Multivate topological methods for scientific visualisation

One of the most prominent tools in the field of scientific visualisation data is called an isosurface. Mathematically, an isosurface is a special type of surface that defines the boundary of a feature in space for a given threshold. However, in many cases it is not clear which thresholds would produce surfaces of interest, and computational topology provides tools to support researchers. This project aims to develop existing computational topology tools further at the theoretical level, at the systems level, and in their application to domain sciences such as high-energy physics and meteorology.

One existing approach is to compute a topological data structure called the contour tree, which encodes how the connectivity and shape of each isosurface changes over all possible thresholds. Historically, these tools have been limited by serial algorithms, and the first part of this project is therefore to collaborate with Lawrence Berkeley National Laboratory (LBNL) to increase efficiency by applying shared-memory parallelism, and to apply the resulting tools to understand physical plasma simulations at LBNL.

Contour trees, however, permit analysis of single physical properties, where scientific data sets commonly generate multiple properties such as temperature, pressure, and so on. Recent work has extended isosurfaces to fiber surfaces, which provide traction for studying more complex data. The second part of this project is therefore to work with climate scientists to apply fiber surfaces to visualise convective cloud formation.

The third part of this project is to extend the tools from the contour tree (for isosurfaces) to the Reeb space (for fiber surfaces), which is a largely theoretical and algorithmic task. Here, in collaboration with Japanese researchers at the University of Kyushu, the goal is to clarify and simplify the analysis of Reeb spaces, so that algorithms to compute them and exploit them for visualisation and analysis can be developed in the future.