Carr H., Fujishiro I., Sadlo F., Takahashi S. (Eds.) Topological Methods in Data Analysis and Visualization V: Theory, Algorithms, and Applications

Springer, 2020. — 264 p. — (Mathematics and Visualization). — ISBN: 978-3-030-43035-1.This collection of peer-reviewed workshop papers provides comprehensive coverage of cutting-edge research into topological approaches to data analysis and visualization. It encompasses the full range of new algorithms and insights, including fast homology computation, comparative analysis of simplification techniques, and key applications in materials and medical science. The book also addresses core research challenges such as the representation of large and complex datasets, and integrating numerical methods with robust combinatorial algorithms.
In keeping with the focus of the TopoInVis 2017 Workshop, the contributions reflect the latest advances in finding experimental solutions to open problems in the sector. They provide an essential snapshot of state-of-the-art research, helping researchers to keep abreast of the latest developments and providing a basis for future work. Gathering papers by some of the world’s leading experts on topological techniques, the book represents a valuable contribution to a field of growing importance, with applications in disciplines ranging from engineering to medicine.Hierarchies and Ranks for Persistence Pairs
Triplet Merge Trees
Persistent Intersection Homology for the Analysis of Discrete Data
Coarse-Graining Large Search Landscapes Using Massive Edge Collapse
Adjusting Control Parameters of Topology-Accentuated Transfer Functions for Volume Raycasting
Topological Machine Learning with Persistence Indicator Functions
Pathological and Test Cases for Reeb Analysis
Abstracted Visualization of Halo Topologies in Dark Matter Simulations
Persistence Concepts for 2D Skeleton Evolution Analysis
Fast Topology-Based Feature Tracking using a Directed Acyclic Graph
The Approximation of Pareto Sets Using Directed Joint Contour Nets
Flexible Fiber Surfaces: A Reeb-Free Approach
Topological Subdivision Graphs for Comparative and Multifield Visualization
Interpreting Galilean Invariant Vector Field Analysis via Extended Robustness
Maximum Number of Transition Points in 3D Linear Symmetric Tensor Fields
Discrete Poincaré Duality Angles as Shape Signatures on Simplicial Surfaces with Boundary