36 citations · 42 across the 14 of their papers we have counts for
14 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…
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…
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…
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…
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…
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,…
Learning from landmarks, curves, surfaces, and shapes in Geomstats
Luís F. Pereira, Alice Le Brigant, Adele Myers +7
We introduce the shape module of the Python package Geomstats to analyze shapes of objects represented as landmarks, curves and surfaces across fields of natural sciences and engin…
Basis restricted elastic shape analysis on the space of unregistered surfaces
Emmanuel Hartman, Emery Pierson, Martin Bauer +2
This paper introduces a new mathematical and numerical framework for surface analysis derived from the general setting of elastic Riemannian metrics on shape spaces. Traditionally,…
VariGrad: A Novel Feature Vector Architecture for Geometric Deep Learning on Unregistered Data
Emmanuel Hartman, Emery Pierson
We present a novel geometric deep learning layer that leverages the varifold gradient (VariGrad) to compute feature vector representations of 3D geometric data. These feature vecto…
Square Root Normal Fields for Lipschitz surfaces and the Wasserstein Fisher Rao metric
Emmanuel Hartman, Martin Bauer, Eric Klassen
The Square Root Normal Field (SRNF) framework is a method in the area of shape analysis that defines a (pseudo) distance between unparametrized surfaces. For piecewise linear (PL)…
BaRe-ESA: A Riemannian Framework for Unregistered Human Body Shapes
Emmanuel Hartman, Emery Pierson, Martin Bauer +2
We present Basis Restricted Elastic Shape Analysis (BaRe-ESA), a novel Riemannian framework for human body scan representation, interpolation and extrapolation. BaRe-ESA operates d…
Elastic shape analysis of surfaces with second-order Sobolev metrics: a comprehensive numerical framework
Emmanuel Hartman, Yashil Sukurdeep, Eric Klassen +2
This paper introduces a set of numerical methods for Riemannian shape analysis of 3D surfaces within the setting of invariant (elastic) second-order Sobolev metrics. More specifica…
The Square Root Normal Field Distance and Unbalanced Optimal Transport
Martin Bauer, Emmanuel Hartman, Eric Klassen
This paper explores a novel connection between two areas: shape analysis of surfaces and unbalanced optimal transport. Specifically, we characterize the square root normal field (S…
Supervised deep learning of elastic SRV distances on the shape space of curves
Emmanuel Hartman, Yashil Sukurdeep, Nicolas Charon +2
Motivated by applications from computer vision to bioinformatics, the field of shape analysis deals with problems where one wants to analyze geometric objects, such as curves, whil…