In this paper, we show that several well-known nonlinear surface registration algorithms can be put in an ICP-like framework, and thus boil down to the successive estimation of point-to-point correspondences and of a transformation between the two surfaces. We propose to enrich the ICP-like criterion with additional constraints and show that it is possible to minimise it in the same way as the original formulation, with only minor modifications in the update formulas and the same convergence properties. These constraints help the algorithm to converge to a more realistic solution and can be encoded in an affinity term between the points of the surfaces to register. This term is able to encode both a priori knowledge and higher order geometrical information in a unified manner. We illustrate the high added value of this new term on synthetic and real data