Spatiotemporal optimization on cross correlation for particle image velocimetry

We introduce an optimization method for the cross-correlation operation in particle image velocimetry by locating the correlation peaks assisted with constraint conditions. In this study, an objective function was constructed to include the residual of the normalized cross-correlation term, a component in charge of spatial smoothness (inspired by the optical flow method as used in a previous study) and a component for temporal smoothness (inspired by the concept of trajectory selection in particle tracking velocimetry). Minimizing the objective function gives optimized velocity fields for a series of tracer images for spatiotemporal smoothness. The proposed method was examined in synthetic images of turbulent flow and Batchelor vortex and in a laboratory experiment of vortex rings. The effect of image background noises and the initial guess for the optimization process were examined and discussed. Published under an exclusive license by AIP Publishing.