An accurate optical flow estimation of PIV using fluid velocity decomposition

In this study, we propose a novel optical flow formulation for estimating high-accuracy velocity fields from tracer particle image sequences. According to the Helmholtz velocity decomposition theorem, the proposed optical flow method decomposes the two-dimensional velocity field into four components: translation motion, linear distortion motion, shear distortion motion and rotation motion. In this context, regularization terms for different motion components are designed, which have a reasonable physical interpretation for the flow characteristics of the fluid. Subsequently, we design specific regularization parameters for the corresponding regularization terms according to the flow characteristics of the motion components. These regularization parameters can be adaptively adjusted with changes in the image space and velocity field. In addition, the data term of the optical flow formulation is based on the projected-motion equation derived from the continuity equation, which maintains the compressibility of the fluid in the two-dimensional plane. Velocity fields are estimated from synthetic tracer particle images and hypersonic experimental image sequences, and the velocity results are compared to those of an advanced cross-correlation-based PIV method and previous advanced optical flow methods. The results and comparisons indicate that the proposed method shows good performance and high measurement accuracy when acquiring compressible flow structures from fluid measurements.