A physical interpretation of regularization for optical flow methods in fluids

Abstract

This Letter establishes a physical interpretation of the regularization process that occurs as part of the solution to an optical flow problem within fluids. In doing so, a new regularization scheme for optical flow velocimetry (OFV) methods is developed through direct inspection of the Navier–Stokes equations. To the authors’ knowledge, this is the first time that a regularization scheme has been derived using the governing fluid transport equations for viscous fluids. The current regularization scheme is based on the insight that regularization in OFV should play the same role as viscosity in fluid dynamics. Evaluation on synthetic particle image data from 2D and 3D direct numerical simulations of nonreacting and reacting flows show that the proposed regularization scheme reduces the absolute error and leads to enhanced robustness with respect to the choice of the strength of regularization.

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Acknowledgements

The authors thank Julia Dobrosotskaya for helpful and insightful discussions regarding regularization schemes. The authors thank Peter Hamlington, Colin Towery, and Ryan Darragh at Colorado University for performing the 3D simulations.

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Schmidt, B.E., Sutton, J.A. A physical interpretation of regularization for optical flow methods in fluids. Exp Fluids 62, 34 (2021). https://doi.org/10.1007/s00348-021-03147-1

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