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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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