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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 studythe consistency of a smoothed Procrustean mean curve when the observations obeya deformable model including some nuisance parameters such as randomtranslations, rotations and scaling. The main contribution of the paper is toanalyze the influence of the dimension $k$ of the data and of the number $J$ ofobserved configurations on the convergence of the smoothed Procrusteanestimator to the mean curve of the model. Some numerical experiments illustratethese results.

Consistent estimation of a mean planar curve modulo similarities