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Coherent Topological Landscapes for Simulation Ensembles

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Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2020)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1474))

Abstract

The topological structure is an intrinsic feature of a scalar field of any spatial dimensionality. The dependence of the topology on the isovalue of the field can be represented in the form of merge and split trees, which are usually combined to a contour tree. Topological landscapes are algorithmically constructed 2D scalar fields, which have the same topological structure (and, therefore, correspond to the same contour tree) as the given multidimensional scalar field and serve as an intuitive low-dimensional depiction of its topological features. Topological landscapes computed for a set of scalar fields, e.g., created by varying over time or by varying simulation parameter values in a simulation ensemble, are not necessarily coherent among themselves. Therefore, a comparative analysis of topology in an ensemble is hindered. We propose a concept for the generation of coherent contour trees for simulation ensembles that is based on merging contour trees of all scalar fields of the ensemble. The coherent contour tree can be exploited to generate coherent topological landscapes. Visual analysis of varying scalar field topology is, then, supported by animating landscapes or by volume rendering of a stack of temporal slices representing color-coded landscapes. We apply the proposed methodology to synthetic data for evaluation purposes as well as to 2D and 3D simulation ensemble data.

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Acknowledgements

This work was supported in part by DFG grants MO 3050/2-1 and LI 1530/21-2.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Westfälische Wilhelms-Universität Münster, Einsteinstr. 62, 48149, Münster, Germany

    Marina Evers, Maria Herick, Vladimir Molchanov & Lars Linsen

Authors
  1. Marina Evers
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  2. Maria Herick
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  3. Vladimir Molchanov
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  4. Lars Linsen
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Corresponding author

Correspondence to Vladimir Molchanov .

Editor information

Editors and Affiliations

  1. IRISA, University of Rennes 1, Rennes, France

    Kadi Bouatouch

  2. Universidade do Porto, Porto, Portugal

    A. Augusto de Sousa

  3. University of Genova, Genova, Italy

    Manuela Chessa

  4. Mines ParisTech, Paris, France

    Alexis Paljic

  5. Linnaeus University, Växjö, Sweden

    Andreas Kerren

  6. French Civil Aviation University (ENAC), Toulouse, France

    Christophe Hurter

  7. Università di Catania, Catania, Italy

    Giovanni Maria Farinella

  8. Universitat de Barcelona, Barcelona, Spain

    Petia Radeva

  9. Escola Superior de Tecnologia de Setúbal, Setúbal, Portugal

    Jose Braz

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Evers, M., Herick, M., Molchanov, V., Linsen, L. (2022). Coherent Topological Landscapes for Simulation Ensembles. In: Bouatouch, K., et al. Computer Vision, Imaging and Computer Graphics Theory and Applications. VISIGRAPP 2020. Communications in Computer and Information Science, vol 1474. Springer, Cham. https://doi.org/10.1007/978-3-030-94893-1_10

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  • DOI: https://doi.org/10.1007/978-3-030-94893-1_10

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