A novel family of 2D and 3D geometrically invariant features, called summation invariants is proposed for the recognition of the 3D surface of human faces. Focusing on a rectangular region surrounding the nose of a 3D facial depth map, a subset of the so called semi-local summation invariant features is extracted. Then the similarity between a pair of 3D facial depth maps is computed to determine whether they belong to the same person. Out of many possible combinations of these set of features, we select, through careful experimentation, a subset of features that yields best combined performance. Tested with the 3D facial data from the on-going Face Recognition Grand Challenge v1.0 dataset, the proposed new features exhibit significant performance improvement over the baseline algorithm distributed with the datase