Go With the Flow, on Jupiter and Snow. Coherence from Model-Free Video Data Without Trajectories

Go With the Flow, on Jupiter and Snow. Coherence from Model-Free Video Data Without Trajectories 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 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Nonlinear Science Springer Journals

Go With the Flow, on Jupiter and Snow. Coherence from Model-Free Video Data Without Trajectories

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Mathematics; Analysis; Theoretical, Mathematical and Computational Physics; Classical Mechanics; Mathematical and Computational Engineering; Economic Theory/Quantitative Economics/Mathematical Methods
ISSN
0938-8974
eISSN
1432-1467
D.O.I.
10.1007/s00332-018-9470-1
Publisher site
See Article on Publisher Site

Abstract

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

Journal of Nonlinear ScienceSpringer Journals

Published: Jun 2, 2018

References

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