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

Jérémie Bigot (1) , Benjamin Charlier (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

A new class of statistical deformable models is introduced to study high-dimensional curves or images. In addition to the standard measurement error term, these deformable models include an extra error term modeling the individual variations in intensity around a mean pattern. It is shown that an appropriate tool for statistical inference in such models is the notion of sample Fréchet means, which leads to estimators of the deformation parameters and the mean pattern. The main contribution of this paper is to study how the behavior of these estimators depends on the number n of design points and the number J of observed curves (or images). Numerical experiments are given to illustrate the finite sample performances of the procedure.

Mots clés: Mean pattern estimation; Fréchet mean; Shape analysis; Deformable models; Curve registration; Image warping; Geometric variability; High-dimensional data

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Jérémie Bigot, Benjamin Charlier. On the consistency of Fréchet means in deformable models for curve and image analysis. 2010. ⟨hal-00522831v4⟩