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some new data samples. Then the Expectation-Maximization (EM) frame-
work [Dempster et al., 1977] can be applied to update the model parameters.
At time
the E-step provides exemplar ownership probabilities defined as
where is the index of the exemplars. In the M-step, the model is adapted
by computing new maximum likelihood estimates of its parameters. Note that
we only adapt the texture part of the model because shape features are less
person-dependent and not sensitive to changes of lighting.
The idea of Maximum Likelihood Linear Regression (MLLR) can be gener-
alized to this adaptation problem, where we estimate a linear transformation of
the GMM mean vectors to maximize the likelihood of new observations. How-
ever, conventional MLLR is not an online method which requires multiple data
samples for maximum likelihood optimization. In the M-step of our online EM
algorithm, only one data sample is available at a time. Thus we constrain the
transformation of the GMM mean vectors to be translation only. The M-step
of our algorithm is then to estimate which denotes the translation of
the GMM mean vectors from initial model, for the facial motion region, the
exemplar at time To weight the current data sample appropriately against
history, we consider the data samples under an exponential envelope located
at the current time as in [Jepson et al., 2001],
For the GMM model of certain value, suppose the GMM has M com-
ponents denoted by Here the subscripts
are dropped for simplicity. Given an adaptation data sample the
ML estimate of the translation can be computed by solving equation (7.9)
according to [Gales and Woodland, 1996]:
where is GMM component occupancy probability defined as the probability
that draws from the component of the GMM given draws from this
GMM. is the texture feature of the current adaptation data. A closed-form
solution for equation (7.9) is feasible when
is diagonal. The
element of
can be computed as
is the
diagonal element of
is the
element of
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