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

✍ Scribed by Hamish Carr, Christoph Garth, Tino Weinkauf (eds.)

• Publisher: Springer International Publishing
• Year: 2017
• Tongue: English
• Leaves: 355
• Series: Mathematics and Visualization
• Edition: 1
• Category: Library

✦ Synopsis

This book presents contributions on topics ranging from novel applications of topological analysis for particular problems, through studies of the effectiveness of modern topological methods, algorithmic improvements on existing methods, and parallel computation of topological structures, all the way to mathematical topologies not previously applied to data analysis.

Topological methods are broadly recognized as valuable tools for analyzing the ever-increasing flood of data generated by simulation or acquisition. This is particularly the case in scientific visualization, where the data sets have long since surpassed the ability of the human mind to absorb every single byte of data.

The biannual TopoInVis workshop has supported researchers in this area for a decade, and continues to serve as a vital forum for the presentation and discussion of novel results in applications in the area, creating a platform to disseminate knowledge about such implementations throughout and beyond the community.

The present volume, resulting from the 2015 TopoInVis workshop held in Annweiler, Germany, will appeal to researchers in the fields of scientific visualization and mathematics, domain scientists with an interest in advanced visualization methods, and developers of visualization software systems.

✦ Table of Contents

Front Matter....Pages i-xi
Front Matter....Pages 1-1
Theory of Singular Fibers and Reeb Spaces for Visualization....Pages 3-33
Topology-Based Analysis for Multimodal Atmospheric Data of Volcano Eruptions....Pages 35-50
A Comparison of Joint Contour Nets and Pareto Sets....Pages 51-65
Front Matter....Pages 67-67
Visualizing Topological Properties of the Search Landscape of Combinatorial Optimization Problems....Pages 69-85
Computing and Visualizing Time-Varying Merge Trees for High-Dimensional Data....Pages 87-101
Agreement Analysis of Quality Measures for Dimensionality Reduction....Pages 103-117
Front Matter....Pages 119-119
Fast Similarity Search in Scalar Fields using Merging Histograms....Pages 121-134
Morse-Smale Analysis of Ion Diffusion in Ab Initio Battery Materials Simulations....Pages 135-149
Piecewise Polynomial Reconstruction of Scalar Fields from Simplified Morse-Smale Complexes....Pages 151-168
Front Matter....Pages 169-169
Topological Extraction of Escape Maps in Divergence-Free Vector Fields....Pages 171-186
Compute and Visualize Discontinuity Among Neighboring Integral Curves of 2D Vector Fields....Pages 187-203
Decomposition of Vector Fields Beyond Problems of First Order and Their Applications....Pages 205-219
Maximum Number of Degenerate Curves in 3D Linear Tensor Fields....Pages 221-234
Front Matter....Pages 235-235
Hierarchical Watershed Ridges for Visualizing Lagrangian Coherent Structures....Pages 237-251
Finite Time Steady 2D Vector Field Topology....Pages 253-266
Comparing Finite-Time Lyapunov Exponents in Approximated Vector Fields....Pages 267-281
Transfer Operator-Based Extraction of Coherent Features on Surfaces....Pages 283-297
Front Matter....Pages 299-299
ADAPT: Adaptive Thresholds for Feature Extraction....Pages 301-315
Efficient Software for Programmable Visual Analysis Using Morse-Smale Complexes....Pages 317-331
Notes on the Distributed Computation of Merge Trees on CW-Complexes....Pages 333-348
Front Matter....Pages 299-299
Computing Invariants of Knotted Graphs Given by Sequences of Points in 3-Dimensional Space....Pages 349-363

✦ Subjects

Visualization;Manifolds and Cell Complexes (incl. Diff.Topology);Computing Methodologies;Computer Graphics