FLEXIBLE APPEARANCE MODEL - 3D Face Processing: Modeling, Analysis and Synthesis - page 62

1.3.2 Person dependency
Facial appearance variations are highly person-dependent‚ because the dif-
ferent people have different facial surface properties and different styles of
motion. To deal with the variations across different people‚ one approach is to
collect training data from a variety of people. Nonetheless‚ the amount of data
needed to achieve good results could be huge.
For a Lambertian object‚ the ratio image [Liu et al.‚ 2001a] of its two aligned
images removes its surface albedo dependency thus allowing illumination terms
(geometry and lighting) to be captured and transferred. Therefore‚ the subtle
appearance changes due to detailed facial motion can be captured independent
of the face albedo. Then‚ the appearance changes can be mapped to people with
different albedos.
1.3.3 Online appearance model
The Expectation-Maximization (EM) technique [Dempster et al.‚ 1977] is
a framework for optimization with partial information. It is widely applied
for computing maximum likelihood estimates for parameters in incomplete
data models. By alternating between an expectation step (E-step)‚ which finds
expected completions of data given the current parameterization‚ and a maxi-
mization step (M-step)‚ which re-estimates parameters on the basis of completed
data‚ the EM algorithm gradually improves the likelihood for the observed data
until convergence at a local maximum.
Using the EM framework‚ Jepson et al. [Jepson et al.‚ 2001] propose an
online appearance model‚ which is updated at every frame by the EM algorithm
for adapting to newly observed facial appearance variations. However‚ only
current stable mode of facial appearance is modeled and the non-rigid facial
motions are not interpreted by the model.
An analogy of the the appearance model adaption problem in speech recog-
nition domain is speaker adaptation. A good survey can be found in [Woodland‚
1999]. One of the most popular schemes is to adjust model parameters such
that the likelihood or posterior probability of new adaptation data is maximized.
The EM algorithm can usually be used for this maximization process‚ treating
the parameters to be adjusted as “missing” parameters of the model. One type
of approach‚ called Maximum Likelihood Linear Regression (MLLR) [Gales
and Woodland‚ 1996]‚ is to linearly transform the parameters of a speaker-
independent model such that the likelihood of the adaptation data of a particular
person is maximized. MLLR has the advantage that the same linear transfor-
mation can be used to update all parameters to be adjusted‚ even if the number
is large. If relatively few parameters to be adjusted‚ MLLR will be robust and
unsupervised adaptation can be used. In practice‚ research has shown that it is
effective to adjust the mean and covariance of the acoustic GMM model using
MLLR.