## Topological Methods in Data Analysis and Visualization: Theory, Algorithms, and ApplicationsValerio Pascucci, Xavier Tricoche, Hans Hagen, Julien Tierny 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). |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

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 |

255 | |

### Other editions - View all

### Common terms and phrases

2-manifold advection algorithm analysis application approach arcs atoms behavior boundary burning regions cancellation cells combinatorial vector field complementary space component Computer Graphics connected construction contour tree corresponding critical points curvature curve data set defined degenerate point discrete dislocations domain dynamics Edelsbrunner edge contraction edges eigenvector extraction filter flow FTLE ridges function value Galilean invariant geometry global gradient identify IEEE incidence graph input integration interpolation intersection isosurface Jacobi set label Lagrangian Lemma level set linear Lyapunov exponent manifold mapping method Morse complexes Morse function Morse theory Morse-Smale complex neighborhood nodes particles Pascucci path line point cloud Reeb graph removal represent representation scalar field Section segmentation separatrices simulation stacking faults step stream lines stream surfaces stream volumes structure sublevel set substructures techniques tensor field tensorlines tetrahedral tetrahedral mesh threshold topological skeleton tracking triangle vector field topology vertex vertices