Collection Statistical Modeling for Shapes and Imaging
Organizer(s)
Date(s)
03/05/2024
Kernel norms on normal cycles and the KeOps library for linear memory reductions over datasets
By Joan Glaunès
In the first part of this talk I will present a model for writing data fidelity terms for shape registration algorithms. This model is based on the notion of normal cycle in geometry, which generalizes curvatures of curves and surfaces, and the use of kernel dual norms, similarly to previous works using currents and varifolds representations. This normal cycle model improves matchings of geometrical data in the presence of high curvature landmarks such as branching points or boundaries. In the second part I will present the KeOps library, which is designed to compute efficiently kernel reductions operations. This library combines a linear memory approach, GPU implementation and automatic differentiation, with a complete integration into the PyTorch library. This allows to perform reductions over datasets with millions of points without memory issue, and has many potential applications. I will present a few examples of its use for shape registration, optimal transport and k-means clustering. Joint works with Pierre Roussillon, Benjamin Charlier and Jean Feydy.
