In this paper we present an approach for 3D face recognition from range data based on the principal curvature, kmax, and Hausdorff distance. We use the principal curvature, kmax, to represent the face image as a 3D binary image called ridge image. The ridge image shows the locations of the ridge lines around the important facial regions on the face (i.e. the eyes, the nose, and the mouth). We utilize Hausdorff distance to match the ridge image of a given probe to the created ridge images of the subjects in the gallery. For pose alignment, we extract the locations of three feature points, the inner corners of the two eyes and the tip of the nose using Gaussian curvature. These three feature points plus an auxiliary point in the center of the triangle, made by averaging the coordinates of the three feature points, are used for initial 3D face alignment. In the face recognition stage, we find the optimum pose alignment between the probe image and the gallery, which gives the minimum Hasusdorff distance between the two sets of features. This approach is used for identification of both neutral faces and faces with smile expression. Experiments on a public face database of 61 subjects resulted in 93.5% ranked one recognition rate for neutral expression and 82.0% for the faces with smile expression.