Computing and Visualizing Time-Varying Merge Trees for High-Dimensional Data

  • Patrick OesterlingEmail author
  • Christian Heine
  • Gunther H. Weber
  • Dmitriy Morozov
  • Gerik Scheuermann
Conference paper
Part of the Mathematics and Visualization book series (MATHVISUAL)


We introduce a new method that identifies and tracks features in arbitrary dimensions using the merge tree—a structure for identifying topological features based on thresholding in scalar fields. This method analyzes the evolution of features of the function by tracking changes in the merge tree and relates features by matching subtrees between consecutive time steps. Using the time-varying merge tree, we present a structural visualization of the changing function that illustrates both features and their temporal evolution. We demonstrate the utility of our approach by applying it to temporal cluster analysis of high-dimensional point clouds.


Point Cloud Feature Tracking Saddle Node Tracking Information Burning Region 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The authors thank anonymous reviewers for valuable comments and assistance in revising the paper. This work was supported by a grant from the German Research Foundation (DFG) within the strategic research initiative on Scalable Visual Analytics (SPP 1335). This work was supported by the Director, Office of Advanced Scientific Computing Research, Office of Science, of the U.S. DOE under Contract No. DE-AC02-05CH11231 (Lawrence Berkeley National Laboratory) through the grant “Topology-based Visualization and Analysis of High-dimensional Data and Time-varying Data at the Extreme Scale”, program manager Lucy Nowell.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Patrick Oesterling
    • 1
    Email author
  • Christian Heine
    • 2
  • Gunther H. Weber
    • 3
  • Dmitriy Morozov
    • 3
  • Gerik Scheuermann
    • 1
  1. 1.Computer Science DepartmentUniversity of LeipzigLeipzigGermany
  2. 2.AG Computational TopologyUniversity of KaiserslauternKaiserslauternGermany
  3. 3.Computational Research DivisionLawrence Berkeley National LaboratoryBerkeleyUSA

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