META: Multifield Extension of Topological Analysis

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.

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.