On the consistency of Fréchet mean 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. These models are useful to analyze the geometric modes of variation of a data set around a common mean pattern. It is shown that an appropriate tool for statistical inference in such models is the notion of empirical Fréchet mean. This leads to a new procedure to construct a mean pattern from a set of curves or images, and to estimate the shape variability of such data. Using a non-asymptotic framework, we propose consistent estimators of the mean pattern and the deformation parameters modeling the geometric variability of curves or images. Numerical experiments are given to illustrate the finite sample performances of the procedure. An application to the analysis of the geometric variability of a set of images is also proposed.

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

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

Jérémie Bigot, Benjamin Charlier. On the consistency of Fréchet mean in deformable models for curve and image analysis. 2010. ⟨hal-00522831v1⟩