Neural Optical Flow Velocimetry

Optical flow (OF) is a computer vision framework for estimating dense displacement fields between images. It can be used for particle image velocimetry (PIV) processing, and has been shown to enhance the accuracy and resolution of PIV relative to cross-correlation. The discrete nature of current OF methods limits the accuracy of velocity gradients, hampering data assimilation efforts and analysis of turbulence. We report Neural Optical Flow (NOF), which uses a coordinate neural network and differentiable image-warping operator for OF. A continuous 2D or 3D neural velocity field is used to advect the discrete intensity field from t_i to t_i+1. Residuals between the advected image at t_i+1 and its real counterpart are squared and summed to form a data loss. Exact, continuous regularization functionals may be included (Navier–Stokes, Euler, div–curl, etc.) to improve accuracy and potentially infer pressure. We also show how the continuity equation can be included as a hard constraint in both 2D and 3D. Velocity fields are reconstructed by minimizing the aggregate loss. Our method is demonstrated using synthetic planar and stereo PIV measurements of turbulent flows. We compare NOF to a state-of-the-art wavelet OF technique, and discuss the application of NOF to other diagnostics.