Topological Data Analysis for Scientific Visualization

✍ Scribed by Julien Tierny

• Publisher: Springer
• Year: 2018
• Tongue: English
• Leaves: 158
• Edition: 1st ed. 2017
• Category: Library

✦ Table of Contents

Content: Intro
Preface
Acknowledgements
Contents
Notations
1 Introduction
2 Background
2.1 Data Representation
2.1.1 Domain Representation
Preliminary Notions
Domain Formalization
Topological Invariants
2.1.2 Range Representation
Piecewise Linear Scalar Fields
Related Geometrical Constructions
2.2 Topological Abstractions
2.2.1 Critical Points
2.2.2 Notions of Persistent Homology
2.2.3 Reeb Graph
2.2.4 Morse-Smale Complex
2.3 Algorithms and Applications
2.3.1 Persistent Homology
2.3.2 Reeb Graph
2.3.3 Morse-Smale Complex
3 Abstraction. 3.1 Efficient Topological Simplification of Scalar Fields3.1.1 Preliminaries
General Simplification of Scalar Fields on Surfaces
Closed Surfaces
Surfaces with Boundary
Surface Scalar Field Constrained Topology
Minima
Regular Vertices
Interior Saddles
Boundary Saddles
Maximum
3.1.2 Algorithm
Algorithm Description
Sub-level Set Constrained Reconstruction
Sur-level Set Constrained Reconstruction
Overall Algorithm
Convergence
From Symbolic to Numerical Perturbation
Algorithm Properties
3.1.3 Results and Discussion
Time Requirement
Discussion
Limitations
Application. Concluding Remarks3.2 Efficient Reeb Graph Computation for Volumetric Meshes
3.2.1 Preliminaries
Loops in Reeb Graphs on PL 3-Manifolds in R3
Loop Surgery
Loop Free Reeb Graph Computation
3.2.2 Algorithm
Loop Surgery
Genus Diagnostic
Loop Saddles
Cutting Surfaces
Loop Free Reeb Graph Computation
Inverse Cuts
3.2.3 Results and Discussion
Time Complexity
Performance Comparison
Asymptotic Stress Tests
Limitations
Concluding Remarks
4 Interaction
4.1 Topological Simplification of Isosurfaces
4.2 Interactive Editing of Topological Abstractions
4.2.1 Morse-Smale Complex Editing. Conforming Discrete GradientAlgorithm
Editable Morse-Smale Complexes
Identity Map
Termination Map
Boundary Map
User Edits
A Histological Example
Concluding Remarks
4.2.2 Reeb Graph Editing
Harmonic Scalar Fields
Reeb-Graph Based Surface Segmentation and Parameterization
Editing Operations
Chart Boundary
Chart Number
Chart Corners
Preliminary Results
Concluding Remarks
5 Analysis
5.1 Exploration of Turbulent Combustion Simulations
5.1.1 Applicative Problem
5.1.2 Algorithm
Data Segmentation
Feature Tracking
Tracking Graph Simplification
5.1.3 Results. Interactive Exploration InterfaceQuantitative Analysis
Concluding Remarks
5.2 Quantitative Analysis of Molecular Interactions
5.2.1 Applicative Problem
Interactions in Molecular Systems
Input Data
5.2.2 Algorithm
Feature Definition
Technical Challenges
Interaction Sites
Bonding Graph
Repulsive Bond-Cycles
5.2.3 Results
Validation
Quantitative Analysis and Visual Exploration
Concluding Remarks
6 Perspectives
6.1 Emerging Constraints
6.1.1 Hardware Constraints
Preliminary Results
6.1.2 Software Constraints
Research Directions
6.1.3 Exploration Constraints.

✦ Subjects

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