Radial Basis Function Regression Of Lagrangian Three-Dimensional Particle Tracking Data

Abstract

Flow characterization by means of Particle Tracking Velocimetry (PTV) has gained significant importance in recent years. This is especially true in microfluidics, where the limited optical access only allows for using one camera. A commonly used technique is the Astigmatism Particle Tracking Velocimetry (APTV), which provides reliable 3D3C measurements. However, the resulting data is available on scattered points and usually requires interpolation onto regular grids for further processing. In this work, we test Radial Basis Function (RBF) with the Partition of Unity Method (PUM) for the regression and mesh-free derivative evaluation in large velocity fields. The RBF-PUM approach is first benchmarked on a synthetic test case against the classic Gaussian Window interpolation (AGW) and global RBF. Then, we test the RBF-PUM approach on a three-dimensional experimental dataset consisting of 500.000 data points in a vortex flow. The results prove that the RBF-PUM allows for accurate regression at an accessible computational cost.