A fully automatic 3D face recognition algorithm is presented. Several novelties are introduced to make the recognition robust to facial expressions and efficient. These novelties include: (1) Automatic 3D face detection by detecting the nose; (2) Automatic pose correction and normalization of the 3D face as well as its corresponding 2D face using the Hotelling Transform; (3) A Spherical Face Representation and its use as a rejection classifier to quickly reject a large number of candidate faces for efficient recognition; and (4) Robustness to facial expressions by automatically segmenting the face into expression sensitive and insensitive regions. Experiments performed on the FRGC Ver 2.0 dataset (9,500 2D/3D faces) show that our algorithm outperforms existing 3D recognition algorithms. We achieved verification rates of 99.47% and 94.09% at 0.001 FAR and identification rates of 98.03% and 89.25% for probes with neutral and non-neutral expression respectively.