Multivariate topology simplification

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

研究成果: ジャーナルへの寄稿学術誌査読

9 被引用数 (Scopus)


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.

ジャーナルComputational Geometry: Theory and Applications
出版ステータス出版済み - 10月 2016

!!!All Science Journal Classification (ASJC) codes

  • コンピュータ サイエンスの応用
  • 幾何学とトポロジー
  • 制御と最適化
  • 計算理論と計算数学
  • 計算数学


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