Gaussian mixture 3D morphable face model

3D Morphable Face Models (3DMM) have been used in pattern recognition for some time now. They have been applied as a basis for 3D face recognition, as well as in an assistive role for 2D face recognition to perform geometric and photometric normalisation of the input image, or in 2D face recognition system training. The statistical distribution underlying 3DMM is Gaussian. However, the single-Gaussian model seems at odds with reality when we consider different cohorts of data, e.g. Black and Chinese faces. Their means are clearly different. This paper introduces the Gaussian Mixture 3DMM (GM-3DMM) which models the global population as a mixture of Gaussian subpopulations, each with its own mean. The proposed GM-3DMM extends the traditional 3DMM naturally, by adopting a shared covariance structure to mitigate small sample estimation problems associated with data in high dimensional spaces. We construct a GM-3DMM, the training of which involves a multiple cohort dataset, SURREY-JNU, comprising 942 3D face scans of people with mixed backgrounds. Experiments in fitting the GM-3DMM to 2D face images to facilitate their geometric and photometric normalisation for pose and illumination invariant face recognition demonstrate the merits of the proposed mixture of Gaussians 3D face model.