Related papers: A Python implementation of some geometric tools on…

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 engineering. The shape module first implements widely used shape…

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. We…

We introduce geomstats, a python package that performs computations on manifolds such as hyperspheres, hyperbolic spaces, spaces of symmetric positive definite matrices and Lie groups of transformations. We provide efficient and extensively…

Shape analysis and compuational anatomy both make use of sophisticated tools from infinite-dimensional differential manifolds and Riemannian geometry on spaces of functions. While comprehensive references for the mathematical foundations…

We propose a framework for 2D shape analysis using positive definite kernels defined on Kendall's shape manifold. Different representations of 2D shapes are known to generate different nonlinear spaces. Due to the nonlinearity of these…

The generalized partially linear models on Riemannian manifolds are introduced. These models, like ordinary generalized linear models, are a generalization of partially linear models on Riemannian manifolds that allow for response variables…

In the statistical analysis of shape a goal beyond the analysis of static shapes lies in the quantification of `same' deformation of different shapes. Typically, shape spaces are modelled as Riemannian manifolds on which parallel transport…

We introduce the information geometry module of the Python package Geomstats. The module first implements Fisher-Rao Riemannian manifolds of widely used parametric families of probability distributions, such as normal, gamma, beta,…

We analytically determine Jacobi fields and parallel transports and compute geodesic regression in Kendall's shape space. Using the derived expressions, we can fully leverage the geometry via Riemannian optimization and thereby reduce the…

Computer-aided design (CAD) has become a critical element in the creation of nanopatterned structures and devices. In particular, with the increased adoption of easy-to-learn programming languages like Python there has been a significant…

This paper presents tensorflow-riemopt, a Python library for geometric machine learning in TensorFlow. The library provides efficient implementations of neural network layers with manifold-constrained parameters, geometric operations on…

An increasingly common viewpoint is that protein dynamics data sets reside in a non-linear subspace of low conformational energy. Ideal data analysis tools for such data sets should therefore account for such non-linear geometry. The…

Computer simulation has become one of the most important tools in scientific research in many disciplines. Benefiting from the dynamical trajectories regulated by versatile interatomic interactions, various material properties can be…

We propose a novel sparse dictionary learning method for planar shapes in the sense of Kendall, namely configurations of landmarks in the plane considered up to similitudes. Our shape dictionary method provides a good trade-off between…

This paper introduces a novel approach to statistics and data analysis, departing from the conventional assumption of data residing in Euclidean space to consider a Riemannian Manifold. The challenge lies in the absence of vector space…

Data sets tend to live in low-dimensional non-linear subspaces. Ideal data analysis tools for such data sets should therefore account for such non-linear geometry. The symmetric Riemannian geometry setting can be suitable for a variety of…

Deep Learning architectures, albeit successful in most computer vision tasks, were designed for data with an underlying Euclidean structure, which is not usually fulfilled since pre-processed data may lie on a non-linear space. In this…

Symmetric positive definite (SPD) matrices arising from functional connectivity analysis of neuroimaging data can be endowed with a Riemannian geometric structure that standard methods fail to respect. While existing R packages provide some…

3D shapes provide substantially more information than 2D images. However, the acquisition of 3D shapes is sometimes very difficult or even impossible in comparison with acquiring 2D images, making it necessary to derive the 3D shape from 2D…

The analysis of manifold-valued data requires efficient tools from Riemannian geometry to cope with the computational complexity at stake. This complexity arises from the always-increasing dimension of the data, and the absence of…