This project regroups a community of researchers from different universities in the US, with worldwide collaborators, who develop theoretical and computational models to characterize shapes. Their combined expertises span Mathematics (Geometry and Topology), Computer Science (Scientific Computing and Complexity Theory), and domain sciences, from Data Sciences to Computational Biology.
Scientific research benefits from the development of an ever growing number of sensors that are able to capture details of the world at resolutions never achieved before The seemingly unlimited breadth and depth of their sources provide the means to move beyond reductionism and develop efforts to study complex systems in a more comprehensive approach. At the same time however, these sensors are generating a huge amount of data. These data come with a high level of complexity and heterogeneity, usually providing indirect measurements of hidden albeit essential processes that are keys to the systems under study. This is leading to new challenges and opportunity in data analysis. Our focus is on image data, with a specific interest in the shapes they represent. Recent advances in geometry and topology have led to a renewed interest in applying geometric methods to representing, searching, simulating, analyzing, and comparing such shapes. These methods are developed and applied in a wide range of fields, including computer vision, biological imaging, brain mapping, target recognition (for military and civil purposes), and for satellite image analysis.