The main goal of this project is to develop theoretical tools and design efficient computational methods for
analyzing, quantifying and exploring relations and variability in structured data sets such as geometric
shapes, graphs or 3D
Our ultimate goal is to design a unified framework in which variability can be processed in a way that would be largely agnostic to the
underlying data modality. Key to our study is the exploration of relations between objects using the functional maps framework, which was originally
introduced for solving shape correspondence problems, and has since then expanded to
many other areas of geometric data analysis. Thus, we aim to develop a theoretical and computational
framework for analyzing and comparing geometric objects by considering them as functional spaces that be easily manipulated and
analyzed, exploiting their rich algebraic structure. Such an approach can provide a completely novel unified framework for representing and processing different types of data.
For this, we bring together and develop tools from areas as diverse as functional analysis,
numerical linear algebra, spectral geometry, computer graphics and geometry processing to name a few. We also work with
researchers in other areas (paleontology, comparative anatomy and computational bio-informatics, etc.) who are
interested in analyzing structure and variability in their own datasets.
The project is generously funded through the European Commission's ERC program. Please see also the project page
on the official European Commission website.