Topological Methods in Data Analysis and Visualization

1. Front Matter

   Pages i-viii

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2. Geometric Topology & Visualizing 1-Manifolds

   • Kirk E. Jordan, Lance E. Miller, Thomas J. Peters, Alexander C. Russell

   Pages 1-12

3. Stripe Parameterization of Tubular Surfaces

   • Felix Kälberer, Matthias Nieser, Konrad Polthier

   Pages 13-26

4. The Stability of the Apparent Contour of an Orientable 2-Manifold

   • Herbert Edelsbrunner, Dmitriy Morozov, Amit Patel

   Pages 27-41

5. Reconstructing Cell Complexes From Cross-sections

   • Scott E. Dillard, Dan Thoma, Bernd Hamann

   Pages 43-54

6. Substructure Topology Preserving Simplification of Tetrahedral Meshes

   • Fabien Vivodtzev, Georges-Pierre Bonneau, Stefanie Hahmann, Hans Hagen

   Pages 55-66

7. Practical Considerations in Morse-Smale Complex Computation

   • Attila Gyulassy, Peer-Timo Bremer, Bernd Hamann, Valerio Pascucci

   Pages 67-78

8. Modeling and Simplifying Morse Complexes in Arbitrary Dimensions

   • Lidija Čomić, Leila De Floriani

   Pages 79-90

9. Simplification of Jacobi Sets

   • Suthambhara N, Vijay Natarajan

   Pages 91-102

10. Combinatorial 2D Vector Field Topology Extraction and Simplification

    • Jan Reininghaus, Ingrid Hotz

    Pages 103-114

11. On the Extraction of Long-living Features in Unsteady Fluid Flows

    • Jens Kasten, Ingrid Hotz, Bernd R. Noack, Hans-Christian Hege

    Pages 115-126

12. Stream Volume Segmentation of Grid-Less Flow Simulation

    • Harald Obermaier, Jörg Kuhnert, Martin Hering-Bertram, Hans Hagen

    Pages 127-138

13. Eigenvector-based Interpolation and Segmentation of 2D Tensor Fields

    • Jaya Sreevalsan-Nair, Cornelia Auer, Bernd Hamann, Ingrid Hotz

    Pages 139-150

14. Time-Dependent Visualization of Lagrangian Coherent Structures by Grid Advection

    • Filip Sadlo, Alessandro Rigazzi, Ronald Peikert

    Pages 151-165

15. Topological Extraction and Tracking of Defects in Crystal Structures

    • Sebastian Grottel, Carlos A. Dietrich, João L. D. Comba, Thomas Ertl

    Pages 167-178

16. Extracting and Visualizing Structural Features in Environmental Point Cloud LiDaR Data Sets

    • Patric Keller, Oliver Kreylos, Marek Vanco, Martin Hering-Bertram, Eric S. Cowgill, Louise H. Kellogg et al.

    Pages 179-192

17. Topological Flow Structures in a Mathematical Model for Rotation-Mediated Cell Aggregation

    • Alexander Wiebel, Raymond Chan, Christina Wolf, Andrea Robitzki, Angela Stevens, Gerik Scheuermann

    Pages 193-204

18. A Categorical Approach to Contour, Split and Join Trees with Application to Airway Segmentation

    • Andrzej Szymczak

    Pages 205-216

19. Complementary Space for Enhanced Uncertainty and Dynamics Visualization

    • Chandrajit Bajaj, Andrew Gillette, Samrat Goswami, Bong June Kwon, Jose Rivera

    Pages 217-228

20. Topological Feature Extraction for Comparison of Terascale Combustion Simulation Data

    • Ajith Mascarenhas, Ray W. Grout, Peer-Timo Bremer, Evatt R. Hawkes, Valerio Pascucci, Jacqueline H. Chen

    Pages 229-240

Topology-based methods are of increasing importance in the analysis and visualization of datasets from a wide variety of scientific domains such as biology, physics, engineering, and medicine. Current challenges of topology-based techniques include the management of time-dependent data, the representation of large and complex datasets, the characterization of noise and uncertainty, the effective integration of numerical methods with robust combinatorial algorithms, etc. . The editors have brought together the most prominent and best recognized researchers in the field of topology-based data analysis and visualization for a joint discussion and scientific exchange of the latest results in the field. This book contains the best 20 peer-reviewed papers resulting from the discussions and presentations at the third workshop on "Topological Methods in Data Analysis and Visualization", held 2009 in Snowbird, Utah, US. The 2009 "TopoInVis" workshop follows the two successful workshops in 2005 (Slovakia) and 2007 (Germany).

• Data Analysis
• Geometry
• Topology
• Visualization

• School of Computing, Scientific Computing and Imaging, University of Utah, Salt Lake City, USA

  Valerio Pascucci

• Department of Computer Science, Purdue University, West Lafayette, USA

  Xavier Tricoche

• FB Informatik, Universität Kaiserslautern, Kaiserslautern, Germany

  Hans Hagen

• LTCI - Telecom ParisTech, CNRS, Paris Cedex 13, France

  Julien Tierny

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