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We propose an algorithm for non-rigidly registering a 3D template mesh with a dense point cloud, using a morphable shape model to control the deformation of the template mesh. A cost function involving nonrigid shape as well as rigid pose is proposed. Registration is performed by minimizing a first-order approximation of the cost function in the Iterative Closest Points framework. We show how a complex shape model, consisting of multiple PCA models for individual regions of the template, can be seamlessly integrated in the parameter estimation scheme. An appropriate Tikhonov regularization is introduced to guarantee the smoothness of the full mesh despite the splitting into local models. The proposed algorithm is compared to a recent generic nonrigid registration scheme. We show that the data-driven approach is faster, as the linear systems to be solved in the iterations are significantly smaller when a model is available. Also, we show that simultaneous optimization of pose and shape yields better registration results than shape alone.