Modeling and Synthesis of Realistic Visual Speech in 3D - 3D Modeling and Animation: Synthesis and Analysis Techniques for the Human Body - page 285

process. The animation tool described in this paper only proposes the speech-
based face animation as a point of departure. The animator can thereafter still
change the different visemes and their influences, as well as the complete splines
that define the trajectory in “Viseme Space.”
In terms of the space of possible deformations, PCA and ICA basically yield the
same result. As already mentioned, PCA is part of the ICA algorithm, and
determines the degrees of freedom to be kept. The importance of ICA mainly lies
in the more intuitive, manual changes that the animator can make afterwards. A
face contains many muscles, and several will be active together to produce the
different visemes. In as far as their joint effect can be modeled as a linear
combination of their individual effects, ICA is the way to decouple the net effect
again (Kalberer et al., 2002b). Of course, this model is a bit naive but,
nevertheless, one would hope that ICA is able to yield a reasonable decompo-
sition of face deformations into components that themselves are more strongly
correlated with the facial anatomy than the principal components. This hope has
proved not to be in vain.
From a mathematical point of view, there also is a good indication that ICA may
be more appropriate than PCA to deliver the basis of a Viseme Space. The
distribution of the extracted visemes comes out to have a shape that is quite non-
Gaussian, which can clearly be observed from

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χ plots.
Independent Component Analysis tries to explain data as a linear combination of
maximally independent basis signals, the “Independent Components.” Basically,
these independent components are found as the linear combinations of principal
components that have, in terms of information theory, minimal mutual informa-
tion between each pair of input. This is mathematically related to finding
combinations with distributions that are maximally non-Gaussian. As the central
limit theorem makes clear, distributions of composed signals will tend to be more
Gaussian than those of the underlying, original signals. For these reasons, ICA
often is successful in retrieving a set of original signals that can only be observed
together, e.g., to split mixed audio signals into their different components. These
separate, original components typically correspond to the maximally non-
Gaussian directions of the distribution that represents the joint probabilities of the
observed signal values. If the original signals have Gaussian distributions, ICA
will fail. The fact that the composed distributions in our case are already non-
Gaussian is an indication the ICA can make sense.
The advantage that independent components have over principal components
doesn't lie in their respective numbers, as, in fact, these are the same. Indeed,
the ICs are found in the reduced space spanned by the dominant PCs and this
space's dimension determines the number of ICs that ICA extracts (our
implementation of ICA follows that propounded by Hyvärinen (1997)). As
already mentioned, 16 components were used, which together cover 98.5% of