Nonparametric estimation of means on Hilbert manifolds and extrinsic analysis of mean shapes of contours

DOI10.1016/j.jmva.2013.08.010zbMath1280.62083arXiv1302.2126OpenAlexW2085997191MaRDI QIDQ391896

Leif Ellingson, Victor Patrangenaru, Frits H. Ruymgaart

Publication date: 13 January 2014

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.2126

zbMATH Keywords

nonparametric bootstrapdigital image analysisautomated randomized landmark selectiondata analysis on Hilbert manifoldsextrinsic meanplanar contoursstatistical shape analysis

Mathematics Subject Classification ID

Related Items (14)

Evaluation and prediction of polygon approximations of planar contours for shape analysis ⋮ A nonparametric approach to 3D shape analysis from digital camera images – II ⋮ Statistical inference on the Hilbert sphere with application to random densities ⋮ Projective shape analysis of contours and finite 3D configurations from digital camera images ⋮ Regression models using the LINEX loss to predict lower bounds for the number of points for approximating planar contour shapes ⋮ Statistics on manifolds and landmarks based image analysis: a nonparametric theory with applications ⋮ Rates of the strong uniform consistency for the kernel-type regression function estimators with general kernels on manifolds ⋮ Test for homogeneity of random objects on manifolds with applications to biological shape analysis ⋮ Differential Geometry for Model Independent Analysis of Images and Other Non-Euclidean Data: Recent Developments ⋮ Topological Object Data Analysis Methods with an Application to Medical Imaging ⋮ A smeary central limit theorem for manifolds with application to high-dimensional spheres ⋮ Omnibus CLTs for Fréchet means and nonparametric inference on non-Euclidean spaces ⋮ Challenges in topological object data analysis ⋮ Linear models for statistical shape analysis based on parametrized closed curves

Uses Software

• fda (R)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference
• Nonparametric inference for extrinsic means on size-and-(reflection)-shape manifolds with applications in medical imaging
• On shape of plane elastic curves
• A metric on shape space with explicit geodesics
• Bootstrap confidence regions for the planar mean shape
• The Fréchet derivative of an analytic function of a bounded operator with some applications
• Pattern analysis. Lectures in pattern theory. Vol. II
• Bootstrap methods: another look at the jackknife
• Nonparametric comparison of several regression functions: Exact and asymptotic theory
• Large sample theory of intrinsic and extrinsic sample means on manifolds. I
• Validation of linear regression models
• The statistical theory of shape
• The one- and multi-sample problem for functional data with application to projective shape analysis
• Functional data analysis.
• Riemannian geometries on spaces of plane curves
• Properties of principal component methods for functional and longitudinal data analysis
• Locating Fréchet means with application to shape spaces
• Gait-Based Human Recognition by Classification of Cyclostationary Processes on Nonlinear Shape Manifolds
• Shape Manifolds, Procrustean Metrics, and Complex Projective Spaces
• Computable Elastic Distances Between Shapes
• On Fréchet means in simplex shape spaces
• Testing the Goodness of Fit of Parametric Regression Models with Random Toeplitz Forms
• The Fréchet mean shape and the shape of the means
• Estimating Fréchet means in Bookstein's shape space
• Interpolations with elasticae in Euclidean spaces
• Mean Figures and Mean Shapes Applied to Biological Figure and Shape Distributions in the Plane
• Principal component analysis for Riemannian manifolds, with an application to triangular shape spaces
• Fourier Descriptors for Plane Closed Curves
• Statistical Analysis Based on a Certain Multivariate Complex Gaussian Distribution (An Introduction)
• Functional Variance Processes
• The bootstrap and Edgeworth expansion

This page was built for publication: Nonparametric estimation of means on Hilbert manifolds and extrinsic analysis of mean shapes of contours