Simplifying Multivariate Topology (Extended Abstract)

Abstract Topological simplification is effective for analysis and visualisation of scalar data. However, topological simplifi-cationofmultivariatedataislesswelldeveloped. Wedescribe multi-fieldtopology simplificationstrategybasedonthe Reeb Space. We generalise critical nodes in the Reeb Graph to the Jacobi Structure of the Reeb Space that di-vides itintoregions. Thedual graph for these regions, the ReebSkeleton, has properties similartothe Reebgraph,and can be simplified using importance measures based on generalising persistence to Measure Persistence. Categories and Subject Descriptors (according to ACM CCS) : I.3.6 [Computer Graphics]: Methodology andTechniques—Graphics data structures and data types1. ContextScientific data is complex in nature and difficult to vi-sualise. Topological tools have therefore become impor-tant in scientific visualisation, especially for scalar fields[CSvdP10,TP12]. Multivariate topology has been based onJacobi sets - a generalisation of critical points to multi-fields [EH04,BBD