  Face frontalization consists of synthesizing a frontally-viewed face from an
arbitrarily-viewed one. The main contribution of this paper is a robust face
alignment method that enables pixel-to-pixel warping. The method simultaneously
estimates the rigid transformation (scale, rotation, and translation) and the
non-rigid deformation between two 3D point sets: a set of 3D landmarks
extracted from an arbitrary-viewed face, and a set of 3D landmarks
parameterized by a frontally-viewed deformable face model. An important merit
of the proposed method is its ability to deal both with noise (small
perturbations) and with outliers (large errors). We propose to model inliers
and outliers with the generalized Student's t-probability distribution
function, a heavy-tailed distribution that is immune to non-Gaussian errors in
the data. We describe in detail the associated expectation-maximization (EM)
algorithm that alternates between the estimation of (i) the rigid parameters,
(ii) the deformation parameters, and (iii) the Student-t distribution
parameters. We also propose to use the zero-mean normalized cross-correlation,
between a frontalized face and the corresponding ground-truth frontally-viewed
face, to evaluate the performance of frontalization. To this end, we use a
dataset that contains pairs of profile-viewed and frontally-viewed faces. This
evaluation, based on direct image-to-image comparison, stands in contrast with
indirect evaluation, based on analyzing the effect of frontalization on face
recognition.
