Graphics Reference
In-Depth Information
To explain the face appearance variation, we choose exemplars set
which are semantically meaningful such as face expressions
or visemes. A texture image is interpreted as a state variable
X
of the exemplars.
Unlike [Toyama and Blake, 2002], these exemplars incur both shape and texture
changes. Let
and
denote the shape and texture features respectively.
The observation is
We assume
and
are conditionally
independent given
X.
The observation likelihood is
In addition, we assume the texture features in different facial motion regions
are independent given
X.
Their log likelihoods are weighted by confidence
coefficients
to account for foreshortening effect. That is
where
Q
is the number of facial motion regions (
Q =
11). and
are modelled using Gaussian Mixture Model (GMM), assuming di-
agonal covariance matrices. The feature vectors are normalized by their mag-
nitudes. If the neutral face is chosen as an exemplar, we assign the likelihood
using a neutral face classifier such as [Tian and Bolle, 2001].
Based on the observation likelihoods in equation (7.5) and a dynamics model
(e.g. the HMM-based model described in [Toyama and Blake, 2002]),
can be computed using equation (7.7) according to [Rabiner,
1989]
In our experiment, we assume uniform conditional density
for
the dynamics model. Assuming uniform priors, we have
The exemplar tracking result can be displayed as
1.4 Online EM-based adaptation
A trained model for facial motion exemplars may work poorly if it can not
adapt to lighting changes, or differences in a new individual's exemplars. Fast
adaptation algorithm is needed to avoid re-training the model from scratch.
Furthermore, it is tedious to collect and label new training data for each new
condition. Therefore, we propose to progressively update the model during
tracking in an unsupervised way. Because the geometric features are less
person-dependent and less sensitive to lighting changes, we assume the geo-
metric component of the initial exemplar model can help to “confidently” track
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