We propose and evaluate a three-dimensional (3D) face recognition approach that applies the speeded up robust feature (SURF) algorithm to the depth representation of shape index map, under real-world conditions, using only a single gallery sample for each subject. First, the 3D scans are preprocessed, then SURF is applied on the shape index map to find interest points and their descriptors. Each 3D face scan is represented by keypoints descriptors, and a large dictionary is built from all the gallery descriptors. At the recognition step, descriptors of a probe face scan are sparsely represented by the dictionary. A multitask sparse representation classification is used to determine the identity of each probe face. The feasibility of the approach that uses the SURF algorithm on the shape index map for face identification/authentication is checked through an experimental investigation conducted on Bosphorus, University of Milano Bicocca, and CASIA 3D datasets. It achieves an overall rank one recognition rate of 97.75%, 80.85%, and 95.12%, respectively, on these datasets.