Particle image models for optical flow-based velocity field estimation in image velocimetry

This paper examines two models for image representation used for optical flow estimation in Particle Image Velocimetry (PIV). The common approach for flow estimation bases on a cross-correlation between PIV images. An alternative solution bases on an optical flow, which has the advantage of calculating vector fields with much better spatial resolution. The optical flow-based estimation requires calculations of temporal and spatial derivatives of the image intensity, which is usually achieved by using finite differences. Due to rapid intensity changes in the PIV images caused by particles having small diameters, an exact estimation of spatial derivatives using finite differences may lead to numerical errors that render data interpretation limited or even impractical. The present study aims at solving this problem by introducing two algorithms for PIV image processing, which differs in terms of a digital image representation. Both algorithms rely on a PIV image model, wherein the particle image complies with an Airy disc, which is well approximated by using a Gaussian function. Numerical analysis of sample PIV images (uniform and turbulent fields) show that both methods allow for high precision flow-velocity fields estimates in conjunction with the Lucas-Kanade algorithm.