Topological Methods in Data Analysis and Visualization

Theory, Algorithms, and Applications

By: Valerio Pascucci (Editor), Xavier Tricoche (Editor), Hans Hagen (Editor)

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Hardcover | 19 November 2010

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272 Pages

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24.77 x 16.51 x 1.27

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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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Non-Fiction Mathematics Calculus & Mathematical Analysis Topology Computing & I.T.Graphical & Digital Media Applications Geometry Combinatorics & Graph Theory Engineering & Technology Mechanical Engineering & Materials Mechanical Engineering Computer Programming & Software Development

Graphics Programming Computer Science Artificial Intelligence Technology in General Engineering in General Human-Computer Interaction Information Visualisation

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Published: 23rd August 2016

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Foundations of Computational Topology	p. 1
Geometric Topology & Visualizing 1-Manifolds	p. 1
Stripe Parameterization of Tubular Surfaces	p. 13
The Stability of the Apparent Contour of an Orientable 2-Manifold	p. 27
Reconstructing Cell Complexes from Cross-Sections	p. 43
Hierarchical Topological Data-Structures	p. 55
Substructure Topology Preserving Simplification of Tetrahedral Meshes	p. 55
Practical Considerations in Morse-Smale Complex Computation	p. 67
Modeling and Simplifying Morse Complexes in Arbitrary Dimensions	p. 79
Simplification of Jacobi Sets	p. 91
Combinatorial 2D Vector Field Topology Extraction and Simplification	p. 103
Topological Feature Extraction Algorithms	p. 115
On the Extraction of Long-living Features in Unsteady Fluid Flows	p. 115
Stream Volume Segmentation of Grid-Less Flow Simulation	p. 127
Eigenvector-based Interpolation and Segmentation of 2D Tensor Fields	p. 139
Time-Dependent Visualization of Lagrangian Coherent Structures by Grid Advection	p. 151
Applications in Scientific Data Analysis and Visualization	p. 167
Topological Extraction and Tracking of Defects in Crystal Structures	p. 167
Extracting and Visualizing Structural Features in Environmental Point Cloud LiDaR Data Sets	p. 179
Topological Flow Structures in a Mathematical Model for Rotation-Mediated Cell Aggregation	p. 193
A Categorical Approach to Contour, Split and Join Trees with Application to Airway Segmentation	p. 205
Complementary Space for Enhanced Uncertainty and Dynamics Visualization	p. 217
Topological Analysis of Large-Scale Scientific Data	p. 229
Topological Feature Extraction for Comparison of Terascale Combustion Simulation Data	p. 229
Feature Tracking Using Reeb Graphs	p. 241
Author Index	p. 255
Subject Index	p. 257
Table of Contents provided by Ingram. All Rights Reserved.

Topological Methods in Data Analysis and Visualization

Theory, Algorithms, and Applications

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Hardcover

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You Can Find This Book In

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