Exponential Barycenters of the Canonical Cartan Connection and Invariant Means on Lie Groups

DOI10.1007/978-3-642-30232-9_7zbMath1270.53078OpenAlexW2201034663MaRDI QIDQ5325897

Xavier Pennec, Vincent Arsigny

Publication date: 31 July 2013

Published in: Matrix Information Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-642-30232-9_7

zbMATH Keywords

invariant meanMahalanobis distancebiomedical image registrationbarycentric equationcanonical Cartan connection

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Biomedical imaging and signal processing (92C55) Analysis on real and complex Lie groups (22E30) Dynamics of a rigid body and of multibody systems (70E99) Applications of differential geometry to sciences and engineering (53Z99)

Related Items (11)

Introduction to Riemannian Geometry and Geometric Statistics: From Basic Theory to Implementation with Geomstats ⋮ Bi-Invariant Dissimilarity Measures for Sample Distributions in Lie Groups ⋮ Invariant nonholonomic Riemannian structures on three-dimensional Lie groups ⋮ Locally adaptive frames in the roto-translation group and their applications in medical imaging ⋮ Advances in Geometric Statistics for Manifold Dimension Reduction ⋮ Barycentric subspace analysis on manifolds ⋮ Geodesics, parallel transport \& one-parameter subgroups for diffeomorphic image registration ⋮ Information-Theoretic Matrix Inequalities and Diffusion Processes on Unimodular Lie Groups ⋮ Unnamed Item ⋮ Wrapped Statistical Models on Manifolds: Motivations, The Case SE(n), and Generalization to Symmetric Spaces ⋮ A reduced parallel transport equation on Lie groups with a left-invariant metric

Uses Software

• MATLAB expm

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