arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2011.12267cs.CVmath.AP
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使用基于约束的细化方法的流体运动估计框架

A Framework for Fluid Motion Estimation using a Constraint-Based Refinement Approach

Sri Sathya Sai Institute of Higher Learning(斯里·萨蒂亚·赛高等学习学院)

Hirak Doshi, N. Uday Kiran

AI总结:

本文提出一个基于约束细化方法的流体运动估计通用理论框架,证明了其与经典连续性方程方法的联系及适定性,并发现涉及流旋度的细化过程优于经典物理光流方法。

摘要:

基于物理的光流模型在捕捉数字图像中产生的流体运动变形方面取得了成功。然而,目前缺乏一个分析多种基于物理模型的通用理论框架。在这方面,我们使用基于约束的细化方法,构建了一个用于流体运动估计的通用框架。我们证明,对于特定的约束选择,我们的结果与经典的基于连续性方程的流体流动方法非常接近。这种接近性通过增广拉格朗日方法以一种新颖的方式得到了理论证明。Uzawa迭代的收敛性通过改进的有界约束算法得以证明。在Hilbert空间设定下研究了数学适定性。此外,我们观察到一个与Cauchy-Riemann算子的惊人联系,该算子使系统对角化,导致涉及流的散度和旋度的扩散现象。进行了多次数值实验,并在不同数据集上展示了结果。另外,我们证明了一个涉及流旋度的流驱动细化过程,在不增加任何图像数据假设的情况下,优于经典的基于物理的光流方法。

英文摘要:

Physics-based optical flow models have been successful in capturing the deformities in fluid motion arising from digital imagery. However, a common theoretical framework analyzing several physics-based models is missing. In this regard, we formulate a general framework for fluid motion estimation using a constraint-based refinement approach. We demonstrate that for a particular choice of constraint, our results closely approximate the classical continuity equation-based method for fluid flow. This closeness is theoretically justified by augmented Lagrangian method in a novel way. The convergence of Uzawa iterates is shown using a modified bounded constraint algorithm. The mathematical wellposedness is studied in a Hilbert space setting. Further, we observe a surprising connection to the Cauchy-Riemann operator that diagonalizes the system leading to a diffusive phenomenon involving the divergence and the curl of the flow. Several numerical experiments are performed and the results are shown on different datasets. Additionally, we demonstrate that a flow-driven refinement process involving the curl of the flow outperforms the classical physics-based optical flow method without any additional assumptions on the image data.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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