Consistent estimation of a mean pattern in deformable models for high-dimensional shape analysis

Jérémie Bigot (1) , Benjamin Charlier (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

We consider the problem of estimating a mean shape from a set of J planar configurations described by a sequence of k landmarks. We study the consistency of a smoothed Procrustean mean when the observations obey a deformable model including some nuisance parameters such as random translations, rotations and scaling. The main contribution of the paper is to analyze the influence of the dimension k of the data and of the number J of observed configurations on the convergence of the smoothed Procrustean estimator to the mean pattern of the model. Some numerical experiments illustrate these results.

Mots clés: Shape spaces; Perturbation models; Consistency; Procrustes Means; Nonparametric inference; High-dimensional data; Linear smoothing

Domaines: Méthodologie [stat.ME]

Jérémie Bigot, Benjamin Charlier. Consistent estimation of a mean pattern in deformable models for high-dimensional shape analysis. 2011. ⟨hal-00634899v1⟩