Topological Analysis

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S. Bachthaler, F. Sadlo, C. Dachsbacher, D. Weiskopf:

Space-Time Visualization of Dynamics in Lagrangian Coherent Structures of Time-Dependent 2D Vector Fields

In Proceedings of International Conference on Information Visualization Theory and Applications (IVAPP), pp. 573–583, 2012.

Abstract

Lagrangian coherent structures (LCS), apparent as ridges in the finite-time Lyapunov exponent (FTLE) field, represent a time-dependent alternative to the concept of separatrices in vector field topology. Traditionally, LCS are analyzed and visualized in terms of their geometric shape only, neglecting stretching and compression in tangent directions. These effects are, however, of particular interest in mixing phenomena and turbulence. Hyperbolicity plays an important role in these processes and gives rise to hyperbolic trajectories originating at the intersections of forward and reverse LCS. Since integration of hyperbolic trajectories is difficult, we propose to visualize the corresponding space-time intersection curves of LCS instead. By stacking the traditional 2D FTLE video frames of time-dependent vector fields, a space-time FTLE field is obtained. In this field, ridge lines turn into ridge surfaces representing LCS, and their intersection forms curves that are a robust alternative to hyperbolic trajectories. Additionally, we use a space-time representation of the time-dependent vector field, leading to a steady 3D space-time vector field. In this field, the LCS become stream surfaces given that their advection property is sufficiently met. This makes visualization of the dynamics within LCS amenable to line integral convolution (LIC), conveying in particular the dynamics around hyperbolic trajectories. To avoid occlusion, the LCS can be constrained to space-time bands around the intersection curves, resembling visualization by saddle connectors. We evaluate our approach using synthetic, simulated, and measured vector fields.

Available Files

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Publications

To Appear
Reviewed Conference Papers
B. Rieck, M. Banagl, F. Sadlo, H. Leitte:
Persistent Intersection Homology for the Analysis of Discrete Data
In Topological Methods in Data Analysis and Visualization V, Springer International Publishing, to appear.
Available files: [BibTeX]

B. Rieck, F. Sadlo, H. Leitte:
Topological Machine Learning with Persistence Indicator Functions
In Topological Methods in Data Analysis and Visualization V, Springer International Publishing, to appear.
Available files: [BibTeX]

B. Rieck, F. Sadlo, H. Leitte:
Hierarchies and Ranks for Persistence Pairs
In Topological Methods in Data Analysis and Visualization V, Springer International Publishing, to appear.
Available files: [BibTeX]

B. Rieck, F. Sadlo, H. Leitte:
Persistence Concepts for 2D Skeleton Evolution Analysis
In Topological Methods in Data Analysis and Visualization V, Springer International Publishing, to appear.
Available files: [BibTeX]

2018
Reviewed Journal Papers
L. Hofmann, B. Rieck, F. Sadlo:
Visualization of 4D Vector Field Topology
Computer Graphics Forum, vol. 37, no. 3, pp. 301–313, 2018.
Available files: [BibTeX] [DOI] [PDF] [Highres PDF] [Video] [Video] [Slides] [Details]

B. Rieck, U. Fugacci, J. Lukasczyk, H. Leitte:
Clique Community Persistence: A Topological Visual Analysis Approach for Complex Networks
IEEE Transactions on Visualization and Computer Graphics, vol. 24, no. 1, pp. 822–831, 2018.
Available files: [BibTeX] [DOI] [PDF] [Details]

Reviewed Conference Papers
K. Hanser, O. Klein, B. Rieck, B. Wiebe, T. Selz, M. Piatkowski, A. Sagristà, B. Zheng, M. Lukácová, G. Craig, H. Leitte, F. Sadlo:
Visualization of Parameter Sensitivity of 2D Time-Dependent Flow
In Lecture Notes in Computer Science: Advances in Visual Computing (Proceedings of International Symposium on Visual Computing), pp. 359–370, 2018.
Available files: [BibTeX] [DOI] [PDF] [Highres PDF] [Slides] [Details]

2017
Reviewed Journal Papers
A. Sagristà, S. Jordan, A. Just, F. Dias, L. G. Nonato, F. Sadlo:
Topological Analysis of Inertial Dynamics
IEEE Transactions on Visualization and Computer Graphics, vol. 23, no. 1, pp. 950–959, 2017.
Available files: [BibTeX] [DOI] [PDF] [Highres PDF] [Technical Addendum] [Video] [Details]

Reviewed Conference Papers
R. Peikert, G. M. Machado, F. Sadlo:
Topological Extraction of Escape Maps in Divergence-Free Vector Fields
In Topological Methods in Data Analysis and Visualization IV, Springer International Publishing, pp. 171–186, 2017.
Available files: [BibTeX] [DOI] [Details]

2016
Reviewed Journal Papers
G. M. Machado, S. Boblest, T. Ertl, F. Sadlo:
Space-Time Bifurcation Lines for Extraction of 2D Lagrangian Coherent Structures
Computer Graphics Forum, vol. 35, no. 3, pp. 91–100, 2016.
Available files: [BibTeX] [DOI] [PDF] [Details]

B. Rieck, H. Leitte:
Exploring and Comparing Clusterings of Multivariate Data Sets Using Persistent Homology
Computer Graphics Forum, vol. 35, no. 3, pp. 81–90, 2016.
Available files: [BibTeX] [DOI] [PDF]

Reviewed Conference Papers
B. Rieck, H. Leitte:
Shall I compare thee to a network? -- Visualizing the Topological Structure of Shakespeare's Plays
In Proceedings of Workshop on Visualization for the Digital Humanities at IEEE VIS, 2016.
Available files: [BibTeX] [DOI] [PDF]

2015
Reviewed Journal Papers
T. Müller, F. Sadlo:
Visual Exploration of 2D Autonomous Dynamical Systems
European Journal of Physics, vol. 36, no. 3, pp. 035007, 2015.
Available files: [BibTeX] [DOI] [Details]

Reviewed Conference Papers
F. Sadlo:
Lyapunov Time for 2D Lagrangian Visualization
In Topological and Statistical Methods for Complex Data, Springer Berlin Heidelberg, pp. 167–181, 2015.
Available files: [BibTeX] [DOI] [PDF] [Details]

2014
Reviewed Journal Papers
G. M. Machado, F. Sadlo, T. Müller, T. Ertl:
Escape Maps
IEEE Transactions on Visualization and Computer Graphics, vol. 20, no. 12, pp. 2604–2613, 2014.
Available files: [BibTeX] [DOI] [PDF] [Highres PDF] [Details]

Reviewed Conference Papers
R. Peikert, A. Pobitzer, F. Sadlo, B. Schindler:
A Comparison of Finite-Time and Finite-Size Lyapunov Exponents
In Topological Methods in Data Analysis and Visualization III, Springer International Publishing, pp. 187–200, 2014.
Available files: [BibTeX] [DOI] [PDF] [Details]

B. Rieck, H. Leitte:
Enhancing Comparative Model Analysis Using Persistent Homology
In Proceedings of Workshop on Visualization for Predictive Analytics at IEEE VIS, 2014.
Available files: [BibTeX] [PDF]

F. Sadlo, G. K. Karch, T. Ertl:
Topological Features in Time-Dependent Advection-Diffusion Flow
In Topological Methods in Data Analysis and Visualization III, Springer International Publishing, pp. 217–231, 2014.
Available files: [BibTeX] [DOI] [PDF] [Details]

2013
Reviewed Journal Papers
M. Üffinger, F. Sadlo, T. Ertl:
A Time-Dependent Vector Field Topology Based on Streak Surfaces
IEEE Transactions on Visualization and Computer Graphics, vol. 19, no. 3, pp. 379–392, 2013.
Available files: [BibTeX] [DOI] [PDF] [Video] [Video] [Details]

M. Hlawatsch, F. Sadlo, D. Weiskopf:
Predictability-Based Adaptive Mouse Interaction and Zooming for Visual Flow Exploration
International Journal for Uncertainty Quantification, vol. 3, no. 3, pp. 225–240, 2013.
Available files: [BibTeX] [DOI] [PDF] [Details]

Reviewed Conference Papers
G. M. Machado, F. Sadlo, T. Ertl:
Local Extraction of Bifurcation Lines
In Proceedings of International Workshop on Vision, Modeling and Visualization (VMV), pp. 17–24, 2013.
Available files: [BibTeX] [DOI] [PDF] [Details]

F. Sadlo, S. Bachthaler, C. Dachsbacher, D. Weiskopf:
Space-Time Flow Visualization of Dynamics in 2D Lagrangian Coherent Structures
In Computer Vision, Imaging and Computer Graphics. Theory and Application, Springer Berlin Heidelberg, pp. 145–159, 2013.
Available files: [BibTeX] [DOI] [Details]

2012
Reviewed Journal Papers
S. Bachthaler, F. Sadlo, R. Weeber, S. Kantorovich, C. Holm, D. Weiskopf:
Magnetic Flux Topology of 2D Point Dipoles
Computer Graphics Forum, vol. 31, no. 3, pp. 955–964, 2012.
Available files: [BibTeX] [DOI] [PDF] [Details]

B. Rieck, H. Mara, H. Leitte:
Multivariate Data Analysis Using Persistence-based Filtering and Topological Signatures
IEEE Transactions on Visualization and Computer Graphics, vol. 18, no. 12, pp. 2382–2391, 2012.
Available files: [BibTeX] [DOI] [PDF]

Reviewed Conference Papers
M. Üffinger, F. Sadlo, M. Kirby, C. Hansen, T. Ertl:
FTLE Computation Beyond First-Order Approximation
In Short Paper Proceedings of Eurographics 2012, pp. 61–64, 2012.
Available files: [BibTeX] [DOI] [PDF] [Details]

S. Bachthaler, F. Sadlo, C. Dachsbacher, D. Weiskopf:
Space-Time Visualization of Dynamics in Lagrangian Coherent Structures of Time-Dependent 2D Vector Fields
In Proceedings of International Conference on Information Visualization Theory and Applications (IVAPP), pp. 573–583, 2012.
Available files: [BibTeX] [PDF] [Details]

A. Panagiotidis, D. Kauker, F. Sadlo, T. Ertl:
Distributed Computation and Large-Scale Visualization in Heterogeneous Compute Environments
In Proceedings of 11th International Symposium on Parallel and Distributed Computing (ISPDC), pp. 87–94, 2012.
Available files: [BibTeX] [DOI] [Details]

F. Sadlo, M. Üffinger, T. Ertl, D. Weiskopf:
On the Finite-Time Scope for Computing Lagrangian Coherent Structures from Lyapunov Exponents
In Topological Methods in Data Analysis and Visualization II, Springer Berlin Heidelberg, pp. 269–281, 2012.
Available files: [BibTeX] [DOI] [PDF] [Slides] [Details]

2011
Reviewed Journal Papers
M. Hlawatsch, J. Vollrath, F. Sadlo, D. Weiskopf:
Coherent Structures of Characteristic Curves in Symmetric Second Order Tensor Fields
IEEE Transactions on Visualization and Computer Graphics, vol. 17, no. 6, pp. 781–794, 2011.
Available files: [BibTeX] [DOI] [PDF] [Details]

Reviewed Conference Papers
M. Ament, S. Frey, F. Sadlo, T. Ertl, D. Weiskopf:
GPU-Based Two-Dimensional Flow Simulation Steering using Coherent Structures
In Proceedings of the Second International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering, 2011.
Available files: [BibTeX] [DOI] [PDF]

F. Sadlo, A. Rigazzi, R. Peikert:
Time-Dependent Visualization of Lagrangian Coherent Structures by Grid Advection
In Topological Methods in Data Analysis and Visualization, Springer Berlin Heidelberg, pp. 151–165, 2011.
Available files: [BibTeX] [DOI] [PDF] [Slides] [Details]

2010
Reviewed Journal Papers
R. Fuchs, J. Kemmler, B. Schindler, J. Waser, F. Sadlo, H. Hauser, R. Peikert:
Toward a Lagrangian Vector Field Topology
Computer Graphics Forum, vol. 29, no. 3, pp. 1163–1172, 2010.
Available files: [BibTeX] [DOI] [PDF] [Details]

R. Peikert, F. Sadlo:
A Robust Stream Surface Method for the Visualization of Vector Field Singularities
Computer Graphics and Geometry, vol. 12, no. 2, pp. 2–13, 2010.
Available files: [BibTeX] [URL]

F. Sadlo, D. Weiskopf:
Time-Dependent 2-D Vector Field Topology: An Approach Inspired by Lagrangian Coherent Structures
Computer Graphics Forum, vol. 29, no. 1, pp. 88–100, 2010.
Available files: [BibTeX] [DOI] [PDF] [Slides] [Details]

Conference Papers with Reviewed Abstract
M. Falk, A. Seizinger, M. Üffinger, F. Sadlo, D. Weiskopf:
Trajectory-Augmented Visualization of Lagrangian Coherent Structures in Unsteady Flow
In Proceedings of International Symposium on Flow Visualization (ISFV14), 2010.
Available files: [BibTeX] [PDF]

2009
Reviewed Conference Papers
R. Peikert, F. Sadlo:
Flow Topology Beyond Skeletons: Visualization of Features in Recirculating Flow
In Topology-Based Methods in Visualization II, Springer Berlin Heidelberg, pp. 145–160, 2009.
Available files: [BibTeX] [DOI] [PDF] [Details]

R. Peikert, F. Sadlo:
Topologically Relevant Stream Surfaces for Flow Visualization
In Proceedings of 2009 Spring Conference on Computer Graphics, pp. 35–42, 2009.
Available files: [BibTeX] [DOI] [PDF] [Details]

F. Sadlo, R. Peikert:
Visualizing Lagrangian Coherent Structures and Comparison to Vector Field Topology
In Topology-Based Methods in Visualization II, Springer Berlin Heidelberg, pp. 15–29, 2009.
Available files: [BibTeX] [DOI] [PDF] [Details]

2007
Reviewed Journal Papers
F. Sadlo, R. Peikert:
Efficient Visualization of Lagrangian Coherent Structures by Filtered AMR Ridge Extraction
IEEE Transactions on Visualization and Computer Graphics, vol. 13, no. 6, pp. 1456–1463, 2007.
Available files: [BibTeX] [DOI] [PDF] [Video] [Video] [Video] [Slides] [Details]

Reviewed Conference Papers
R. Peikert, F. Sadlo:
Topology-guided Visualization of Constrained Vector Fields
In Topology-Based Methods in Visualization, Springer Berlin Heidelberg, pp. 21–33, 2007.
Available files: [BibTeX] [DOI] [PDF] [Details]

Theses

2017
B. Rieck:
Persistent Homology in Multivariate Data Visualization
, Heidelberg University, 2017.
Available files: [BibTeX] [DOI] [PDF] [Details]