We consider the problem of estimating a mean planar curve from a set of J
random planar curves observed on a k-points deterministic design. We study
the consistency of a smoothed Procrustean mean curve when the observations obey
a deformable model including some nuisance parameters such as random
translations, rotations and scaling. The main contribution of the paper is to
analyze the influence of the dimension k of the data and of the number J of
observed configurations on the convergence of the smoothed Procrustean
estimator to the mean curve of the model. Some numerical experiments illustrate
these results
