Mathematics and Visualization

Topological Methods in Data Analysis and Visualization II

Theory, Algorithms, and Applications

Editors: Peikert, R., Hauser, H., Carr, H., Fuchs, R. (Eds.)

  • Latest, peer-reviewed results in a growing research area
  • Topic with close interaction of mathematics and computer science
  • Many applications to science and engineering
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About this book

When scientists analyze datasets in a search for underlying phenomena, patterns or causal factors, their first step is often an automatic or semi-automatic search for structures in the data. Of these feature-extraction methods, topological ones stand out due to their solid mathematical foundation. Topologically defined structures—as found in scalar, vector and tensor fields—have proven their merit in a wide range of scientific domains, and scientists have found them to be revealing in subjects such as physics, engineering, and medicine.

 

Full of state-of-the-art research and contemporary hot topics in the subject, this volume is a selection of peer-reviewed papers originally presented at the fourth Workshop on Topology-Based Methods in Data Analysis and Visualization, TopoInVis 2011, held in Zurich, Switzerland. The workshop brought together many of the leading lights in the field for a mixture of formal presentations and discussion. One topic currently generating a great deal of interest, and explored in several chapters here, is the search for topological structures in time-dependent flows, and their relationship with Lagrangian coherent structures. Contributors also focus on discrete topologies of scalar and vector fields, and on persistence-based simplification, among other issues of note. The new research results included in this volume relate to all three key areas in data analysis—theory, algorithms and applications.

Table of contents (19 chapters)

  • Computational Discrete Morse Theory for Divergence-Free 2D Vector Fields

    Reininghaus, Jan (et al.)

    Pages 3-14

  • Efficient Computation of a Hierarchy of Discrete 3D Gradient Vector Fields

    Günther, David (et al.)

    Pages 15-29

  • Computing Simply-Connected Cells in Three-Dimensional Morse-Smale Complexes

    Gyulassy, Attila (et al.)

    Pages 31-45

  • Combinatorial Vector Field Topology in Three Dimensions

    Reich, Wieland (et al.)

    Pages 47-59

  • Topological Cacti: Visualizing Contour-Based Statistics

    Weber, Gunther H. (et al.)

    Pages 63-76

Buy this book

eBook $129.00
price for USA (gross)
  • ISBN 978-3-642-23175-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.00
price for USA
  • ISBN 978-3-642-23174-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Topological Methods in Data Analysis and Visualization II
Book Subtitle
Theory, Algorithms, and Applications
Editors
  • Ronald Peikert
  • Helwig Hauser
  • Hamish Carr
  • Raphael Fuchs
Series Title
Mathematics and Visualization
Copyright
2012
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-23175-9
DOI
10.1007/978-3-642-23175-9
Hardcover ISBN
978-3-642-23174-2
Series ISSN
1612-3786
Edition Number
1
Number of Pages
XI, 299
Topics