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 Fr\'echet 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