This paper presents a computationally efficient 3D face recognition system based on a novel facial signature called Angular Radial Signature (ARS) which is extracted from the semi-rigid region of the face. Kernel Principal Component Analysis (KPCA) is then used to extract the mid-level features from the extracted ARSs to improve the discriminative power. The mid-level features are then concatenated into a single feature vector and fed into a Support Vector Machine (SVM) to perform face recognition. The proposed approach addresses the expression variation problem by using facial scans with various expressions of different individuals for training. We conducted a number of experiments on the Face Recognition Grand Challenge (FRGC v2.0) and the 3D track of Shape Retrieval Contest (SHREC 2008) datasets, and a superior recognition performance has been achieved. Our experimental results show that the proposed system achieves very high Verification Rates (VRs) of 97.8% and 88.5% at a 0.1% False Acceptance Rate (FAR) for the "neutral vs. nonneutral" experiments on the FRGC v2.0 and the SHREC 2008 datasets respectively, and 96.7% for the ROC III experiment of the FRGC v2.0 dataset. Our experiments also demonstrate the computational efficiency of the proposed approach.