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    Objective Observer-Relative Flow Visualization in Curved Spaces for Unsteady 2D Geophysical Flows

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    2020_rautek_killingsurfaces_with_appendixes_hq.pdf
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    2020_rautek_killingsurfaces.mp4
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    observer-relative-on-curved-manifolds-prerecorded-talk-vis2020_v03.mp4
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    Type
    Article
    Authors
    Rautek, Peter
    Mlejnek, Matej
    Beyer, Johanna
    Troidl, Jakob
    Pfister, Hanspeter
    Theußl, Thomas
    Hadwiger, Markus cc
    KAUST Department
    Visual Computing Center (VCC)
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Core Labs
    Computer Science Program
    KAUST Grant Number
    OSR-2015-CCF-2533-01
    Date
    2020-10-13
    Online Publication Date
    2020-10-13
    Print Publication Date
    2021-02
    Permanent link to this record
    http://hdl.handle.net/10754/665572
    
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    Abstract
    Computing and visualizing features in fluid flow often depends on the observer, or reference frame, relative to which the input velocity field is given. A desired property of feature detectors is therefore that they are objective, meaning independent of the input reference frame. However, the standard definition of objectivity is only given for Euclidean domains and cannot be applied in curved spaces. We build on methods from mathematical physics and Riemannian geometry to generalize objectivity to curved spaces, using the powerful notion of symmetry groups as the basis for definition. From this, we develop a general mathematical framework for the objective computation of observer fields for curved spaces, relative to which other computed measures become objective. An important property of our framework is that it works intrinsically in 2D, instead of in the 3D ambient space. This enables a direct generalization of the 2D computation via optimization of observer fields in flat space to curved domains, without having to perform optimization in 3D. We specifically develop the case of unsteady 2D geophysical flows given on spheres, such as the Earth. Our observer fields in curved spaces then enable objective feature computation as well as the visualization of the time evolution of scalar and vector fields, such that the automatically computed reference frames follow moving structures like vortices in a way that makes them appear to be steady.
    Citation
    Rautek, P., Mlejnek, M., Beyer, J., Troidl, J., Pfister, H., Theussl, T., & Hadwiger, M. (2020). Objective Observer-Relative Flow Visualization in Curved Spaces for Unsteady 2D Geophysical Flows. IEEE Transactions on Visualization and Computer Graphics, 1–1. doi:10.1109/tvcg.2020.3030454
    Sponsors
    We thank Anna Fruhstück for the illustrations and for help with the figures and the video. Hurricane Isabel data courtesy of EU Copernicus project, path from National Hurricane Center/Wikipedia. This work was supported by King Abdullah University of Science and Technology (KAUST), and the KAUST Office of Sponsored Research (OSR) award OSR-2015-CCF-2533-01. This research used resources of the Core Labs of KAUST.
    Publisher
    Institute of Electrical and Electronics Engineers (IEEE)
    Journal
    IEEE Transactions on Visualization and Computer Graphics
    DOI
    10.1109/TVCG.2020.3030454
    Additional Links
    https://ieeexplore.ieee.org/document/9222512/
    https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=9222512
    ae974a485f413a2113503eed53cd6c53
    10.1109/TVCG.2020.3030454
    Scopus Count
    Collections
    Articles; Computer Science Program; Visual Computing Center (VCC); Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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