Diff. Geom, Math. Phys., PDE Seminar: Louis-Philippe Saumier Demers

Particle Image Velocimetry (PIV) is a technique using successive laser images of particles immersed in a fluid to measure the velocity field of the fluid flow. Traditionally, cross-correlation is employed to extract the field from each pair of recorded images. This talk will introduce a new approach based on Optimal Transport (OT) to approximate the velocity field. More specifically, we consider the solution of the L2 OT problem with initial and final densities given by successive images of tracers. We will first present a model for this situation and investigate the behaviour of the OT map with respect to the model's key parameters. Then, we will present some algorithms and numerical results applying this theory to synthetic and real examples. This is joint work with B.Khouider and M.Agueh.