Modeling Shapes and Fields - A Sheaf Theoretic Perspective

Explore the application of topological and lifted-topological transforms in modeling shapes and fields. Delve into the practical use of the Euler Characteristic Transform and the Lifted Euler Characteristic Transform for statistical analysis of shape and field data. Examine the Lifted Euler Characteristic as an alternative to the Euler calculus for real-valued functions. Discover a moduli space of shapes with a provided complexity metric. Investigate a sheaf theoretic construction of shape space that eliminates the need for diffeomorphisms or correspondence. Learn how this construction leads to the characterization of three-dimensional shapes using only 0-dimensional homology for meshes.

Sayan Mukherjee (8/29/21): Modeling shapes and fields: a sheaf theoretic perspective