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AN OPTICAL FLOW APPROACH TO ANALYZING SPECIES DENSITY DYNAMICS AND TRANSPORT

Journal of Computational Mathematics 2012年第3期30卷 249-261页

作者： aaron luttman Erik Bollt Jason Holloway Department of Mathematics Clarkson UniversityPotsdamNYUSA Department of Electrical Engineering Rice UniversityHoustonTXUSA

Classical optical flow techniques were developed for computing virtual motion fields between two images of the same scene, assuming conservation of intensity and a smooth- ness of the flow field. If these assumptions are dropped, such techniques can be adapted to compute apparent fows 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 computa- tions 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 mix- ing of the species, as well as the transport of the populations throughout the domain.

关键词： Optical flow Finite-time Lyapunov exponent Mass transport Data-drivendynamical systems.

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