This paper explores the use of morphological operators for feature extraction in range images and curvature maps of the human face. Two general procedures are described. The first is the identification of connected part boundaries for convex structures, which is used to extract the nose outline and the eye socket outlines of the face. The part boundaries are defined locally based on minima of minimum principal curvature on the surface. The locus of these points suggests boundary lines which surround most convex regions on the surface. However, most of these boundaries are not completely connected. To remedy this problem, a general two-step connection procedure is developed: the partial boundaries are first dilated in such a way that the gaps between them are filled. Second, the resulting dilated outlines are skeletonized with the constraint that the pixels belonging to the original boundary parts cannot be removed. A marker which identifies the convex region being described is then used to select the region enclosed by the new connected outline. Examples are given of this procedure in the extraction of the nose boundary and eye socket boundary. The second general procedure discussed is the identification of connected ridge lines, which is demonstrated in the extraction of the browline and the chin/jaw line. Ridge lines are defined as local maxima of maximum curvature in the direction of maximum curvature. The same skeleton-based procedure as above is first used to connect the ridge lines. Skeletonization is then used again to reduce these lines to simply connected ones. The last step primarily consists in extracting the longest path within the obtained components: this is achieved by using the propagation function to find the extremities of these paths and then connecting them within the components by means of geodesic distance functions. The entire process provides a robust and accurate extraction of brow and chin/jaw lines.