N-dimensional surface reconstruction from a noisy normal vector field

We present a method to reconstruct an implicit hypersurface of a N-dimensional vector space from a normal vector field supposed to be unreliable and noisy. Either the surface boundary or a point belonging to the surface is required. Assuming that a basis is known in which the surface is explicit, our approach consists in an accurate and noise robust global optimization technique based on a non linear partial derivative equation relied on local dip. The key point is the expression of the local dip in the new basis.