A Bayesian approach to locally varying regularization in optical flow velocimetry
Gauresh Raj Jassal, Erkki Somersalo, Daniela Calvetti, Bryan Eric Schmidt · Physics of Fluids · 2025
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.