CMStatistics 2021: Start Registration
View Submission - CMStatistics
B1479
Title: Modeling shapes and fields Authors:  Sayan Mukherjee - Duke University (United States) [presenting]
Abstract: Modeling shapes and fields is considered via topological and lifted-topological transforms. Specifically, we show how the Euler Characteristic Transform and the Lifted Euler Characteristic Transform can be used in practice for statistical analysis of shape and field data. The Lifted Euler Characteristic is an alternative to the Euler calculus for real-valued functions. We also state a moduli space of shapes for which we can provide a complexity metric for the shapes. Furthermore, we provide a sheaf theoretic construction of shape space that does not require diffeomorphisms or correspondence. A direct result of this sheaf theoretic construction is that in three dimensions for meshes, 0-dimensional homology is enough to characterize the shape.