Intrinsic polynomials for regression on Riemannian manifolds

DOI10.1007/s10851-013-0489-5zbMath1310.53038OpenAlexW2117145236WikidataQ59400776 ScholiaQ59400776MaRDI QIDQ2513409

Jacob Hinkle, P. Thomas Fletcher, Sarang Joshi

Publication date: 28 January 2015

Published in: Journal of Mathematical Imaging and Vision (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10851-013-0489-5

zbMATH Keywords

Riemannian geometryLie groupspolynomialregressionshape spacerolling maps

Mathematics Subject Classification ID

Directional data; spatial statistics (62H11) Nonparametric regression and quantile regression (62G08) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Geodesics in global differential geometry (53C22)

Related Items

About simple variational splines from the Hamiltonian viewpoint ⋮ Graph-valued regression: prediction of unlabelled networks in a non-Euclidean graph space ⋮ Intrinsic Riemannian functional data analysis for sparse longitudinal observations ⋮ Diffeomorphic Surface Registration with Atrophy Constraints ⋮ A hierarchical geodesic model for longitudinal analysis on manifolds ⋮ Time-varying spectral matrix estimation via intrinsic wavelet regression for surfaces of Hermitian positive definite matrices ⋮ Variational point-obstacle avoidance on Riemannian manifolds ⋮ Recent advances in directional statistics ⋮ Fast diffeomorphic image registration via Fourier-approximated Lie algebras ⋮ Functional Additive Models on Manifolds of Planar Shapes and Forms ⋮ Fréchet single index models for object response regression ⋮ Sasaki metric for spline models of manifold-valued trajectories ⋮ Statistics for data with geometric structure. Abstracts from the workshop held January 21--27, 2018 ⋮ Geodesic analysis in Kendall's shape space with epidemiological applications ⋮ Data fitting on manifolds with composite Bézier-like curves and blended cubic splines ⋮ Longitudinal image analysis via path regression on the image manifold ⋮ Minimal time splines on the sphere ⋮ Robust Geodesic Regression ⋮ Geometry and statistics: manifolds and stratified spaces ⋮ Canonical Correlation Analysis on SPD(n) Manifolds ⋮ Bayesian linear size-and-shape regression with applications to face data ⋮ Total variation regularized Fréchet regression for metric-space valued data ⋮ A longitudinal model for shapes through triangulation ⋮ Intrinsic Wavelet Regression for Curves of Hermitian Positive Definite Matrices ⋮ Low-rank multi-parametric covariance identification

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Higher-order smoothing splines versus least squares problems on Riemannian manifolds
• Hamilton-Pontryagin integrators on Lie groups. I: Introduction and structure-preserving properties
• The Euler-Poincaré equations and semidirect products with applications to continuum theories
• The Riemannian structure of Euclidean shape spaces: A novel environment for statistics
• A survey of the statistical theory of shape. With discussion and a reply by the author
• Geodesic regression and the theory of least squares on Riemannian manifolds
• Transport of relational structures in groups of diffeomorphisms
• The momentum map representation of images
• Geodesic shooting for computational anatomy
• The fundamental equations of a submersion
• Shape curves and geodesic modelling
• Sectional Curvature in Terms of the Cometric, with Applications to the Riemannian Manifolds of Landmarks
• A multi-dimensional scaling approach to shape analysis
• Cubic Splines on Curved Spaces
• Shape Manifolds, Procrustean Metrics, and Complex Projective Spaces
• Configuration Controllability of Simple Mechanical Control Systems
• Model Selection and Multimodel Inference
• Fitting Smooth Paths to Speherical Data
• An analytical theory for Riemannian cubic polynomials
• Shape-space smoothing splines for planar landmark data

This page was built for publication: Intrinsic polynomials for regression on Riemannian manifolds