Multivariate topology simplification

Amit Chattopadhyay, Hamish Carr, David Duke, Zhao Geng, Osamu Saeki

Research output: Contribution to journalArticle

3 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)1-24
Number of pages24
JournalComputational Geometry: Theory and Applications
Volume58
DOIs
Publication statusPublished - Oct 1 2016

Fingerprint

Simplification
Visualization
Reeb Graph
Topology
Jacobi
Skeleton
Total ordering
Dual Graph
Multivariate Data
Pruning
Range of data
Scalar Field
Vector Field
Scalar
Projection
Scaling
Invariant
Approximation

All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Geometry and Topology
  • Control and Optimization
  • Computational Theory and Mathematics
  • Computational Mathematics

Cite this

Multivariate topology simplification. / Chattopadhyay, Amit; Carr, Hamish; Duke, David; Geng, Zhao; Saeki, Osamu.

In: Computational Geometry: Theory and Applications, Vol. 58, 01.10.2016, p. 1-24.

Research output: Contribution to journalArticle

Chattopadhyay, Amit ; Carr, Hamish ; Duke, David ; Geng, Zhao ; Saeki, Osamu. / Multivariate topology simplification. In: Computational Geometry: Theory and Applications. 2016 ; Vol. 58. pp. 1-24.
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