The Project on Geometric and Topological Methods for Analyzing Shapes

This project brings together a community of researchers who develop theoretical and computational models to characterize shapes. Their combined interests 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 increasingly fine resolutions. The seemingly unlimited breadth and depth of these sources provide the means to study complex systems in a more comprehensive way. At the same time however, these sensors are generating a huge amount of data that comes with a high level of complexity and heterogeneity, providing indirect measurements of hidden processes that provide keys to the systems under study. This has led to new challenges and opportunities in data analysis. Our focus is on image data and the shapes they represent. Advances in geometry and topology have led to a powerful new tools that can be applied to geometric methods for representing, searching, simulating, analyzing, and comparing shapes. These methods and tools can be applied in a wide range of fields, including computer vision, biological imaging, brain mapping, target recognition, and satellite image analysis.

Coming September 20 - 22, 2019 in Davis CA:
Workshop on Geometric Methods for Analyzing Discrete Shapes.

Supported by the National Science Foundation Division of Mathematical Sciences: NSF DMS-1760485

National Science Foundation

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