Abstract: This paper presents a novel formulation, which derives in a smooth minimization problem, to tackle the rigid registration between a given point set and a model set. Unlike most of the existing works, which are based on minimizing a point-wise correspondence term, we propose to describe the model set by means of an implicit representation. It allows a new definition of the registration error, which works beyond the point level representation. Moreover, it could be used in a gradient-based optimization framework. The proposed approach consists of two stages. Firstly, a novel formulation is proposed that relates the registration parameters with the distance between the model and data set. Secondly, the registration parameters are obtained by means of the Levengberg-Marquardt algorithm. Experimental results and comparisons with state of the art show the validity of the proposed framework.