Globally optimized cross-correlation for particle image velocimetry

We propose a global optimization method to automatically search for the correlation peak instead of computing the entire cross-correlation map throughout an interrogation window (IW) using a fast Fourier transform (FFT)-based method. The proposed method, named globally optimized cross-correlation for particle image velocimetry (GOCCPIV), minimizes an objective function consisting of a residual term for cross-correlation and a penalty term for smoothness to solve the optimal velocity field. A very small IW is adopted in GOCCPIV to obtain a dense velocity field with a high spatial resolution. The proposed method is quantitatively validated on synthetic particle image pairs with different flow patterns and is compared with the mainstream FFT-based cross-correlation method (FFTCCPIV) and physical-based optical flow (OpticalFlow). We consider the influences of the IW size, particle concentration, particle image diameter, large displacements and image noise on the velocity measurements. Error analysis indicates that GOCCPIV outperforms FFTCCPIV in resolving small-scale vortices and reducing the measurement error. Finally, the proposed method is applied to a real PIV experiment with an impinging jet. The results indicate that GOCCPIV is more suitable than FFTCCPIV for resolving high-velocity-gradient regions.