基于非线性演化偏微分方程的光流精化
Nonlinear Evolutionary PDE-Based Refinement of Optical Flow
AI总结：
本文提出两种非线性变分模型用于光流精化，通过演化PDE证明正确性并利用一阶原始-对偶Chambolle-Pock格式实现高效数值求解，实验表明两阶段模型在保持同等精度下比单阶段模型更高效。
摘要：
本文的目标是提出两种非线性变分模型，用于从图像序列中获取精化的运动估计。所提出的两种模型均可被视为用于精确估计基于物理的流场（如旋转流和流体流）的广义框架的一部分。第一个模型的新颖之处在于它被分为两个阶段：第一阶段获得光流的粗略估计，然后第二阶段使用附加约束对该估计进行精化。使用演化偏微分方程（PDE）方法证明了该模型的正确性。第二个模型以标准方式使用单一泛函实现了与第一个模型相同的精化。我们模型的一个显著特征是，它们允许我们通过一阶原始-对偶 Chambolle-Pock 格式提供高效的数值实现。通过分别对流的散度和旋度进行各向异性正则化，在精确角度估计的背景下对两种模型进行了比较。我们观察到，尽管两种模型获得了相同的精度水平，但两阶段模型效率更高。事实上，我们根据经验证明，单阶段模型和两阶段模型的收敛率分别为 $O(1/N^2)$ 和 $O(1/N)$。
英文摘要：
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 primal-dual 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.
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