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1.2 Influences of lighting
Under the assumptions of Lambertian faces, distant illumination and ignoring
cast shadows, the proposed appearance features are not sensitive to changes of
lighting conditions. According to [Basri and Jacobs, 2001, Ramamoorthi and
Hanrahan, 2001b], the irradiance can be represented by a linear combination
of spherical harmonic basis function. For Lambertian surfaces, only the first 2
orders of the basis functions (9 basis) are needed to approximate the irradiance,
that is
where is a constant, is a coefficient decided by lighting, and is the
spherical harmonic basis function. Assuming that neutral face and the deformed
face are in the same lighting condition, we have
The high frequency facial motion can produce high frequency dif-
ferences between and and therefore between
and The irradiance will contain a linear combination
of these high frequency differences weighted by the lighting coefficients. In
other words, high frequency changes in are due to facial deformation
details, while lighting will only modulate them in low frequency. If the neutral
face and the deformed face are in different lighting conditions, the neutral face
texture can be relit to the lighting of the deformed face using face relighting
technique in [Wen et al., 2003]. According to [Wen et al., 2003], the relighting
is a low-frequency filtering processing so that the above arguments are still true.
1.3 Exemplar-based texture analysis
The appearance model are designed to model facial motion details that are not
captured by low dimensional geometric models. These motion details exhibit
much larger variation than geometric motions across different individuals and
lighting conditions. Thus a good low-dimensional subspace approximation of
motion details variation may be difficult. Nevertheless, facial motions exhibit
common semantic exemplars such as typical expressions and visemes, which
makes it meaningful to use exemplar-based approach such as [Toyama and
Blake, 2002]. In exemplar-based approach, an observation is interpreted using
the probability of the observation being each exemplar.
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