A velocity decomposition-based 3D optical flow method for accurate Tomo-PIV measurement

3D velocity field estimation is the key to high spatial resolution and high-accuracy measurements in tomographic particle image velocimetry (Tomo-PIV), especially when characterizing flow fields with delicate vortex structures. However, the cross-correlation velocity estimation method has limited spatial resolution due to the limitation of the interrogation sub-volume size. The 3D optical flow method can improve the spatial resolution of the velocity field, but its accuracy needs to be improved because it does not take into account the physical properties of the fluids. In this study, we propose a novel velocity decomposition-based 3D variational optical flow (VD-3DVOF) method to achieve high spatial resolution and high-accuracy measurement of 3D fluids. First, we present a novel regularization term based on the velocity decomposition theorem to constrain the different physical quantities, which can prevent the physical quantities from being over-smoothed. Second, we present a novel data term based on particle volume reconstruction feature weighting to reduce the influence of reconstruction errors on the velocity field estimation accuracy. Third, we present a multiscale technique and a volume warping operation to prevent the solution from falling into local optimal solutions. The newly proposed method considers both the physical properties of the fluid and the errors of reconstructed particle volumes. Velocity fields are estimated over synthetic and experimental particle volumes, and the results and comparisons show that the newly proposed VD-3DVOF method successfully achieves better performance and greater measurement accuracy than existing 3D motion estimation methods. Graphical abstract