Unbalanced Optimal Transport for Particle Tracking in PTV

Non-invasive flow measurement techniques, such as particle tracking velocimetry, resolve 3D velocity fields by pairing tracer particle positions in successive time steps. These trajectories are crucial for evaluating physical quantities like vorticity, shear stress, pressure, and coherent structures. However, reliable track estimation is challenging due to measurement noise caused by high particle density, particle image overlap, and falsely reconstructed 3D positions. To overcome this, we employ a probabilistic approach that combines reconstructed 3D position uncertainty with unbalanced optimal transport theory, yielding a robust particle tracking method. Our algorithm utilizes Bayesian reconstruction, producing Gaussian posterior distributions of particle positions, allowing for uncertainty quantification. This method accounts for epistemic uncertainty, unlike a standard PTV process that deterministically reconstructs particle positions. Subsequently, we optimize a transport plan by moving all particle position distributions between time frames to achieve effective particle tracking. We validate our method using synthetic datasets, compare the results with FlowFit, and demonstrate the performance for an experimental aneurysm flow.