This paper presents an innovative restoration strategy which allows for an effective recognition of 3D faces, even when they are partially occluded by unforeseen, extraneous objects such as scarves, hats, glasses, and so on. First, the occluded regions are detected by considering their effects on the projections of the faces in a suitable face space; the non-occluded regions are then used to restore the missing information. Any recognition algorithm can be applied as usual to restored faces. This restoration strategy led to very satisfactory results on a test set of 52 three-dimensional faces presenting various kinds of occlusions.