research-article

Topological Landscapes: A Terrain Metaphor for Scientific Data

Authors:

Peer-Timo Bremer,

Valerio PascucciAuthors Info & Claims

IEEE Transactions on Visualization and Computer Graphics, Volume 13, Issue 6

Pages 1416 - 1423

https://doi.org/10.1109/TVCG.2007.70601

Published: 01 November 2007 Publication History

Abstract

Scientific visualization and illustration tools are designed to help people understand the structure and complexity of scientific data with images that are as informative and intuitive as possible. In this context the use of metaphors plays an important role since they make complex information easily accessible by using commonly known concepts. In this paper we propose a new metaphor, called “Topological Landscapes,” which facilitates understanding the topological structure of scalar functions. The basic idea is to construct a terrain with the same topology as a given dataset and to display the terrain as an easily understood representation of the actual input data. In this projection from an $n$-dimensional scalar function to a two-dimensional (2D) model we preserve function values of critical points, the persistence (function span) of topological features, and one possible additional metric property (in our examples volume). By displaying this topologically equivalent landscape together with the original data we harness the natural human proficiency in understanding terrain topography and make complex topological information easily accessible.

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Cited By

Guardieiro Vde Oliveira FDoraiswamy HNonato LSilva C(2024)TopoMap++: A Faster and More Space Efficient Technique to Compute Projections with Topological GuaranteesIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2024.345636531:1(229-239)Online publication date: 10-Sep-2024
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https://dl.acm.org/doi/10.1109/TVCG.2023.3326601
Werner KGarth C(2021)Unordered Task-Parallel Augmented Merge Tree ConstructionIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2021.307687527:8(3585-3596)Online publication date: 1-Aug-2021
https://dl.acm.org/doi/10.1109/TVCG.2021.3076875
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Index Terms

Topological Landscapes: A Terrain Metaphor for Scientific Data
1. Computing methodologies
  1. Machine learning
    1. Machine learning algorithms
      1. Feature selection
2. Human-centered computing
  1. Human computer interaction (HCI)
    1. Interactive systems and tools

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cover image IEEE Transactions on Visualization and Computer Graphics

IEEE Transactions on Visualization and Computer Graphics Volume 13, Issue 6

November 2007

662 pages

ISSN:1077-2626

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Copyright © 2007.

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IEEE Educational Activities Department

United States

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Published: 01 November 2007

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https://dl.acm.org/doi/10.1109/TVCG.2024.3456365
Wetzels FPont MTierny JGarth C(2024)Merge Tree Geodesics and Barycenters with Path MappingsIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2023.332660130:1(1095-1105)Online publication date: 1-Jan-2024
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Werner KGarth C(2021)Unordered Task-Parallel Augmented Merge Tree ConstructionIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2021.307687527:8(3585-3596)Online publication date: 1-Aug-2021
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Heine CLeitte HHlawitschka MIuricich FDe Floriani LScheuermann GHagen HGarth C(2016)A Survey of Topology-based Methods in VisualizationComputer Graphics Forum10.5555/3071534.307159335:3(643-667)Online publication date: 1-Jun-2016
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