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Topological Methods in Data Analysis and Visualization II

Theory, Algorithms, and Applications

  • Ronald Peikert
  • Helwig Hauser
  • Hamish Carr
  • Raphael Fuchs

Part of the Mathematics and Visualization book series (MATHVISUAL)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Discrete Morse Theory

    1. Front Matter
      Pages 1-1
    2. David Günther, Jan Reininghaus, Steffen Prohaska, Tino Weinkauf, Hans-Christian Hege
      Pages 15-29
    3. Wieland Reich, Dominic Schneider, Christian Heine, Alexander Wiebel, Guoning Chen, Gerik Scheuermann
      Pages 47-59
  3. Hierarchical methods for extracting and visualizing topological structures

    1. Front Matter
      Pages 61-61
    2. Gunther H. Weber, Peer-Timo Bremer, Valerio Pascucci
      Pages 63-76
    3. W. Harvey, O. Rübel, V. Pascucci, P.-T. Bremer, Y. Wang
      Pages 77-90
    4. Hubert Wagner, Chao Chen, Erald Vuçini
      Pages 91-106
  4. Visualization of dynamical systems, vector and tensor fields

    1. Front Matter
      Pages 107-107
    2. Xavier Tricoche, Christoph Garth, Allen Sanderson, Ken Joy
      Pages 109-124
    3. Allen Sanderson, Guoning Chen, Xavier Tricoche, Elaine Cohen
      Pages 125-140
    4. Shreeraj Jadhav, Harsh Bhatia, Peer-Timo Bremer, Joshua A. Levine, Luis Gustavo Nonato, Valerio Pascucci
      Pages 141-159
    5. Alexander Wiebel, Stefan Koch, Gerik Scheuermann
      Pages 177-190
    6. Zhongzang Lin, Harry Yeh, Robert S. Laramee, Eugene Zhang
      Pages 191-204
  5. Topological Visualization of unsteady flow

    1. Front Matter
      Pages 205-205
    2. Jens Kasten, Ingrid Hotz, Hans-Christian Hege
      Pages 207-220
    3. Benjamin Schindler, Ronald Peikert, Raphael Fuchs, Holger Theisel
      Pages 221-235
    4. Armin Pobitzer, Ronald Peikert, Raphael Fuchs, Holger Theisel, Helwig Hauser
      Pages 237-253
    5. Dominic Schneider, Jan Fuhrmann, Wieland Reich, Gerik Scheuermann
      Pages 255-268
    6. Filip Sadlo, Markus Üffinger, Thomas Ertl, Daniel Weiskopf
      Pages 269-281
    7. Raphael Fuchs, Benjamin Schindler, Ronald Peikert
      Pages 283-296
  6. Back Matter
    Pages 297-299

About this book

Introduction

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.

Keywords

Data Analysis Geometry Topology Visualization

Editors and affiliations

  • Ronald Peikert
    • 1
  • Helwig Hauser
    • 2
  • Hamish Carr
    • 3
  • Raphael Fuchs
    • 4
  1. 1.Inst. Computational Science, CAB G 65.1ETH ZürichZürichSwitzerland
  2. 2., Dept. of InformaticsUniversity of BergenBergenNorway
  3. 3., School of ComputingUniversity of LeedsLeedsUnited Kingdom
  4. 4., Computational ScienceETH ZürichZürichSwitzerland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-23175-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 2012
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-23174-2
  • Online ISBN 978-3-642-23175-9
  • Series Print ISSN 1612-3786
  • Buy this book on publisher's site