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dc.contributor.authorRautek, Peter
dc.contributor.authorMlejnek, Matej
dc.contributor.authorBeyer, Johanna
dc.contributor.authorTroidl, Jakob
dc.contributor.authorPfister, Hanspeter
dc.contributor.authorTheußl, Thomas
dc.contributor.authorHadwiger, Markus
dc.date.accessioned2020-10-14T09:29:18Z
dc.date.available2020-10-14T09:29:18Z
dc.date.issued2020
dc.identifier.citationRautek, 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
dc.identifier.issn2160-9306
dc.identifier.doi10.1109/TVCG.2020.3030454
dc.identifier.urihttp://hdl.handle.net/10754/665572
dc.description.abstractComputing 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.
dc.description.sponsorshipWe 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.
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)
dc.relation.urlhttps://ieeexplore.ieee.org/document/9222512/
dc.relation.urlhttps://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=9222512
dc.rightsArchived with thanks to IEEE Transactions on Visualization and Computer Graphics
dc.subjectFlow visualization
dc.subjectobserver fields
dc.subjectframes of reference
dc.subjectobjectivity
dc.subjectsymmetry groups
dc.subjectintrinsic covariant derivatives
dc.titleObjective Observer-Relative Flow Visualization in Curved Spaces for Unsteady 2D Geophysical Flows
dc.typeArticle
dc.contributor.departmentVisual Computing Center (VCC)
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentCore Labs
dc.contributor.departmentComputer Science Program
dc.identifier.journalIEEE Transactions on Visualization and Computer Graphics
dc.eprint.versionPost-print
dc.contributor.institutionHarvard University, Cambridge, MA USA
dc.contributor.institutionTU Wien, Vienna, Austria
kaust.personRautek, Peter
kaust.personMlejnek, Matej
kaust.personTroidl, Jakob
kaust.personTheußl, Thomas
kaust.personHadwiger, Markus
kaust.grant.numberOSR-2015-CCF-2533-01
refterms.dateFOA2020-10-27T06:02:26Z
kaust.acknowledged.supportUnitCCF
kaust.acknowledged.supportUnitCore Labs
kaust.acknowledged.supportUnitKAUST Office of Sponsored Research (OSR)


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