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This paper presents an innovative three dimensional occlusion detection and restoration strategy for the recognition of three dimensional faces partially occluded by unforeseen, extraneous objects. The detection method considers occlusions as local deformations of the face that correspond to perturbations in a space designed to represent non-occluded faces. Once detected, occlusions represent missing information, or "holes" in the faces. The restoration module exploits the information provided by the non-occluded part of the face to recover the whole face, using an appropriate basis for the space in which non-occluded faces lie. The restoration strategy does not depend on the method used to detect occlusions and can also be applied to restore faces in the presence of noise and missing pixels due to acquisition inaccuracies. The strategy has been experimented on the occluded acquisitions taken from the Bosphorus 3D face database. A method for the generation of real-looking occlusions is also presented. Artificial occlusions, applied to the UND database, allowed for an in-depth analysis of the capabilities of our approach. Experimental results demonstrate the robustness and feasibility of our approach.