3D Fluid Flow Estimation from Multi-View Particle Images using Physical Priors

Abstract

High-resolution 3D velocimetry estimation of fluids is a key problem in experimental fluid mechanics. It offers important applications for aero- and hydrodynamic measurements in academia and industry and facilitates fundamental research in turbulent flows. By injecting tracer particles into a fluid and observing their displacements over time from multiple view-points, a dense velocity field can be obtained. However, with increased particle seeding densities, ambiguities in the 3D particle reconstruction arise, which, in turn, affect the reconstruction accuracy of the underlying flow field. Existing approaches are limited to low seeding densities, which limit the spatial resolution of the flow field, or require long time sequences to heuristically resolve ambiguities of large, self-occluding particle sets. This thesis focuses on novel, physically-motivated approaches for high accuracy 3D flow estimation from few time steps. Multiple contributions are presented to tackle high seeding densities and, thus, facilitate high-resolution velocity field estimation. First, a variational formulation of the 3D flow estimation problem is introduced. The coarse- to-fine optimization scheme allows incorporation of physical priors, such as the incompressible stationary Stokes equations. To counteract the high memory requirement of voxel-based representations, a sparse particle reconstruction approach is subsequently proposed, combined with a sparse descriptor for 3D correspondence matching. Finally, a joint energy formulation is presented that optimizes both the sparse 3D particle locations and the dense motion field. Taking into account all available input views and both time steps jointly results in a better disambiguation of particle reconstructions and a more detailed flow field estimation. This favorable formulation is further extended to multiple time steps, allowing to further improve the particle reconstruction. Hence, even higher particle seeding densities can be supported. The proposed approaches were quantitatively validated on synthetic fluid simulations and delivered compelling results on experiments in water and air.