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In this paper, we present an approach for 3D face recognition based on Multi-level Partition of Unity (MPU) Implicits under pose and expression variations. The MPU Implicits are used for reconstructing 3D face surface in a hierarchical way. Three landmarks, nose, left eyehole and right eyehole, can be automatically detected with the analysis of curvature features at lower levels of reconstruted face. Thus, the 3D faces are initially registered to a common coordinate system based on the three landmarks. A variant of Iterative Closest Point (ICP) algorithm is proposed for matching the point surface of a given probe face to the implicits face surface in the gallery. To evaluate the performance of our approach for 3D face recognition, we perform an experiment on GavabDB face database. The results of the experiment show that our method based on MPU Implicits and Adaptive ICP has great capability for 3D face recognition under pose and expression variations.