Abstract: In this paper, we focus on the automation of facial reconstruction. Since they consider the whole head as the object of interest, usual reconstruction techniques are global and involve a large number of parameters to be estimated. We present a local technique which aims at reaching a good trade-off between bias and variance following the paradigm of non-parametric statistics. The estimation is localized on patches delimited by surface geodesics between anatomical points of the skull. The technique relies on a continuous representation of the individual surfaces embedded in the vectorial space of extended normal vector fields. This allows to compute deformations and averages of surfaces. It consists in estimating the soft-tissue surface over patches. Using a homogeneous database described in [31], we obtain results on the chin and nasal regions with an average error below 1 mm, outperforming the global reconstruction techniques.