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 large and complex datasets, the characterization of noise and uncertainty, the effective integration of numerical methods with robust combinatorial algorithms, etc. 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. 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 "TopoInVis" workshop in Snowbird, Utah, follows the two successful workshops in 2005 (Budmerice, Slovakia) and 2007 (Leipzig, Germany).
Author(s): Kirk E. Jordan, Lance E. Miller (auth.), Valerio Pascucci, Xavier Tricoche, Hans Hagen, Julien Tierny (eds.)
Series: Mathematics and Visualization
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2011
Language: English
Pages: 260
Tags: Visualization; Topology; Geometry; Computer Graphics; Mechanical Engineering; Computational Intelligence
Front Matter....Pages i-viii
Geometric Topology & Visualizing 1-Manifolds....Pages 1-12
Stripe Parameterization of Tubular Surfaces....Pages 13-26
The Stability of the Apparent Contour of an Orientable 2-Manifold....Pages 27-41
Reconstructing Cell Complexes From Cross-sections....Pages 43-54
Substructure Topology Preserving Simplification of Tetrahedral Meshes....Pages 55-66
Practical Considerations in Morse-Smale Complex Computation....Pages 67-78
Modeling and Simplifying Morse Complexes in Arbitrary Dimensions....Pages 79-90
Simplification of Jacobi Sets....Pages 91-102
Combinatorial 2D Vector Field Topology Extraction and Simplification....Pages 103-114
On the Extraction of Long-living Features in Unsteady Fluid Flows....Pages 115-126
Stream Volume Segmentation of Grid-Less Flow Simulation....Pages 127-138
Eigenvector-based Interpolation and Segmentation of 2D Tensor Fields....Pages 139-150
Time-Dependent Visualization of Lagrangian Coherent Structures by Grid Advection....Pages 151-165
Topological Extraction and Tracking of Defects in Crystal Structures....Pages 167-178
Extracting and Visualizing Structural Features in Environmental Point Cloud LiDaR Data Sets....Pages 179-192
Topological Flow Structures in a Mathematical Model for Rotation-Mediated Cell Aggregation....Pages 193-204
A Categorical Approach to Contour, Split and Join Trees with Application to Airway Segmentation....Pages 205-216
Complementary Space for Enhanced Uncertainty and Dynamics Visualization....Pages 217-228
Topological Feature Extraction for Comparison of Terascale Combustion Simulation Data....Pages 229-240
Feature Tracking Using Reeb Graphs....Pages 241-253
Back Matter....Pages 255-260
