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Workshop

Modeling shapes and surfaces - Geometry meets machine learning

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. 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. Applications in biomedical imaging and evolutionary anthropology will be stated throughout the talk.

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Katharina Matschke

Max Planck Institute for Mathematics in the Sciences Contact via Mail

Samantha Fairchild

Max Planck Institute for Mathematics in the Sciences

Diaaeldin Taha

Max Planck Institute for Mathematics in the Sciences

Anna Wienhard

Max Planck Institute for Mathematics in the Sciences