Non rigid registration is an important task in computer vision with many applications in shape and motion modeling. A fundamental step of the registration is the data association between the source and the target under consideration. Such association proves difficult in practice, due to the discrete nature of the information and its corruption by various types of noise, e.g. outliers and missing data. In this paper we investigate the benefit of the implicit representation multi-level Partition of Unity (MPU) for the registration of 3D point clouds from coarse to fine resolutions. Using this flexible surface representation, the discrete association between the source and the target can be replaced by a continuous distance field induced by this implicit interface. This significantly eases the registration by avoiding direct association between points. Moreover, by combining this distance field with a proper deformation term, the registration energy can be expressed in a linear least square form that is easy and fast to solve. Experimental results are provided for point clouds from multi-view data sets. The qualitative and quantitative comparisons show the outperformance and robustness of our framework in presence of noise and outliers.