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This paper presents a framework for the computation of a novel 3D facial attribute, namely,the face kernel. The first part of the paper exposes the theoretical background related to the kernel computation and demonstrates some properties of the surface kernel. The second part describes two applications of the kernel concept, namely, spherical facial surface mapping and facial surface alignment. This framework has been tested and experimented on real 3D face surfaces. The usefulness of the face kernel is manifested in two aspects: 1) It provides a simple scheme for an optimal spherical embedding in the sense of minimizing the related distortion error. 2) It can be used for an efficient facial surface alignment.