论文标题
使用基于约束的改进方法进行流体运动估算的框架
A Framework for Fluid Motion Estimation using a Constraint-Based Refinement Approach
论文作者
论文摘要
基于物理学的光流模型已成功捕获数字图像引起的流体运动畸形。但是，缺少一个常见的理论框架来分析几种基于物理的模型。在这方面，我们使用基于约束的改进方法为流体运动估算的一般框架制定了一般框架。我们证明，对于特定的约束选择，我们的结果与基于经典的连续性方程式的流体流相近。理论上通过增强的拉格朗日方法以一种新颖的方式证明了这种亲密关系。使用修改的有界约束算法显示了乌扎瓦迭代的收敛性。在希尔伯特空间环境中研究了数学良好的良好性。此外，我们观察到与Cauchy-Riemann运算符的令人惊讶的联系，该连接将系统对角线化，从而导致涉及分歧和流卷的扩散现象。进行了几个数值实验，结果显示在不同的数据集中。此外，我们证明了涉及流动卷曲的流动驱动改进过程优于基于经典物理学的光流方法，而没有对图像数据进行任何其他假设。
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.
