotropic regularization of the curl of the flow. For implementation we use the first-order primal-dual Chambolle-Pock algorithm. We observe that the results obtained by both methods are comparable in nature. We perform several numerical experiments and empirically demonstrate that by using a two-phase refinement process, a faster convergence rate of the order $O(1/N)$ is achieved than the single-phase process which has a higher convergence rate of the order $O(1/N^2)$.
翻译:本文的目的是提出非线性改进光学流的统一框架,第一个模型是一个两阶段的完善过程,第一阶段获得的初步估计数随后在第二阶段使用额外的限制加以改进,我们采用进化-PDE方法研究这一提法的数学能力,第二个模型是一个单一阶段的改进过程,对流的卷轴进行厌异的正规化。为了实施,我们使用第一级初等-双向查布尔-波克算法。我们观察到,这两种方法取得的结果在性质上是相似的。我们进行数项实验,并用经验证明,通过使用两阶段的完善过程,比单阶段的汇合率更高(1/N2美元)的单阶段程序更快地实现了1美元(1/N2美元)的汇合率。