Estimation of Face Depths by Conditional Densities

The expected value of missing data in a sample taken from a multivariate normal probability distribution is the mean of the conditional distribution of the missing dimensions given the known dimensions. We explain the derivation of this result, demonstrate its application to face image processing, then use it in a new method for recovering shape from image data. The context of our work is the use of 3D facial models to aid in recognition of human faces by humans. We explain the requirement for such models and review the practical possibilities for encoding depth information alongside photographs in identity documents like passports. The best alternative is to derive depths automatically from the photos, as this requires no side information. We show experimentally that conditional density estimation provides accurate face depth recovery, without recourse to explicit modelling of surface shape.