Deformations caused by facial expression variations complicate the task of 3D face registration which is vital for successful 3D face recognition systems. In this work, we propose to use a hierarchical component-based face registration technique capable of handling the difficulties caused by non-rigid nature of faces. Local components independently registered by the Iterative Closest Point (ICP) algorithm provides a fast registration with the use of a generic face model and does not suffer from non-rigidity of human facial surface. Invariance of the proposed approach is further increased by utilizing curvature-based 3D surface descriptors. Identification experiments conducted on the multi-expression Bosphorus database reveal that the accuracy of the classical ICP-based approach can be significantly increased under extreme expression variations.