6 papers
Learning the Geometry of Data: A Mathematical Review of Shape Space Analysis
Gary P. T. Choi, Khanh Dao Duc, Shira Faigenbaum-Golovin +6
A central objective of machine learning is to identify structure and patterns in data. Advances in data acquisition have increasingly produced datasets whose observations possess r…
Conic Formulations of Transport Metrics for Unbalanced Measure Networks and Hypernetworks
Mary Chriselda Antony Oliver, Emmanuel Hartman, Tom Needham
The Gromov-Wasserstein (GW) variant of optimal transport, designed to compare probability densities defined over distinct metric spaces, has emerged as an important tool for the an…
Brownian motion on spaces of discrete regular curves
Karen Habermann, Emmanuel Hartman
We introduce and study Brownian motion on spaces of discrete regular curves in Euclidean space equipped with discrete Sobolev-type metrics. It has been established that these space…
Self Supervised Networks for Learning Latent Space Representations of Human Body Scans and Motions
Emmanuel Hartman, Nicolas Charon, Martin Bauer
This paper introduces self-supervised neural network models to tackle several fundamental problems in the field of 3D human body analysis and processing. First, we propose VariShaP…
SVarM: Linear Support Varifold Machines for Classification and Regression on Geometric Data
Emmanuel Hartman, Nicolas Charon
Despite progress in the rapidly developing field of geometric deep learning, performing statistical analysis on geometric data--where each observation is a shape such as a curve, g…
Sobolev Metrics on Spaces of Discrete Regular Curves
Jonathan Cerqueira, Emmanuel Hartman, Eric Klassen +1
Reparametrization invariant Sobolev metrics on spaces of regular curves have been shown to be of importance in the field of mathematical shape analysis. For practical applications,…