This work addresses the localization of 11 prominent facial landmarks in 3D by fitting state of the art shape models to 2D data. Quantitative results are provided for 34 scans at high resolution (texture maps of 10 M-pixels) in terms of accuracy (with respect to manual measurements) and precision (repeatability on different images from the same individual). We obtain an average accuracy of approximately 3 mm, and median repeatability of inter-landmark distances typically below 2 mm, which are values comparable to current algorithms on automatic localization of facial landmarks. We also show that, in our experiments, the replacement of texture information by curvature features produced little change in performance, which is an important finding as it suggests the applicability of the method to any type of 3D data.