Chattopadhyay, A, Carr, H, Duke, D et al. (2 more authors) (2016) Multivariate Topology Simplification. Computational Geometry, 58. pp. 1-24. ISSN 0925-7721
Abstract
Topological simplification of scalar and vector fields is well-established as an effective method for analysing and visualising complex data sets. For multivariate (alternatively, multi-field) data, topological analysis requires simultaneous advances both mathematically and computationally. We propose a robust multivariate topology simplification method based on “lip”-pruning from the Reeb space. Mathematically, we show that the projection of the Jacobi set of multivariate data into the Reeb space produces a Jacobi structure that separates the Reeb space into simple components. We also show that the dual graph of these components gives rise to a Reeb skeleton that has properties similar to the scalar contour tree and Reeb graph, for topologically simple domains. We then introduce a range measure to give a scaling-invariant total ordering of the components or features that can be used for simplification. Computationally, we show how to compute Jacobi structure, Reeb skeleton, range and geometric measures in the Joint Contour Net (an approximation of the Reeb space) and that these can be used for visualisation similar to the contour tree or Reeb graph.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2016 Elsevier B.V. This is an author produced version of a paper published in Computational Geometry. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Simplification; Multivariate topology; Reeb space; Reeb skeleton; Multi-dimensional Reeb graph |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Funding Information: | Funder Grant number EPSRC EP/J013072/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 24 May 2016 09:00 |
Last Modified: | 11 Sep 2019 15:50 |
Published Version: | http://dx.doi.org/10.1016/j.comgeo.2016.05.006 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.comgeo.2016.05.006 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:100068 |