In this study, we present a new three-dimensional optical flow method based on volumetric segmentation for the velocity estimation of fluid flow. The proposed method uses a segmented smoothness term that is designed on the assumption that the particle velocity varies continuously in each segmented volume and discontinuously on the surfaces of the segmented volumes. Subsequently, the data term is proposed on the basis of the segmented volumes and the fluid mass conservation equation, which is derived from the Reynolds transport equation. In addition, the robust local level-set method is applied to segment the particle volume according to the velocity distribution of fluid flow. The proposed method is evaluated quantitatively on synthetic data and qualitatively on experimental data, and the velocity results are compared to the advanced 3D velocity estimation methods. The results indicate that the proposed method can obtain velocity fields with greater measurement accuracy for Tomo-PIV.

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

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.