Shape-from-shading is an interesting approach to the problem of finding the shape of a face because it only requires one image and no subject participation. However, SfS is not accurate enough to produce good shape models. Previously, SfS has been combined with shape models to produce realistic face reconstructions. In this work, we aim to improve the quality of such models by exploiting a probabilistic SfS model based on Fisher-Bingham 8-parameter distributions (FB_8). The benefits are two-fold; firstly we can correctly weight the contributions of the data and model where the surface normals are uncertain, and secondly we can locate areas of shadow and facial hair using inconsistencies between the data and model. We sample the FBg distributions using a Gibbs sampling algorithm. These are then modelled as Gaussian distributions on the surface tangent plane defined by the model. The shape model provides a second Gaussian distribution describing the likely configurations of the model; these distributions are combined on the tangent plane of the directional sphere to give the most probable surface normal directions for all pixels. The Fisher criterion is used to locate inconsistencies between the two distributions and smoothing is used to deal with outliers originating in the shadowed and specular regions. A surface height model is then used to recover surface heights from surface normals. The combined approach shows improved results over the case when only surface normals from shape-from-shading are used.
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