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Topological Methods in Data Analysis and Visualization II

Theory, Algorithms, and Applications

  • Book
  • © 2012

Overview

Editors:
  1. Ronald Peikert

    1. Inst. Computational Science, CAB G 65.1, ETH Zürich, Zürich, Switzerland

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  2. Helwig Hauser

    1. , Dept. of Informatics, University of Bergen, Bergen, Norway

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  3. Hamish Carr

    1. , School of Computing, University of Leeds, Leeds, United Kingdom

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  4. Raphael Fuchs

    1. , Computational Science, ETH Zürich, Zürich, Switzerland

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  • Latest, peer-reviewed results in a growing research area
  • Topic with close interaction of mathematics and computer science
  • Many applications to science and engineering
  • Includes supplementary material: sn.pub/extras

Part of the book series: Mathematics and Visualization (MATHVISUAL)

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Table of contents (19 chapters)

  1. Front Matter

    Pages i-xi
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  2. Discrete Morse Theory

    1. Front Matter

      Pages 1-1
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  3. Computational discrete morse theory

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

      • Jan Reininghaus, Ingrid Hotz
      Pages 3-14

    2. Efficient Computation of a Hierarchy of Discrete 3D Gradient Vector Fields

      • David Günther, Jan Reininghaus, Steffen Prohaska, Tino Weinkauf, Hans-Christian Hege
      Pages 15-29

    3. Computing Simply-Connected Cells in Three-Dimensional Morse-Smale Complexes

      • Attila Gyulassy, Valerio Pascucci
      Pages 31-45

    4. Combinatorial Vector Field Topology in Three Dimensions

      • Wieland Reich, Dominic Schneider, Christian Heine, Alexander Wiebel, Guoning Chen, Gerik Scheuermann
      Pages 47-59

  4. Hierarchical methods for extracting and visualizing topological structures

    1. Front Matter

      Pages 61-61
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  5. Hierarchical methods

    1. Topological Cacti: Visualizing Contour-Based Statistics

      • Gunther H. Weber, Peer-Timo Bremer, Valerio Pascucci
      Pages 63-76

    2. Enhanced Topology-Sensitive Clustering by Reeb Graph Shattering

      • W. Harvey, O. Rübel, V. Pascucci, P.-T. Bremer, Y. Wang
      Pages 77-90

    3. Efficient Computation of Persistent Homology for Cubical Data

      • Hubert Wagner, Chao Chen, Erald Vuçini
      Pages 91-106

  6. Visualization of dynamical systems, vector and tensor fields

    1. Front Matter

      Pages 107-107
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  7. Hierarchical methods

    1. Visualizing Invariant Manifolds in Area-Preserving Maps

      • Xavier Tricoche, Christoph Garth, Allen Sanderson, Ken Joy
      Pages 109-124

    2. Understanding Quasi-Periodic Fieldlines and Their Topology in Toroidal Magnetic Fields

      • Allen Sanderson, Guoning Chen, Xavier Tricoche, Elaine Cohen
      Pages 125-140

    3. Consistent Approximation of Local Flow Behavior for 2D Vector Fields Using Edge Maps

      • Shreeraj Jadhav, Harsh Bhatia, Peer-Timo Bremer, Joshua A. Levine, Luis Gustavo Nonato, Valerio Pascucci
      Pages 141-159

    4. Cusps of Characteristic Curves and Intersection-Aware Visualization of Path and Streak Lines

      • Tino Weinkauf, Holger Theisel, Olga Sorkine
      Pages 161-175

    5. Glyphs for Non-Linear Vector Field Singularities

      • Alexander Wiebel, Stefan Koch, Gerik Scheuermann
      Pages 177-190

    6. 2D Asymmetric Tensor Field Topology

      • Zhongzang Lin, Harry Yeh, Robert S. Laramee, Eugene Zhang
      Pages 191-204

  8. Topological Visualization of unsteady flow

    1. Front Matter

      Pages 205-205
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  9. Hierarchical methods

    1. On the Elusive Concept of Lagrangian Coherent Structures

      • Jens Kasten, Ingrid Hotz, Hans-Christian Hege
      Pages 207-220

    2. Ridge Concepts for the Visualization of Lagrangian Coherent Structures

      • Benjamin Schindler, Ronald Peikert, Raphael Fuchs, Holger Theisel
      Pages 221-235
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Keywords

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.

Editors and Affiliations

  • Inst. Computational Science, CAB G 65.1, ETH Zürich, Zürich, Switzerland

    Ronald Peikert

  • , Dept. of Informatics, University of Bergen, Bergen, Norway

    Helwig Hauser

  • , School of Computing, University of Leeds, Leeds, United Kingdom

    Hamish Carr

  • , Computational Science, ETH Zürich, Zürich, Switzerland

    Raphael Fuchs

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

  • DOI: https://doi.org/10.1007/978-3-642-23175-9

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2012

  • Hardcover ISBN: 978-3-642-23174-2Published: 25 January 2012

  • Softcover ISBN: 978-3-662-51906-6Published: 23 August 2016

  • eBook ISBN: 978-3-642-23175-9Published: 10 January 2012

  • Series ISSN: 1612-3786

  • Series E-ISSN: 2197-666X

  • Edition Number: 1

  • Number of Pages: XI, 299

  • Topics: Visualization, Algorithms, Artificial Intelligence, Computer Graphics

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