A guided filter-based 3D hybrid variational optical flow for accurate tomographic PIV measurements

High spatial resolution and high accuracy estimation of 3D velocity fields are important for tomographic particle image velocimetry (Tomo-PIV), especially when measuring complex flow fields with delicate 3D structures. However, the widely used cross-correlation-based methods have limited spatial resolution, while the recently developed optical flow-based methods have low robustness and are sensitive to particle volume reconstruction errors. Therefore, 3D velocity estimation methods that simultaneously exhibit high resolution and robustness must be developed. In this study, we propose a novel velocity estimation method for Tomo-PIV measurement using the guided filter-based 3D hybrid variational optical flow (GF-HVOF) method to achieve high spatial resolution and highly accurate measurement of 3D flow field structure. First, we propose a novel L1-norm regularization term based on the Helmholtz decomposition theorem to preserve the divergence and vorticity of the fluid flow. Second, we propose a guided-filter-based constraint term using the result of the cross-correlation-based method as the guided flow field to improve the robustness of the optical flow method. Third, we propose a hybrid constraint term based on particle tracking velocimetry (PTV) method and a spatially weighted data term to reduce the effect of ghost particles and discrete errors generated during the reconstruction of particle volumes. The newly proposed hybrid method combines the advantages of optical-flow-based and cross-correlation-based methods and corrects the flow field using the PTV method. Velocity fields are estimated over synthetic and experimental particle volumes. The results show that the newly proposed GF-HVOF method achieves better performance and greater measurement accuracy than existing 3D fluid motion estimation methods.