A Groupwise Multilinear Correspondence Optimization for 3D Faces

Multilinear face models are widely used to model the space of human faces with expressions. For databases of 3D human faces of different identities performing multiple expressions, these statistical shape models decouple identity and expression variations. To compute a high-quality multilinear face model, the quality of the registration of the database of 3D face scans used for training is essential. Meanwhile, a multilinear face model can be used as an effective prior to register 3D face scans, which are typically noisy and incomplete. Inspired by the minimum description length approach, we propose the first method to jointly optimize a multilinear model and the registration of the 3D scans used for training. Given an initial registration, our approach fully automatically improves the registration by optimizing an objective function that measures the compactness of the multilinear model, resulting in a sparse model. We choose a continuous representation for each face shape that allows to use a quasi-Newton method in parameter space for optimization. We show that our approach is computationally significantly more efficient and leads to correspondences of higher quality than existing methods based on linear statistical models. This allows us to evaluate our approach on large standard 3D face databases and in the presence of noisy initializations.