On the consistency of Fréchet means in deformable models for curve and image analysis

DOI10.1214/11-EJS633zbMath1274.62276arXiv1010.0427OpenAlexW2963057625MaRDI QIDQ1952218

Jérémie Bigot, Benjamin Charlier

Publication date: 28 May 2013

Published in: Electronic Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.0427

zbMATH Keywords

high-dimensional datashape analysisFréchet meancurve registrationdeformable modelsimage warpingmean pattern estimationgeometric variability

Mathematics Subject Classification ID

Random fields; image analysis (62M40) Nonparametric regression and quantile regression (62G08)

Related Items (14)

Topologically Constrained Template Estimation via Morse--Smale Complexes Controls Its Statistical Consistency ⋮ Online EM for functional data ⋮ Minimax properties of Fréchet means of discretely sampled curves ⋮ Convergent stochastic expectation maximization algorithm with efficient sampling in high dimension. Application to deformable template model estimation ⋮ Recursive estimation in a class of models of deformation ⋮ Intensity estimation of non-homogeneous Poisson processes from shifted trajectories ⋮ Weighted Fréchet means as convex combinations in metric spaces: properties and generalized median inequalities ⋮ Fréchet means of curves for signal averaging and application to ECG data analysis ⋮ Characterization of barycenters in the Wasserstein space by averaging optimal transport maps ⋮ Statistical models for deformable templates in image and shape analysis ⋮ Template Shape Estimation: Correcting an Asymptotic Bias ⋮ Estimation of the shift parameter in regression models with unknown distribution of the observations ⋮ Template Estimation in Computational Anatomy: Fréchet Means Top and Quotient Spaces Are Not Consistent ⋮ A novel semi-distance for measuring dissimilarities of curves with sharp local patterns

Cites Work

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• Intrinsic inference on the mean geodesic of planar shapes and tree discrimination by leaf growth
• Intrinsic statistics on Riemannian manifolds: Basic tools for geometric measurements
• Concentration inequalities and model selection. Ecole d'Eté de Probabilités de Saint-Flour XXXIII -- 2003.
• Efficient estimation for a subclass of shape invariant models
• A deconvolution approach to estimation of a common shape in a shifted curves model
• Statistical M-estimation and consistency in large deformable models for image warping
• Statistical tools to analyze data representing a sample of curves
• Minimum contrast estimators on sieves: Exponential bounds and rates of convergence
• Alignment of curves by dynamic time warping
• Large sample theory of intrinsic and extrinsic sample means on manifolds. I
• Group actions, homeomorphisms, and matching: A general framework
• Applications of the van Trees inequality: A Bayesian Cramér-Rao bound
• Intrinsic analysis of statistical estimation
• Convergence and consistency results for self-modeling nonlinear regression
• Semi-parametric estimation of shifts
• Semiparametric estimation of shifts on compact Lie groups for image registration
• Metamorphoses through Lie group action
• Large sample theory of intrinsic and extrinsic sample means on manifolds. II.
• Nonparametric Maximum Likelihood Estimation for Shifted Curves
• A Penalized Likelihood Approach to Image Warping
• Inference on 3D Procrustes Means: Tree Bole Growth, Rank Deficient Diffusion Tensors and Perturbation Models
• Riemannian $L^{p}$ center of mass: Existence, uniqueness, and convexity
• Estimation of Translation, Rotation, and Scaling between Noisy Images Using the Fourier–Mellin Transform
• Shape Manifolds, Procrustean Metrics, and Complex Projective Spaces
• Probability, Convexity, and Harmonic Maps with Small Image I: Uniqueness and Fine Existence
• Riemannian center of mass and mollifier smoothing
• Asymptotic Statistics
• On the consistency of procrustean mean shapes
• The Fréchet mean shape and the shape of the means
• Semiparametric Curve Alignment and Shift Density Estimation for Biological Data
• Functional Convex Averaging and Synchronization for Time-Warped Random Curves

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