J Nonlinear Sci https://doi.org/10.1007/s00332-018-9470-1 Go With the Flow, on Jupiter and Snow. Coherence from Model-Free Video Data Without Trajectories 1,2,4 Abd AlRahman R. AlMomani · 1,2,3,4 Erik Bollt Received: 20 November 2017 / Accepted: 18 May 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract Viewing a data set such as the clouds of Jupiter, coherence is readily appar- ent to human observers, especially the Great Red Spot, but also other great storms and persistent structures. There are now many different deﬁnitions and perspectives mathematically describing coherent structures, but we will take an image processing perspective here. We describe an image processing perspective inference of coherent sets from a ﬂuidic system directly from image data, without attempting to ﬁrst model underlying ﬂow ﬁelds, related to a concept in image processing called motion track- ing. In contrast to standard spectral methods for image processing which are generally related to a symmetric afﬁnity matrix, leading to standard spectral graph theory, we need a not symmetric afﬁnity which arises naturally from the underlying arrow of time. We develop an anisotropic, directed diffusion operator corresponding to ﬂow on a directed graph, from a directed afﬁnity matrix developed with coherence in
Journal of Nonlinear Science – Springer Journals
Published: Jun 2, 2018
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