Rethinking asymmetric image deformation with post-correction for particle image velocimetry

Symmetric image deformation has been considered as the only method for achieving second-order accuracy in particle image velocimetry (PIV). However, two deformed images with interpolation errors might lead to a doubling of the measurement uncertainty. Alternatively, this work proposed a post-correction method (FDI2CDI) to correct the velocity results of asymmetric image deformation to second-order accuracy, aiming at reducing the random interpolation error because only one deformed particle image is required. Specifically, the implicit geometric relationship between asymmetric forward difference interrogation (FDI) and symmetric central difference interrogation (CDI) is derived. And the correction problem is thus modeled as a fixed-point problem, which is solved using iterative updates. Tested on several synthetic velocity fields, massive synthetic particle image pairs, and two captured recordings, our FDI2CDI method demonstrates fast convergence, noise robustness, and significant improvement in accuracy. Besides, our FDI2CDI method also exhibits strong generalizability across different one-pass displacement estimators, as shown through experiments with optical flow and cross correlation. In addition, we provide a publicly available repository of FDI2CDI, including all reported results for the interested practitioners. In summary, our FDI2CDI post-correction method revitalizes the asymmetric image deformation for more accurate PIV measurement.