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Found 9 papers, 3 papers with code
Principal subbundles for dimension reduction
In this paper we demonstrate how sub-Riemannian geometry can be used for manifold learning and surface reconstruction by combining local linear approximations of a point cloud to obtain lower dimensional bundles.
Geodesic squared exponential kernel for non-rigid shape registration
This work addresses the problem of non-rigid registration of 3D scans, which is at the core of shape modeling techniques.
Cardiac Motion Modeling with Parallel Transport and Shape Splines
In cases of pressure or volume overload, probing cardiac function may be difficult because of the interactions between shape and deformations. In this work, we use the LDDMM framework and parallel transport to estimate and reorient deformations of the right ventricle.
Geomstats: A Python Package for Riemannian Geometry in Machine Learning
We introduce Geomstats, an open-source Python toolbox for computations and statistics on nonlinear manifolds, such as hyperbolic spaces, spaces of symmetric positive definite matrices, Lie groups of transformations, and many more.
Curvature effects on the empirical mean in Riemannian and affine Manifolds: a non-asymptotic high concentration expansion in the small-sample regime
For distributions that are highly concentrated around their mean, and for any finite number of samples, we establish explicit Taylor expansions on the first and second moment of the empirical mean thanks to a new Taylor expansion of the Riemannian log-map in affine connection spaces.
Differential Geometry Statistics Theory Statistics Theory
A model of brain morphological changes related to aging and Alzheimer's disease from cross-sectional assessments
In this study we propose a deformation-based framework to jointly model the influence of aging and Alzheimer's disease (AD) on the brain morphological evolution.
Automatically Segmenting the Left Atrium from Cardiac Images Using Successive 3D U-Nets and a Contour Loss
In this preliminary study, we propose automated, two-stage, three-dimensional U-Nets with convolutional neural network, for the challenging task of left atrial segmentation.
geomstats: a Python Package for Riemannian Geometry in Machine Learning
This paper also presents a review of manifolds in machine learning and an overview of the geomstats package with examples demonstrating its use for efficient and user-friendly Riemannian geometry.
Template shape estimation: correcting an asymptotic bias
We use tools from geometric statistics to analyze the usual estimation procedure of a template shape.
