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              <p>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.</p>
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