The problem of matching range images of human faces for the purpose of establishing a correspondence between similar features of two faces is addressed. Distinct facial features correspond to convex regions of the range image of the face, which is obtained by a segmentation of the range image based on the sign of the mean and Gaussian curvature at each point. Each convex region is represented by its extended Gaussian image, a 1-1 mapping between points of the region and points on the unit sphere that have the same normal. Several issues are examined that are associated with the difficult problem of interpolation of the values of the extended Gaussian image and its representation. A similarity measure between two regions is obtained by correlating their extended Gaussian images. To establish the optimal correspondence, a graph matching algorithm is applied. It uses the correlation matrix between convex regions of the two faces and incorporates additional relational constraints that account for the relative spatial locations of the convex regions in the domain of the range image.>