A framework for fluid motion estimation using a constraint-based refinement approach

Main Article Content

Hirak Doshi
Uday Kiran Nori

Keywords : fluid motion estimation, evolutionary PDE, image processing, augmented Lagrangian, bounded constraint algorithm

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 well-posedness 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.

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How to Cite
Doshi, H., & Nori, U. K. (2023). A framework for fluid motion estimation using a constraint-based refinement approach. Machine Graphics and Vision, 32(3/4), 17–43. https://doi.org/10.22630/MGV.2023.32.3.2

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