Topological methods in data analysis and visualization : theory, algorithms, and applications

著者

書誌事項

Topological methods in data analysis and visualization : theory, algorithms, and applications

edited by Valerio Pascucci ... [et al.]

（Mathematics and visualization）

Springer, c2011-

  • [I] : hbk
  • II
  • III
  • IV

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注記

Editors of II: Ronald Peikert ... [et al.], III: Peer-Timo Bremer ... [et al.], IV: Hamish Carr, Christoph Garth, Tino Weinkauf

[I]: viii, 260 p., II: xi, 299 p., III: x, 279 p, IV: xi, 363 p

[I]: "with 146 figures, 122 in color", III: "with 98 figures, 69 in color"

Includes bibliographical references and index

内容説明・目次

巻冊次

III ISBN 9783319040981

内容説明

This collection of peer-reviewed conference papers provides comprehensive coverage of cutting-edge research in 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 volume also features material on core research challenges such as the representation of large and complex datasets and integrating numerical methods with robust combinatorial algorithms. Reflecting the focus of the TopoInVis 2013 conference, the contributions evince the progress currently being made on finding experimental solutions to open problems in the sector. They provide an inclusive snapshot of state-of-the-art research that enables researchers to keep abreast of the latest developments and provides a foundation for future progress. With papers by some of the world's leading experts in topological techniques, this volume is a major contribution to the literature in a field of growing importance with applications in disciplines that range from engineering to medicine.

目次

Part I Robust Topological Analysis: 1 Robust Detection of Singularities in Vector Fields: H. Bhatia, A. Gyulassy, H. Wang, P.-T. Bremer and V. Pascucci.- 2 Interpreting Feature Tracking Through the Lens of Robustness: P. Skraba and B. Wang.- 3 Simplification of Morse Decompositions using Morse Set Mergers: L. Sipeki and A. Szymczak.- 4 Toward the Extraction of Saddle Periodic Orbits: J. Kasten, J. Reininghaus, W. Reich and G. Scheuermann.- Part II Efficient Computation of Topology.- 5 Computational Topology via Functional Programming: A Baseline Analysis: D. Duke and H. Carr.- 6 Distributed Contour Trees: D. Morozov and G.H. Weber.- 7 Clear and Compress: Computing Persistent Homology in Chunks: M. Kerber, J. Reininghaus and U. Bauer.- 8 Parallel Computation of Nearly Recurrent Components of Piecewise Constant Vector Fields: N. Brunhart-Lupo and A. Szymczak.- Part III Simplification, Approximation and Distance Measures.- 9 Notes on the Simplification of the Morse-Smale Complex: D. Gunther, J. Reininghaus, H.-P. Seidel and T. Weinkauf.- 10 Measuring The Distance Between Merge Trees: K. Beketayev, D. Yeliussizov, D. Morozov, G.H. Weber and B. Hamann.- 11 Topological Integrity for Dynamic Spline Models During Visualization of Big Data: H. P. Cassidy, Th. J. Peters, H. Ilies and K.E. Jordan.- Part IV Time-Dependent Analysis: 12 A Comparison of Finite-Time and Finite-Size Lyapunov Exponents: R. Peikert, A. Pobitzer, F. Sadlo and B. Schindler.- 13 Development of an efficient and flexible pipeline for Lagrangian coherent structure computation: S. Ameli, Y. Desai and S. Shadden.- 14 Topological Features in Time-Dependent Advection-Diffusion Flow: F. Sadlo, G. Karch and Th. Ertl.- Part V Applications: 15 Definition, Extraction, and Validation of Pore Structures in Porous Media: U. Homberg, D. Baum, A. Wiebel, S. Prohaska and H.- Ch. Hege.- 16 Visualization of Two-Dimensional Symmetric Positive Definite Tensor Fields Using the Heat Kernel: V. Zobel, J. Reininghaus and I. Hotz.- 17 Topological Features in Glyph-Based Corotation Visualization: S. Shafii, H. Obermaier, B. Hamann and K. Joy.
巻冊次

IV ISBN 9783319446820

内容説明

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.

目次

Part 1: Topology-Based Analysis of Multi-Variate Data Sets: Theory of Singular Fibers and Reeb Spaces for Visualization: O. Saeki.- Topology-Based Analysis for Multimodal Atmospheric Data of Volcano Eruptions: A. Kuhn, W. Engelke, M. Flatken, F. Chen, H.-C. Hege, I. Hotz.- A Comparison of Joint Contour Nets and Pareto Sets: L. Huettenberger, C. Heine, C. Garth.- Part 2: Topological Techniques for High-Dimensional Data: Visualizing Topological Properties of the Search Landscape of Combinatorial Optimization Problems: S. Volke, D. Zeckzer, M. Middendorf, G. Scheuermann.- Computing and Visualizing Time-Varying Merge Trees for High-Dimensional Data: P. Oesterling, C. Heine, G. H. Weber, D. Morozov, G. Scheuermann.- Agreement analysis of quality measures for dimensionality reduction: B. Rieck, H. Leitte.- Part 3: Scalar Field Topology: Fast Similarity Search in Scalar Fields Using Merging Histograms: H. Saikia, H.-P. Seidel, T. Weinkauf.- Morse-Smale Analysis of Ion Diffusion in Ab Initio Battery Materials Simulations: A. Gyulassy, A. Knoll, P.-T. Bremer, B. Wang, K. Chun Lau, M. E. Papka, V. Pascucci, L. Curtiss.- Piecewise Polynomial Reconstruction of Scalar Fields from Simplified Morse-Smale Complexes: L. Allemand-Giorgis, G.-P. Bonneau, S. Hahmann.- Part 4: Vector & Tensor Field Topology: Topological Extraction of Escape Maps in Divergence-Free Vector Fields: R. Peikert, G. Machado, F. Sadlo.- Compute and Visualize Discontinuity Among Neighboring Integral Curves of 2D Vector Fields: L. Zhang, R. Laramee, D. Thompson, A. Sescu, G. Chen.- Decomposition of Vector Fields Beyond Problems of First Order and Their Applications: W. Reich, M. Hlawitschka, G. Scheuermann.- Maximum Number of Degenerate Curves in 3D Linear Tensor Fields: Y. Zhang, Y.-J. Tzeng, E. Zhang.- Part 5: Coherent Structures: Hierarchical Watershed Ridges for Visualizing Lagrangian Coherent Structures: M. Chen, J. C. Hart, S. C. Shadden.- Finite Time Steady 2D Vector Field Topology: A. Friederici, C. Roessl, H. Theisel.- Comparing Finite-Time Lyapunov Exponents in Approximated Vector Fields: S. Koch, S. Volke, G. Scheuermann, H. Hagen, M. Hlawitschka.- Transfer Operator-Based Extraction of Coherent Features on Surfaces: K. Padberg-Gehle, S. Reuther, S. Praetorius, A. Voigt.- Part 6: Software and Algorithms: ADAPT - Adaptive Thresholds for Feature Extraction: P.-T. Bremer.- Efficient Software for Programmable Visual Analysis Using Morse-Smale Complexes: N. Shivashankar, V. Natarajan.- Notes on the Distributed Computation of Merge Trees on CW-Complexes: A. Landge, P.-T. Bremer, A. Gyulassy, V. Pascucci.- Computing Invariants of Knotted Graphs Given by Sequences of Points in 3-Dimensional Space: V. Kurlin.
巻冊次

[I] : hbk ISBN 9783642150135

内容説明

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 of large and complex datasets, the characterization of noise and uncertainty, the effective integration of numerical methods with robust combinatorial algorithms, etc. . 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. This book contains the best 20 peer-reviewed papers resulting from the discussions and presentations at the third workshop on "Topological Methods in Data Analysis and Visualization", held 2009 in Snowbird, Utah, US. The 2009 "TopoInVis" workshop follows the two successful workshops in 2005 (Slovakia) and 2007 (Germany).

目次

Foundations of Computational Topology.- Hierarchical Topological Data-Structures.- Topological Feature Extraction Algorithms.- Applications in Scientific Data Analysis and Visualization.- Topological Analysis of Large-Scale Scientific Data.- Indices.
巻冊次

II ISBN 9783642231742

内容説明

When scientists analyze datasets in a search for underlying phenomena, patterns or causal factors, their first step is often an automatic or semi-automatic search for structures in the data. Of these feature-extraction methods, topological ones stand out due to their solid mathematical foundation. Topologically defined structures-as found in scalar, vector and tensor fields-have proven their merit in a wide range of scientific domains, and scientists have found them to be revealing in subjects such as physics, engineering, and medicine. Full of state-of-the-art research and contemporary hot topics in the subject, this volume is a selection of peer-reviewed papers originally presented at the fourth Workshop on Topology-Based Methods in Data Analysis and Visualization, TopoInVis 2011, held in Zurich, Switzerland. The workshop brought together many of the leading lights in the field for a mixture of formal presentations and discussion. One topic currently generating a great deal of interest, and explored in several chapters here, is the search for topological structures in time-dependent flows, and their relationship with Lagrangian coherent structures. Contributors also focus on discrete topologies of scalar and vector fields, and on persistence-based simplification, among other issues of note. The new research results included in this volume relate to all three key areas in data analysis-theory, algorithms and applications.

目次

Part I: Discrete Morse Theory.- Part II: Hierarchical Methods for Extracting and Visualizing Topological Structures.- Part III: Visualization of Dynamical Systems, Vector and Tensor Fields.- Part IV: Topological Visualization of Unsteady Flow.

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