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We use three dimensional facial shape information for human face identification. We propose a new method to represent faces as 3D registered point clouds. Fine registration of facial surfaces is done by first automatically finding important facial landmarks and, then, establishing a dense correspondence between points on the facial surface with the help of a 3D face template-aided thin plate spline algorithm. After the registration of facial surfaces, similarity between two faces is defined as a discrete approximation of the volume difference between facial surfaces. We call this similarity the point set difference (PSD). A second method proposed is the use of implicit polynomial invariants. Experiments done on the 3D RMA dataset show that the PSD algorithm performs as well as the point signature method, and it is statistically superior to the implicit polynomial based technique, point distribution model-based method and the 2D depth imagery technique. In terms of computational complexity, the proposed algorithm is faster than the point signature method.