In this paper we make two contributions to the problem of recovering surface shape from single images of faces. The first of these is to develop a representation of the distribution of surface normals based on the exponential map, and to show how to model shape-deformations using principal geodesic analysis on the exponential map. The second contribution is to show how ideas from robust statistics can be used to fit the model to facial images in which there is significant self-shadowing. The method is evaluated on both synthetic and real-world images. It is demonstrated to effectively fill-in the facial surface when more than 30% of the area is subject to self-shadowing.
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