MaLGa Colloquia - Modeling shapes and surfaces: geometry meets machine learning
03 Apr 2023, 16:00 — Room 704, UniGe DIMA, Via Dodecaneso 35
![Sayan.Mukherjee - [Fronte Occhiali Sorriso]](/media/images/Sayan_UHs6eAE.width-800.jpg)
Speaker:
Sayan Mukherjee — MPI Leipzig
Sayan Mukherjee — MPI Leipzig
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.
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.
Bio:
Sayan Mukherjee received his PhD from MIT. Since 2022 he is Alexander von Humboldt Professor at Leipzig University and the Max Plank Institute for Mathematics in the Sciences. Before he was Professor at Duke. Sayan research interests are vast and comprise the mathematical foundations of inference and learning with applications to biology, biomedicine, and clinical challenges, all fields in which his work had an important impact. His most recent contributions are in the emerging field of topological data analysis.
Sayan Mukherjee received his PhD from MIT. Since 2022 he is Alexander von Humboldt Professor at Leipzig University and the Max Plank Institute for Mathematics in the Sciences. Before he was Professor at Duke. Sayan research interests are vast and comprise the mathematical foundations of inference and learning with applications to biology, biomedicine, and clinical challenges, all fields in which his work had an important impact. His most recent contributions are in the emerging field of topological data analysis.
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