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Shayn MUKHERJEE (University of Leipzig) “Modeling Shapes and Fields”

October 3 @ 2:00 pm - 3:00 pm

Statistical Seminar: Every Monday.
Time: 2:00 pm
Date: 03 of October 2022
Place: Room 3001

Shayn MUKHERJEE (University of Leipzig) “Modeling Shapes and Fields”

Abstract: We will consider modeling shapes and fields 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 developed by Ghrist and Baryshnikov for real valued functions. We also state a moduli space of shapes for which we can provide a complexity metric for the shapes. We also 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. We will also discuss Gaussian processes on fiber bundles and applications to evolutionary questions about shapes.

 

Organizers:
Cristina BUTUCEA (CREST), Alexandre TSYBAKOV (CREST), Karim LOUNICI (CMAP) , Jaouad MOURTADA (CREST)
Sponsors:
CREST-CMAP