(untitled) (Journal of Computational Mathematics, 2012)
Classical optical flow techniques were developed for computing virtual motion fields between two images of the same scene, assuming conservation of intensity and a smoothness of the flow field. If these assumptions are dropped, such techniques can be adapted to compute apparent flows between time snapshots of data that do not come from images, even if these flows are turbulent and divergent, as in the case of flows representing complex spatiotemporal dynamics. While imaging methods have been used to analyze dynamics in experimental applications, they are only beginning to be applied to dynamics computations in settings outside the laboratory, for example in the analysis of species population dynamics from satellite data. In this work we present a variational optical flow approach based on the continuity equation and total variation regularization for computing the flow fields between population densities generated from a two-species predator-prey model for phyto- and zooplankton interactions. Given the time-varying vector fields produced from the optical flow, computational methods from dynamical systems can be employed to study pseudo-barriers present in the species interaction. This method allows to measure the mixing of the species, as well as the transport of the populations throughout the domain.