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Abstract The influence of several potential error sources and non-ideal experimental effects on the accuracy of a wavelet-based optical flow velocimetry (wOFV) method when applied to tracer particle images is evaluated using data from a series of synthetic flows. Out-of-plane particle displacements, severe image noise, laser sheet thickness reduction, and image intensity non-uniformity are shown to decrease the accuracy of wOFV in a similar manner to correlation-based particle image velocimetry (PIV). For the error sources tested, wOFV displays a similar or slightly increased sensitivity compared to PIV, but the wOFV results are still more accurate than PIV when the magnitude of the non-ideal effects remain within expected experimental bounds. For the majority of test cases, the results are significantly improved by using image pre-processing filters and the magnitude of improvement is consistent between wOFV and PIV. Flow divergence does not appear to have an appreciable effect on the accuracy of wOFV velocity estimation, even though the underlying fluid transport equation on which wOFV is based implicitly assumes that the motion is divergence-free. This is a significant finding for the broader applicability of planar velocimetry measurements using wOFV. Finally, it is noted that the accuracy of wOFV is not reduced notably in regions of the image between tracer particles, as long as the overall seeding density is not too sparse i.e. below 0.02 particles per pixel. This explicitly demonstrates that wOFV (when applied to particle images) yields an accurate whole field measurement, and not only at or adjacent to the discrete particle locations.
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This content will become publicly available on May 1, 2026
A Bayesian approach to locally varying regularization in optical flow velocimetry
Optical flow velocimetry (OFV) is a method for determining dense and accurate velocity fields from a pair of particle images by solving the classical optical flow problem. However, this is an ill-posed inverse problem, which generally entails minimizing a weighted sum of two terms–fidelity and regularization–and the weights in the sum are parameters that require manual tuning based on the properties of both the flow and the particle images. This manual tuning has historically been a consistent challenge that has limited the general applicability of OFV for experimental data, as the calculated velocity field is sensitive to the value of the weights. This work proposes a hierarchical model for the weighting parameters in the framework of a maximum a posteriori-based Bayesian optimization approach. The method replaces the classical Lagrange multiplier weighting parameter with a new, less-sensitive parameter that can be automatically predetermined from experimental images. The resulting method is tested on three different synthetic particle image velocimetry (PIV) datasets and on experimental particle images. The method is found to be capable of self-adjusting the local weights of the optimization process in real-time while simultaneously determining the velocity field, leading to an optimally regularized estimate of the velocity field without requiring any dataset-specific manual tuning of the parameters. The presented approach is the first truly general, parameter-free optical flow method for particle image velocimetry (PIV) images. The developed method is freely available as a part of the PIVlab package.
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- Award ID(s):
- 2204618
- PAR ID:
- 10630131
- Publisher / Repository:
- AIP Publishing
- Date Published:
- Journal Name:
- Physics of Fluids
- Volume:
- 37
- Issue:
- 5
- ISSN:
- 1070-6631
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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