Topological Landscapes: A Terrain Metaphor for Scientific Data

Weber, Gunther H.; Bremer, Peer-Timo; Pascucci, Valerio

doi:10.1109/tvcg.2007.70601

Cited by 94 publications

(104 citation statements)

References 44 publications

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“…We extend this measure to compare subtrees of a contour tree. Contour trees provide an abstract representation of a scalar field and have been recently used to explore high dimensional data via a two-dimensional terrain representation called the topological landscape [17,30,45]. Since our symmetry detection is essentially based on the contour tree, it can be used to identify repeating patterns in any dimension.…”

Section: Contour Tree For Data Exploration and Visualizationmentioning

confidence: 99%

Symmetry in Scalar Field Topology

Thomas

Natarajan

2011

IEEE Trans. Visual. Comput. Graphics

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Abstract-Study of symmetric or repeating patterns in scalar fields is important in scientific data analysis because it gives deep insights into the properties of the underlying phenomenon. Though geometric symmetry has been well studied within areas like shape processing, identifying symmetry in scalar fields has remained largely unexplored due to the high computational cost of the associated algorithms. We propose a computationally efficient algorithm for detecting symmetric patterns in a scalar field distribution by analysing the topology of level sets of the scalar field. Our algorithm computes the contour tree of a given scalar field and identifies subtrees that are similar. We define a robust similarity measure for comparing subtrees of the contour tree and use it to group similar subtrees together. Regions of the domain corresponding to subtrees that belong to a common group are extracted and reported to be symmetric. Identifying symmetry in scalar fields finds applications in visualization, data exploration, and feature detection. We describe two applications in detail: symmetry-aware transfer function design and symmetry-aware isosurface extraction.

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Section: Contour Tree For Data Exploration and Visualizationmentioning

confidence: 99%

Symmetry in Scalar Field Topology

Thomas

Natarajan

2011

IEEE Trans. Visual. Comput. Graphics

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“…The contour tree is a powerful visualization tool for abstract data representations [34], contour extractions [35], [36], transfer function design [37], etc. A number of algorithms have been used to compute contour trees [36], [38], [4].…”

Section: Feature-based Visualizationmentioning

confidence: 99%

“…[39] and Weber et al [34] showed that a contour tree can be decomposed into branches and rebuilt by assembling the branches afterward. Each branch rooted at an interior node, other than the two ends of the branch, is a child branch.…”

Section: Reversed Simplification Sequence and Branchesmentioning

confidence: 99%

Feature-Based Uncertainty Visualization

2014

Innovative Approaches of Data Visualization and Visual Analytics

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While uncertainty in scientific data attracts an increasing research interest in the visualization community, two critical issues remain insufficiently studied: (1) visualizing the impact of the uncertainty of a data set on its features and (2) interactively exploring 3D or large 2D data sets with uncertainties. In this study, a suite of feature-based techniques is developed to address these issues.

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“…Furthermore, the use of icons has been proposed by Shinagawa et al (Shinagawa et al, 1991). As it is difficult to match the resulting graph drawing to the scalar field, the use of colors has been proposed to identify connected components (Carr et al, 2004;Weber et al, 2007b;Weber et al, 2007a). Furthermore, Weber et al suggested the metaphor of a topological landscape (Weber et al, 2007b).…”

Section: Related Workmentioning

confidence: 99%

Visualization of Uncertain Contour Trees

Kraus¹

2010

Proceedings of the International Conference on Imaging Theory and Applications and International Conference on Information Visu

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Abstract:Contour trees can represent the topology of large volume data sets in a relatively compact, discrete data structure. However, the resulting trees often contain many thousands of nodes; thus, many graph drawing techniques fail to produce satisfactory results. Therefore, several visualization methods were proposed recently for the visualization of contour trees. Unfortunately, none of these techniques is able to handle uncertain contour trees although any uncertainty of the volume data inevitably results in partially uncertain contour trees. In this work, we visualize uncertain contour trees by combining the contour trees of two morphologically filtered versions of a volume data set, which represent the range of uncertainty. These two contour trees are combined and visualized within a single image such that a range of potential contour trees is represented by the resulting visualization. Thus, potentially erroneous topological structures are visually distinguished from more certain structures. Moreover, topological structures can be revealed that are otherwise obscured by data errors. We present and discuss results obtained with a prototypical implementation using well-known volume data sets.

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Topological Landscapes: A Terrain Metaphor for Scientific Data

Cited by 94 publications

References 44 publications

Symmetry in Scalar Field Topology

Symmetry in Scalar Field Topology

Feature-Based Uncertainty Visualization

Visualization of Uncertain Contour Trees

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