Topological Cacti: Visualizing Contour-Based Statistics

  • Gunther H. Weber
  • Peer-Timo Bremer
  • Valerio Pascucci
Part of the Mathematics and Visualization book series (MATHVISUAL)


Contours, the connected components of level sets, play an important role in understanding the global structure of a scalar field. In particular their nesting behavior and topology – often represented in form of a contour tree – have been used extensively for visualization and analysis. However, traditional contour trees only encode structural properties like number of contours or the nesting of contours, but little quantitative information such as volume or other statistics. Here we use the segmentation implied by a contour tree to compute a large number of per-contour (interval) based statistics of both the function defining the contour tree as well as other co-located functions. We introduce a new visual metaphor for contour trees, called topological cacti, that extends the traditional toporrery display of a contour tree to display additional quantitative information as width of the cactus trunk and length of its spikes. We apply the new technique to scalar fields of varying dimension and different measures to demonstrate the effectiveness of the approach.


Cube Root Spike Length Root Branch Fuel Consumption Rate Piecewise Polynomial Function 
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.


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This work was supported by the Director, Office of Advanced Scientific Computing Research, Office of Science, of the U.S. Department of Energy under Contract Nos. DE-AC02-05CH11231 (Lawrence Berkeley National Laboratory), DE-AC52-07NA27344 (Lawrence Livermore National Laboratory) and DE-FC02-06ER25781 (University of Utah) and the use of resources of the National Energy Research Scientific Computing Center (NERSC).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Gunther H. Weber
    • 1
  • Peer-Timo Bremer
    • 2
  • Valerio Pascucci
    • 3
  1. 1.Computational Research DivisionLawrence Berkeley National LaboratoryBerkeleyUSA
  2. 2.Center of Applied Scientific ComputingLawrence Livermore National LaboratoryLivermoreUSA
  3. 3.Scientific Computing and Imaging InstituteUniversity of UtahSalt Lake CityUSA

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