META: Multifield Extension of Topological Analysis

Lead Research Organisation: University of Leeds
Department Name: Sch of Computing

Abstract

Physical scientists, engineers and clinicians rely on visualization to obtain insight into data arising from scans and simulation. Since the 1980s, when an influential US NSF report ushered in the use of graphics to make sense of large volumes of numerical data, visualization techniques have advanced in surges marked by major breakthroughs, including: "marching cubes" and its derivatives for interpreting scalar fields, volume rendering for inherently volumetric data; and vector field topology for understanding the structure of flow. However, existing visualization techniques are limited to individual properties of data, temperature, pressure, velocity, vorticity, shear, combustion rate, rainfall, and so on.

Techniques for multivariate (multifield) data do exist in information visualization, where parallel coordinates, spider plots etc are widely used. But these tools are of little use for scientific datasets, where the interpretation of data is intimately tied to physical space/time, or to the scale of scientific datasets, which is routinely measured in gigabytes or terabytes. The key problem is that, until now, we have lacked any suitable mathematical and computational model for multifield analysis. The mathematics is needed to explain what exactly it means to understand how multiple fields interact; the computational model is needed to explain how this interaction can be mapped into visual representations that can be generated efficiently from large volumes of data. Techniques for multifield analysis would be of enormous benefit right across the diverse range of application domains that rely on (scientific) visualization, including aerospace, materials engineering, climatology and meterology, astrophysics, radiology and surgical planning. It would enable new scientific insight, and provide industry with new tools through which to develop competitive advantage.

Recent work by the applicants has achieved a breakthrough result. The "Joint Contour Net" is a new abstraction that hold great promise in providing the mathematical and computational machinery needed for multifields. The origins of the JCN are in computational topology, a field that, over the last decade, has made major contributions to visualization through finding and explaining structure within data. Topology provides a rigorous foundation for identifying features and transitions within data, and these are of particular interest to end users in understanding the original problem. Topological models are also essential in simplifying and presenting massive datasets, as our ability to interpret data has to pass through the bottleneck of screen space (typically around 2M pixels) and the gigabyte limits of the human visual system. The Joint Contour Net provides a first glimpse of how to generalise topological analysis from one field to many fields, and importantly, how to do so efficiently, and in a way that accommodates parallelisation to scale up to processing massive datasets.

This proposal will deliver on the initial promise by developing the mathematical theory for multifield analysis, generating the and the visual abstractions needed to understand multifield behaviour. To achieve this, we will work closely with other international leaders in visualization and computational topology to address specific issues, such as simplification and rendering techniques based on JCNs, and user interfaces for steering analysis that are adapted to the needs of particular applications. To ensure the research has the maximum possible reach, we will embed our software into the most widely used visualization toolkits, with dedicated effort to ensure that the implementation is robust and maintainable, and courses to train end-users in its application.

Planned Impact

The proposed work will deliver a new technology for understanding data in the physical sciences, engineering and medicine. It will, finally, address a major shortcoming in visualization techniques, the limited tools available for analysing multiple fields of data. Such fields arise routinely in nearly every area where visualization is applied, for example:

* aerospace: interaction between pressure, temperature and vorticity of flows over airfoils and within turbine engines;
* material science:
* combustion studies: temperature, combustible material, and the density of by-products generated
* astrophysics: sky surveys typically acquire data across 50+ sensory channels
* climatology and meteorology: temperature, humidity, rainfall, gaseous species
* radiology and biomedical research: relationships between scanner modalities
* clinical medicine, for example surgical planning:

The impact of the research is therefore both broad and indirect; visualization tools are the "user interface" through which raw data from simulations and scanners is converted into insight. It is this insight that represents the ultimate value of the research, whether it be through basic scientific discovery, improved products such as aircraft engines or materials that give UK companies a competitive edge, or longer-term societal benefit resulting, for example, from: high-value manufacturing (improved engine design); better medical diagnosis, treatment and outcomes through the ability to resolve finer levels of detail and structure in radiological data; new insight into performance of low-carbon energy sources.

The project proposal has specific actions to deliver this impact:

* collaboration with leading international researchers who themselves work directly with industrial applications and research end-users;
* collaboration with the developers of the leading tools for scientific data visualization;
* ring-fenced effort for delivering robust software products into leading visualization packages;
* outreach programme of tutorials targeting three of the broader end-user communities;
* focused CPD training directed at UK end-users from industry and research laboratories.

Publications

10 25 50

publication icon
Carr H (2015) Fiber Surfaces: Generalizing Isosurfaces to Bivariate Data in Computer Graphics Forum

publication icon
Carr H (2014) Scientific Visualization

publication icon
Carr H (2014) Joint Contour Nets. in IEEE transactions on visualization and computer graphics

publication icon
Chattopadhyay A (2016) Multivariate topology simplification in Computational Geometry

publication icon
Duke D (2012) Visualizing Nuclear Scission through a Multifield Extension of Topological Analysis. in IEEE transactions on visualization and computer graphics

 
Description How to generalise from topological analysis of scalar (single-value) data to multivariate (multi-value) data in a computational setting, including computation of analytic structures, identification of features, hierarchical simplification to reduce minor features and noise, mapping to physical phenomena, and integration with existing mathematics of fiber topology.

Initial work was also supported on development of faster more scalable algorithms for existing methods.

An additional, unanticipated outcome was the discovery of the first geometric solution to visualising local variable relationships in spatial data.
Exploitation Route By further development of the existing findings to six- and seven- dimensional cases representing time-varying volumetric data, and to higher-dimensional parameter spaces. By development of application-specific tests for particular domain tasks.

Further development on scalability is necessary, and the impact of new visualisation techniques on bivariate data must be explored.
Sectors Aerospace, Defence and Marine,Energy,Environment

URL http://www.engineering.leeds.ac.uk/computing/research/cse/meta/
 
Description For analysis of nuclear scission, aiding in determining the transition between single and multiple nuclei, and triggering further developments in the understanding of the process of fission. For analysis of oceanographic data, exploring and understanding movement of cold saline water. For supporting the development of mathematical understanding of fiber topology. For analysis of time-varying radiological drift after Fukushima. For analysis of large-scale combustion simulations For analysis of chemical relationships
First Year Of Impact 2013
Sector Construction,Energy,Environment
Impact Types Societal

 
Description Collaboration - Kaiserslautern 
Organisation Technical University Kaiserslautern
Country Germany 
Sector Academic/University 
PI Contribution Collaboration with colleagues at Technical University of Kaiserslautern. One paper already resulted.
Collaborator Contribution Collaborative Research
Impact Hüttenberger L, Heine C, Carr H, Scheuermann G, Garth C, Towards Multifield Scalar Topology Based on Pareto Optimality, Computer Graphics Forum 32(3): 341-50, 2013. Garth C, Hüttenberger L, Heine C, Carr H, Scheuermann G, Multivariate Topological Features in Flow Visualization, Workshop on the Analysis of Large-Scale, High-dimensional and Multivariate data Using Topology and Statistics (Le Barp, France, June 12-14, 2013).
Start Year 2013
 
Description Collaboration - Lawrence Livermore 
Organisation Lawrence Livermore National Laboratory
Country United States 
Sector Public 
PI Contribution Collaboration with physicist at Lawrence Livermore. Collaboration with nuclear physicists on visualising nuclear scission. Other collaborators located at Argonne National Laboratory, Oak Ridge National Laboratory, and University Marie Curie-Sklodowska, Poland. One paper in Visualization already published. Two papers in physics in preparation to date.
Collaborator Contribution Application scientists at Livermore & elsewhere provided data & problem to study
Impact Schunck N, Duke DJ, Carr H, Knoll A, Description of induced nuclear fission with Skyrme energy functionals II: II. Finite temperature effects, Physical Review C 91.3: 034527 (2015). Schunck N, Duke DJ, Carr H, Knoll A, Description of induced nuclear fission with Skyrme energy functionals. I. Static potential energy surfaces and fission fragment properties, Physical Review C 90.5: 054305 (2014). Duke D, Carr H, Knoll A, Schunck N, Nam HA, Staszczak A, Visualizing Nuclear Scission Through a Multifield Extension of Topological Analysis, IEEE Transactions on Visualization and Computer Graphics, 18(12): 2033-40, 2012.
Start Year 2012
 
Description Collaboration - Los Alamos National Laboratory 
Organisation Lawrence Berkeley National Laboratory
Country United States 
Sector Public 
PI Contribution Massively Parallel Algorithms for Computational Topology
Collaborator Contribution Expertise in massively parallel algorithm development: datasets and systems for large-scale performance tests.
Impact H. Carr, C. Sewell, L.-T. Lo, and J. Ahrens. Hybrid data-parallel contour tree computation. Technical Report LA-UR-15-24579, Los Alamos National Laboratory, 2015. Carr H, Sewell C, Lo LT, Ahrens J. Hybrid data-parallel contour tree computation, Computer Graphics & Visual Computing 2016. Carr H, Weber G, Sewell C, Ahrens J, Parallel Peak Pruning for Scalable SMP Contour Tree Computation, Best Paper, IEEE Large Data Analysis & Visualization (LDAV 2016). Contribution of filters to vtk-m toolkit
Start Year 2015
 
Description Collaboration - Los Alamos National Laboratory 
Organisation Los Alamos National Laboratory
Department Data Science at Scale
Country United States 
Sector Public 
PI Contribution Massively Parallel Algorithms for Computational Topology
Collaborator Contribution Expertise in massively parallel algorithm development: datasets and systems for large-scale performance tests.
Impact H. Carr, C. Sewell, L.-T. Lo, and J. Ahrens. Hybrid data-parallel contour tree computation. Technical Report LA-UR-15-24579, Los Alamos National Laboratory, 2015. Carr H, Sewell C, Lo LT, Ahrens J. Hybrid data-parallel contour tree computation, Computer Graphics & Visual Computing 2016. Carr H, Weber G, Sewell C, Ahrens J, Parallel Peak Pruning for Scalable SMP Contour Tree Computation, Best Paper, IEEE Large Data Analysis & Visualization (LDAV 2016). Contribution of filters to vtk-m toolkit
Start Year 2015
 
Description Collaboration - Paris UPMC 6 & University of Utah 
Organisation Pierre and Marie Curie University - Paris 6
Country France 
Sector Academic/University 
PI Contribution Expertise in topological visualisation
Collaborator Contribution Data sets; expertise in visualisation
Impact Tierny J, Carr H, Jacobi Fiber Surfaces for Bivariate Reeb Space Computation, 23(1): 960-9 (2017). Best Scientific Visualization Paper (IEEE Vis 2016) Klacansky P, Tierny J, Carr H, Geng Z, Fast and Exact Fiber Surfaces for Tetrahedral Meshes, IEEE Transactions on Visualization and Computer Graphics 99: 1-1 (2016). Wu K, Knoll A, Isaac BJ, Carr H, Pascucci V, Direct Multifield Volume Ray Casting of Fiber Surfaces, 23(1): 941-9 (2017). Carr H, Geng Z, Tierny J, Chattopadhyay A, Knoll A, Fiber Surfaces: Generalizing Isosurfaces to Bivariate Data, Computer Graphics Forum 34(3): 241-250 (2015). Contribution of filters to open-source vtk toolkit
Start Year 2014
 
Description Collaboration - Paris UPMC 6 & University of Utah 
Organisation University of Utah
Department Scientific Computing and Imaging Institute
Country United States 
Sector Academic/University 
PI Contribution Expertise in topological visualisation
Collaborator Contribution Data sets; expertise in visualisation
Impact Tierny J, Carr H, Jacobi Fiber Surfaces for Bivariate Reeb Space Computation, 23(1): 960-9 (2017). Best Scientific Visualization Paper (IEEE Vis 2016) Klacansky P, Tierny J, Carr H, Geng Z, Fast and Exact Fiber Surfaces for Tetrahedral Meshes, IEEE Transactions on Visualization and Computer Graphics 99: 1-1 (2016). Wu K, Knoll A, Isaac BJ, Carr H, Pascucci V, Direct Multifield Volume Ray Casting of Fiber Surfaces, 23(1): 941-9 (2017). Carr H, Geng Z, Tierny J, Chattopadhyay A, Knoll A, Fiber Surfaces: Generalizing Isosurfaces to Bivariate Data, Computer Graphics Forum 34(3): 241-250 (2015). Contribution of filters to open-source vtk toolkit
Start Year 2014
 
Description Collaboration - University of Tokyo 
Organisation Kyushu University
Country Japan 
Sector Academic/University 
PI Contribution Collaboration with University of Tokyo. Research on the META project led to collaborative visit to groups in Tokyo & Kyushu, reciprocal visit by student: development of collaborative publications has begun.
Collaborator Contribution Mathematical expertise & problems.
Impact Chattopadhyay A, Carr H, Duke DJ, Geng Z, Saeki O, Multivariate Topology Simplification and Measure Persistence, Computational Geometry: Theory & Algorithms 58:1-24 (2017). Sakurai D, Saeki O, Carr H, Wu, Hsiang-Yun, Yamamoto T, Duke D, Takahashi S, Interactive Visualization for Singular Fibers of Functions f:R3->R2, IEEE VisWeek 2015 (IEEE Transactions on Visualization and Computer Graphics 22(1): 945-954 (2016)). Saeki O, Takahashi S, Sakurai D, Wu H-Y, Kikuchi K, Carr H, Duke D, Visualizing Multivariate Data Using Singularity Theory, in Wakayama M, Anderssen RS, Cheng J, Fukumoto Y, McKibbin R, Polthier K, Takagi T, Toh K-C, The Impact of Applications on Mathematics, Springer-Verlag, Berlin, 2014.
Start Year 2013
 
Description Collaboration - University of Tokyo 
Organisation Swiss National Supercomputer Centre (CSCS)
Country Switzerland 
Sector Academic/University 
PI Contribution Collaboration with University of Tokyo. Research on the META project led to collaborative visit to groups in Tokyo & Kyushu, reciprocal visit by student: development of collaborative publications has begun.
Collaborator Contribution Mathematical expertise & problems.
Impact Chattopadhyay A, Carr H, Duke DJ, Geng Z, Saeki O, Multivariate Topology Simplification and Measure Persistence, Computational Geometry: Theory & Algorithms 58:1-24 (2017). Sakurai D, Saeki O, Carr H, Wu, Hsiang-Yun, Yamamoto T, Duke D, Takahashi S, Interactive Visualization for Singular Fibers of Functions f:R3->R2, IEEE VisWeek 2015 (IEEE Transactions on Visualization and Computer Graphics 22(1): 945-954 (2016)). Saeki O, Takahashi S, Sakurai D, Wu H-Y, Kikuchi K, Carr H, Duke D, Visualizing Multivariate Data Using Singularity Theory, in Wakayama M, Anderssen RS, Cheng J, Fukumoto Y, McKibbin R, Polthier K, Takagi T, Toh K-C, The Impact of Applications on Mathematics, Springer-Verlag, Berlin, 2014.
Start Year 2013
 
Description Collaboration - University of Tokyo 
Organisation University of Aizu
Country Japan 
Sector Academic/University 
PI Contribution Collaboration with University of Tokyo. Research on the META project led to collaborative visit to groups in Tokyo & Kyushu, reciprocal visit by student: development of collaborative publications has begun.
Collaborator Contribution Mathematical expertise & problems.
Impact Chattopadhyay A, Carr H, Duke DJ, Geng Z, Saeki O, Multivariate Topology Simplification and Measure Persistence, Computational Geometry: Theory & Algorithms 58:1-24 (2017). Sakurai D, Saeki O, Carr H, Wu, Hsiang-Yun, Yamamoto T, Duke D, Takahashi S, Interactive Visualization for Singular Fibers of Functions f:R3->R2, IEEE VisWeek 2015 (IEEE Transactions on Visualization and Computer Graphics 22(1): 945-954 (2016)). Saeki O, Takahashi S, Sakurai D, Wu H-Y, Kikuchi K, Carr H, Duke D, Visualizing Multivariate Data Using Singularity Theory, in Wakayama M, Anderssen RS, Cheng J, Fukumoto Y, McKibbin R, Polthier K, Takagi T, Toh K-C, The Impact of Applications on Mathematics, Springer-Verlag, Berlin, 2014.
Start Year 2013
 
Title Fiber Surface Filters 
Description Contributions to industry-leading vtk toolkit 
Type Of Technology Software 
Year Produced 2017 
Open Source License? Yes  
Impact To be determined 
 
Title Joint Contour Net 
Description Joint Contour Net - code for multivariate topological analysis of data 
Type Of Technology Software 
Year Produced 2014 
Open Source License? Yes  
Impact Adopted by other users 
URL https://www.engineering.leeds.ac.uk/computing/research/cse/meta/
 
Title vtk-m Parallel Contour Tree 
Description Contribution of novel algorithm for contour trees to vtk-m toolkit through Los Alamos National Laboratory 
Type Of Technology Software 
Year Produced 2016 
Open Source License? Yes  
Impact To be determined