Topological Methods in Data Analysis and Visualization: Theory, Algorithms, and Applications

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Valerio Pascucci, Xavier Tricoche, Hans Hagen, Julien Tierny
Springer Science & Business Media, Nov 23, 2010 - Mathematics - 260 pages
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Topology-based methods are of increasing importance in the analysis and visualization of dataset 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 large and complex datasets, the characterization of noise and uncertainty, the effective integration of numerical methods with robust combinatorial algorithms, etc. (see also below for a list of selected issues). While there is an increasing number of high-quality publications in this field, many fundamental questions remain unsolved. New focused efforts are needed in a variety of techniques ranging from the theoretical foundations of topological models, algorithmic issues related to the representation power of computer-based implementations as well as their computational efficiency, user interfaces for presentation of quantitative topological information, and the development of new techniques for systematic mapping of science problems in topological constructs that can be solved computationally. In this forum 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. The 2009 workshop in Snowbird, Utah, follows the two successful workshops in 2005 (Budmerice, Slovakia) and 2007 (Leipzig, Germany).
 

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Contents

Geometric Topology Visualizing 1Manifolds
1
Stripe Parameterization of Tubular Surfaces
13
The Stability of the Apparent Contour of an Orientable 2Manifold
27
Reconstructing Cell Complexes From Crosssections
43
Substructure Topology Preserving Simplification of Tetrahedral Meshes
55
Practical Considerations in MorseSmale Complex Computation
67
Modeling and Simplifying Morse Complexes in Arbitrary Dimensions
79
Simplification of Jacobi Sets
91
TimeDependent Visualization of Lagrangian Coherent Structures by Grid Advection
151
Topological Extraction and Tracking of Defects in Crystal Structures
166
Extracting and Visualizing Structural Features in Environmental Point Cloud LiDaR Data Sets
179
Topological Flow Structures in a Mathematical Model for RotationMediated Cell Aggregation
193
A Categorical Approach to Contour Split and Join Trees with Application to Airway Segmentation
205
Complementary Space for Enhanced Uncertainty and Dynamics Visualization
217
Topological Feature Extraction for Comparison of Terascale Combustion Simulation Data
229
Feature Tracking Using Reeb Graphs
241

Combinatorial 2D Vector Field Topology Extraction and Simplification
103
On the Extraction of Longliving Features in Unsteady Fluid Flows
115
Stream Volume Segmentation of GridLess Flow Simulation
127
Eigenvectorbased Interpolation and Segmentation of 2D Tensor Fields
139
Author Index
254
Subject Index
255
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