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We propose a novel 3D face recognition algorithm based on facial range image matching using the complex wavelet structural similarity metric (CW-SSIM) metric. Compared with many existing 3D surface matching methods, CWSSIM is computationally efficient and is robust to small geometrical distortions. Using a data set that contains 360 3D face models of 12 subjects, we tested the performance of the proposed method and compared it with existing 3D surface matching based face recognition algorithms. Verification and identification performance of each algorithm was evaluated by means of the receiver operating characteristic curve and the cumulative match characteristic curve. Among the algorithms tested, the proposed algorithm based on the CW-SSIM resulted in the best overall performance with an equal error rate of 9.13% and a rank 1 recognition rate of 98.6%, significantly better than all the other algorithms. Besides the introduction of a novel approach for 3D face recognition, this is also the first attempt to expand the application scope of complex wavelet domain similarity measure to range image matching in general.