Open Access
2011 On the consistency of Fréchet means in deformable models for curve and image analysis
Jérémie Bigot, Benjamin Charlier
Electron. J. Statist. 5: 1054-1089 (2011). DOI: 10.1214/11-EJS633


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.


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Jérémie Bigot. Benjamin Charlier. "On the consistency of Fréchet means in deformable models for curve and image analysis." Electron. J. Statist. 5 1054 - 1089, 2011.


Published: 2011
First available in Project Euclid: 15 September 2011

zbMATH: 1274.62276
MathSciNet: MR2836769
Digital Object Identifier: 10.1214/11-EJS633

Primary: 62G08
Secondary: ‎42C40

Keywords: Curve registration , deformable models , Fréchet mean , geometric variability , High-dimensional data , image warping , Mean pattern estimation , shape analysis

Rights: Copyright © 2011 The Institute of Mathematical Statistics and the Bernoulli Society

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