Lucas-Kanade fluid trajectories for time-resolved PIV

We introduce a new method for estimating fluid trajectories in time-resolved PIV. It relies on a Lucas-Kanade paradigm and consists in a simple and direct extension of a two-frame estimation with FOLKI-PIV (Champagnat et al 2011 Exp. Fluids 50 1169-82). The so-called Lucas-Kanade Fluid Trajectories (LKFT) are assumed to be polynomial in time, and are found as the minimizer of a global functional, in which displacements are sought so as to match the intensities of a series of images pairs in the sequence, in the least-squares sense. All pairs involve the central image, similar to other recent time-resolved approaches (FTC (Lynch and Scarano 2013 Meas. Sci. Technol. 24 035305) and FTEE (Jeon et al 2014 Exp. Fluids 55 1-16)). As switching from a two-frame to a time-resolved objective simply amounts to adding terms in a functional, no significant additional algorithmic element is required. Similar to FOLKI-PIV the method is very well suited for GPU acceleration, which is an important feature as computational complexity increases with the image sequence size. Tests on synthetic data exhibiting peak-locking show that increasing the image sequence size strongly reduces both associated bias and random error, and that LKFT has a remaining total error comparable to that of FTEE on this case. Results on case B of the third PIV challenge (Stanislas et al 2008 Exp. Fluids 45 27-71) also show its ability to drastically reduce the error in situations with low signal-to-noise ratio. These results are finally confirmed on experimental images acquired in the near-field of a low Reynolds number jet. Strong reductions in peak-locking, spatial and temporal noise compared to two-frame estimation are also observed, on the displacement components themselves, as well as on spatial or temporal derivatives, such as vorticity and material acceleration.