Multivariate topology simplification

作者：Chattopadhyay Amit; Carr Hamish; Duke David; Geng Zhao; Saeki Osamu

来源：Computational Geometry-Theory and Applications, 2016, 58: 1-24.

DOI：10.1016/j.comgeo.2016.05.006

• Simplification
• Multivariate topology
• Reeb space
• Reeb skeleton
• Multi-dimensional Reeb graph

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.

• 出版日期2016-10