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A new class of statistical deformable models is introduced to studyhigh-dimensional curves or images. In addition to the standard measurementerror term, these deformable models include an extra error term modeling theindividual variations in intensity around a mean pattern. It is shown that anappropriate tool for statistical inference in such models is the notion ofsample Fr\'echet means, which leads to estimators of the deformation parametersand the mean pattern. The main contribution of this paper is to study how thebehavior of these estimators depends on the number n of design points and thenumber J of observed curves (or images). Numerical experiments are given toillustrate the finite sample performances of the procedure.

On the consistency of Fr\'echet means in deformable models for curve and image analysis