Topological methods in data analysis and visualization . VI Theory, applications, and software / / Ingrid Hotz [and three others] editors

• Pubblicazione: Cham, Switzerland : , : Springer, , [2021]; ©2021
• Descrizione fisica: 1 online resource (372 pages)
• Disciplina: 514
• Soggetto topico: Topology; Mathematical analysis; Information visualization; Topologia; Anàlisi matemàtica; Visualització de la informació
• Soggetto genere / forma: Congressos; Llibres electrònics
• Persona (resp. second.): HotzIngrid
• Nota di contenuto: Intro -- Preface -- Contents -- Part I: Scalar Field Topology - Algorithms and Applications -- W-Structures in Contour Trees -- 1 Introduction -- 2 Background -- 2.1 Contour Trees -- 2.2 Contour Tree Algorithms -- 2.3 Contour Tree Simplification -- 3 W-Structures in Contour Trees -- 3.1 Spatial Characterization -- 3.2 W-Diameter Algorithms -- 3.3 Algorithm 1-Multi BFS -- 3.4 Algorithm 2-Double BFS -- 3.5 Algorithm 3-Dynamic -- 4 Empirical Study -- 4.1 Results -- 5 W-Structure Simplification -- 5.1 Persistent Homology Overview -- 5.2 Comparison of Critical Point Pairs -- 6 Conclusion -- References -- Mergemaps: Treemaps for Scientific Data -- 1 Introduction -- 1.1 Related Work -- 1.2 Summary of Results -- 2 Background -- 2.1 Merge Tree -- 2.2 Treemap -- 3 Mergemap -- 3.1 Motivation -- 3.2 Algorithm -- 3.3 Interaction -- 3.4 Operations -- 3.5 Area Distortion -- 4 Case Studies -- 4.1 Ethane-1,2-diol -- 4.2 Fuel -- 4.3 Silicium -- 4.4 von K225rm225n Street -- 5 Conclusions -- References -- Notes on Percolation Analysis of Sampled Scalar Fields -- 1 Introduction -- 2 Related Work and Background -- 3 From Infinite to Finite -- 3.1 The Extremes of the Value Range -- 3.2 Histogram Distribution -- 4 Analysis and Visualization of Percolation Curve Ensembles -- 4.1 Analysis of a Single Percolation Curve -- 4.2 Analysis of Percolation Curve Ensembles -- 5 Experiments -- 5.1 Randomness and Structure: Gaussian Random Fields -- 5.2 Turbulent Flow: Duct Data Set -- 6 Conclusions and Future Work -- References -- Distributed Task-Parallel Topology-Controlled Volume Rendering -- 1 Introduction -- 2 Related Work -- 3 System Design -- 4 Implementation -- 4.1 Merge -- 4.2 Simplify -- 4.3 Update -- 4.4 Branch Decomposition Assembly -- 4.5 Transfer Function Assignment -- 4.6 Rendering -- 5 Results -- 5.1 Experimental Design -- 5.2 General Observations. ; 5.3 Algorithm Validation -- 5.4 Strong Scaling -- 5.5 Weak Scaling -- 6 Conclusion -- References -- Topology-Based Feature Design and Tracking for Multi-center Cyclones -- 1 Introduction -- 2 Background -- 3 Full Tracking Graph Computation -- 4 Feature Definition and Tracking of Cyclonic Systems -- 5 Implementation Details -- 6 Case Study -- 7 Conclusion and Discussion -- References -- Using Contour Trees in the Analysis and Visualization of Radio Astronomy Data Cubes -- 1 Introduction -- 2 Science Case -- 3 Technical Background -- 4 Application Development Process -- 4.1 Designing to Serve the ALMA Community -- 5 Software Design -- 5.1 Visual Elements -- 5.2 Interaction Process -- 6 Case Studies -- 6.1 Ghost of Mirach Galaxy Data Set -- 6.2 CMZ Data Set -- 7 Discussion -- References -- Part II: Topological Methods in Complex Fields - Flow Fields, Tensor Fields, and Multi-fields -- Objective Finite-Time Flow Topology from Flowmap Expansion and Contraction -- 1 Introduction -- 2 Related Work -- 2.1 Classic Steady Vector Field Topology -- 2.2 Streamlines vs. Pathlines -- 2.3 Reference Frames -- 2.4 Lagrangian Coherent Structures -- 2.5 Time-Dependent Saddles -- 3 Intuitive Approach -- 4 Theory -- 4.1 Mathematical Definition -- 4.2 Relation to the Lagrangian Definition -- 4.3 Objectivity -- 4.4 Linear Approximation -- 4.5 Strength -- 4.6 Weighting Related to FTLE -- 4.7 Separatrices -- 5 Experiments -- 6 Discussion -- 7 Conclusion -- References -- Coreline Criteria for Inertial Particle Motion -- 1 Introduction -- 2 Related Work -- 2.1 Galilean Invariance -- 2.2 Inertial Particle Motion -- 2.3 Vortex Corelines of Massless Flows -- 2.4 Vortex Corelines of Inertial Particles -- 3 Vortex Coreline Criteria for Inertial Particles -- 3.1 Generalized Inertial Particle Motion -- 3.2 Inertial Motion in Steady Frame -- 3.3 First-Order Corelines. ; 3.4 Second-Order Corelines -- 4 Implementation -- 5 Results -- 5.1 Comparison of Inertial Particle Parameters -- 5.2 Comparison of Inertial Particle Models -- 5.3 Second-Order Corelines in 3D -- 5.4 Memory Consumption and Performance -- 5.5 Discussion -- 6 Conclusion -- Appendix 1 - Derivation of First-order 3D Criterion -- Appendix 2 - Tracer Particles as Limit Case -- References -- Implicit Visualization of 2D Vector Field Topology for Periodic Orbit Detection -- 1 Introduction -- 2 Related Work -- 3 Motivation -- 4 Method -- 5 Algorithm -- 5.1 Integration -- 5.2 Refinement -- 5.3 Implementation -- 6 Results -- 6.1 Rotated Flow -- 6.2 Buoyant Flow -- 6.3 Buoyant Flow II -- 6.4 Discussion -- 7 Conclusion -- References -- Visually Evaluating the Topological Equivalence of Bounded Bivariate Fields -- 1 Introduction -- 2 Related Work in Visualization -- 3 Set-Up -- 3.1 The mathcalB+-Equivalence and Fiber Topology -- 3.2 Invariants -- 4 Reeb Space Visualization and Computation -- 4.1 Visualization -- 4.2 Computation -- 5 Invariants for Bounded Map Germs -- 6 Outcome -- 6.1 Comparing Forms of Equivalence Through Visual Investigation -- 6.2 Germs of Corank 2 -- 7 Discussion -- 8 Conclusion -- References -- Topological Feature Search in Time-Varying Multifield Data -- 1 Introduction -- 2 Related Work -- 3 Background -- 3.1 Histogram and Isosurface Statistics, Continuous Scatter Plot -- 3.2 Multifield Topology and Jacobi Set -- 3.3 Reeb Space and Joint Contour Net -- 3.4 Histogram Distance Measures -- 4 Our Method -- 4.1 Fiber-Component Distribution over the Range Space -- 4.2 Distance Between Two Fiber-Component Distributions -- 4.3 Weighted Distance for the Singular Values -- 4.4 Metric Space Properties of the Distance Measures -- 5 Implementation -- 6 Applications -- 6.1 Synthetic Data -- 6.2 Plutonium Atom Dataset -- 6.3 Fermium Atom Dataset. ; 6.4 Chemistry Data: Pt-CO Bond -- 7 Single Scalar Field vs. Multifield -- 8 Conclusions and Future Work -- References -- Tensor Fields for Data Extraction from Chart Images: Bar Charts and Scatter Plots -- 1 Introduction -- 2 Related Work -- 3 Background on Local Geometric Descriptors -- 4 Our Proposed Method -- 5 Experiments and Results -- 6 Conclusions -- References -- Part III: Topology for Geometric Data -- A Fast Approximate Skeleton with Guarantees for Any Cloud of Points in a Euclidean Space -- 1 Introduction: Reconstructions from Unorganized Clouds -- 2 Basic Definitions and a Review of the Related Past Work -- 3 A New Tree core(C) Defined for Any Point Cloud CsubsetmathbbRm -- 4 ASk(C): Approximate Skeleton of a Cloud CsubsetmathbbRm -- 5 Comparisons of Five Algorithms on Real and Synthetic Data -- 6 Conclusions and a Discussion of the Approximate Skeleton -- References -- Topologically Robust B-spline Reconstruction of Fibers from 3D Images -- 1 Introduction -- 2 Related Work -- 3 Pipeline -- 4 B-Spline Approximation -- 4.1 B-Spline Surface Notation -- 4.2 Single B-Spline Surface Approximation -- 4.3 Constructing a Continuous Surface Model -- 5 Results -- 6 Conclusions -- References -- Part IV: Overview Articles, Software and Viewpoints -- Introduction to Vector Field Topology -- 1 Introduction -- 2 Steady Vector Fields -- 2.1 Two-Dimensional Flows -- 2.2 Three-Dimensional Flows -- 2.3 Remarks -- 3 Unsteady Flows -- 3.1 Streamline-Oriented Topology -- 3.2 Pathline-Oriented Topology -- 4 Concepts -- 4.1 Reference Frame Transformation -- 4.2 Reference Frame Invariance -- 4.3 Topology in Steady Reference Frames -- 4.4 High-Dimensional Flows -- 4.5 Uncertainty -- 5 Outlook -- References -- An Overview of the Topology ToolKit -- 1 Introduction -- 2 Scalar Data -- 3 Bivariate Scalar Data -- 4 Uncertain Scalar Data -- 5 Time-Varying Scalar Data. ; 6 High-Dimensional Point Cloud Data -- 7 In Situ Topological Analysis -- 8 Convenience -- 9 Conclusion and Perspectives -- References -- Implementing Persistence-Based Clustering of Point Clouds in the Topology ToolKit -- 1 Introduction -- 1.1 Contributions -- 2 Related Work -- 3 Software Design Overview -- 4 Computing Scalar Fields from Point Clouds -- 4.1 Parameter Setting -- 5 Persistence-Based Clustering -- 5.1 User Options -- 5.2 Automatic Parameter Setting -- 6 Experimental Results -- 6.1 Automatic Feature Detection -- 6.2 Comparison Against Other Clustering Methods -- 7 Discussion -- References -- Report of the TopoInVis TTK Hackathon: Experiences, Lessons Learned, and Perspectives -- 1 Introduction -- 2 Organization -- 2.1 Preparation -- 2.2 Program -- 3 Results -- 3.1 Packaging -- 3.2 Vector Field Robustness Module -- 3.3 Extending the Integration of TTK in Inviwo -- 3.4 Periodic Grids -- 4 Conclusion -- 4.1 Workgroup Results -- 4.2 Organizational Aspects -- 4.3 TTK Development Directions -- References.
• Titolo autorizzato: Topological methods in data analysis and visualization
• ISBN: 3-030-83500-6
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910502997603321
• Lo trovi qui: Univ. Federico II
• Serie: Mathematics and visualization.