The goal of this paper is to propose two nonlinear variational models for obtaining a refined motion estimation from an image sequence. Both the proposed models can be considered as a part of a generalized framework for an accurate estimation of physics-based flow fields such as rotational and fluid flow. The first model is novel in the sense that it is divided into two phases: the first phase obtains a crude estimate of the optical flow and then the second phase refines this estimate using additional constraints. The correctness of this model is proved using an Evolutionary PDE approach. The second model achieves the same refinement as the first model, but in a standard manner, using a single functional. A special feature of our models is that they permit us to provide efficient numerical implementations through the first-order primaldual Chambolle-Pock scheme. Both the models are compared in the context of accurate estimation of angle by performing an anisotropic regularization of the divergence and curl of the flow respectively. We observe that, although both the models obtain the same level of accuracy, the two-phase model is more efficient. In fact, we empirically demonstrate that the single-phase and the two-phase models have convergence rates of order $O(1/N^2)$ and $O(1/N)$ respectively.
翻译:本文的目的是提出两个非线性变异模型,以便从图像序列中获得精细的动量估计。两种拟议模型都可被视为精确估计以物理为基础的流流场(如旋转和流体流流)的通用框架的一部分。第一个模型是新颖的,因为它分为两个阶段:第一阶段对光学流进行粗略估计,然后第二阶段用额外的限制来完善这一估计数。该模型的正确性用进化式PDE方法证明。第二个模型与第一个模型一样,但以标准的方式,使用单一功能。我们模型的一个特殊特点是,它们使我们能够通过第一级初等查布尔-波克计划提供高效的数字执行。两个模型都是在精确估计角度的背景下加以比较的,对流的偏差和卷曲进行亚化调节。我们注意到,虽然这两个模型都获得了相同的精确度,但两阶段模型的效率却与第一个模型相同,但以标准的方式,使用单一功能。事实上,我们从实验上看,单阶段和两阶段的美元/美元(美元)的趋同率分别为美元/美元/美元。