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Improvements in the accuracy of wavelet-based optical flow velocimetry (wOFV) using an efficient and physically based implementation of velocity regularization

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Abstract

This manuscript details recent improvements in a wavelet-based optical flow velocimetry (wOFV) method that represents a more physically sound implementation and results in increased accuracy of the velocity estimation. A novel regularization scheme is presented that is based on penalization of directional derivatives of the estimated velocity field or more specifically, second-order penalization of the gradients of divergence and curl, which enforces realistic flow structure. The regularization is performed in the wavelet domain with symmetric boundary conditions for the first time using an alternative wavelet transform approach of matrix multiplications. The method for the computation of full two-dimensional wavelet transforms by a single pair of matrix multiplications is described and shown to be significantly more efficient than a lifting implementation or convolution in MATLAB. Velocity fields are estimated from synthetic tracer particle images generated from 2D DNS of isotropic turbulence and from experimental results from a turbulent flow. Results are compared to an advanced correlation-based PIV algorithm and previous advanced optical flow methods. The velocity results estimated with the new regularization scheme are shown to be more accurate and exhibit a significant reduction in non-physical small-scale artifacts compared to previous results. A significant result from the current method is the ability to generate 2D velocity field images that resolve the dissipative scales in high-Reynolds number, turbulent flows.

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Notes

  1. The use of non-periodic boundary conditions are important for experimental data and are used in the current wOFV implementation regardless of evaluating synthetic or experimental data.

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Acknowledgements

The current work was partially supported by the Air Force Office of Scientific Research (Grant FA9550-16-1-0366; Dr. Chiping Li, Program Officer). The authors thank Pierre Dérian for helpful discussions clarifying the implementation of the regularization scheme in his work and Julia Dobrosotskaya for helping the authors frame the representation of wavelet transforms as matrix multiplications in an appropriate mathematical context. Finally, the authors thank Aaron Skiba, Campbell Carter, and Steve Hammack for providing the experimental particle image data used in the current work.

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  1. Ohio State University, 201 W 19th Avenue Columbus, Columbus, OH, 43210, USA

    B. E. Schmidt & J. A. Sutton

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  1. B. E. Schmidt
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  2. J. A. Sutton
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This work was partially sponsored by the Air Force Office of Scientific Research under grant FA9550-16-1-0366 (Chiping Li, Program Manager).

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Schmidt, B.E., Sutton, J.A. Improvements in the accuracy of wavelet-based optical flow velocimetry (wOFV) using an efficient and physically based implementation of velocity regularization. Exp Fluids 61, 32 (2020). https://doi.org/10.1007/s00348-019-2869-0

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