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Figure 6.1.
A face albedo map.
we obtain the radiance environment map with reflectance coefficient equal to
the average albedo of the surface. This observation agrees with [Ramamoorthi
and Hanrahan‚ 2001b] and perception literature (such as Land's retinex the-
ory [Land and McCann‚ 1971])‚ where on Lambertian surface high-frequency
variation is due to texture‚ and low-frequency variation probably associated
with illumination.
We believe that human face skins are approximately this type of surfaces. The
skin color of a person's face has dominant constant component‚ but there are
some fine details corresponding to high frequency components in frequency
domain. Therefore the first four order components must be very small. To
verify this‚ we used
SpharmonicKit
[SphericalHarmonic‚ 2002] to compute
the spherical harmonic coefficients for the function of the albedo map
shown in Figure 6.1 which was obtained by Marschner et al. [Marschner et al.‚
2000]. There are normals that are not sampled by the albedo map‚ where we
assigned the mean of existing samples. We find that the coefficients of
order 1‚ 2‚ 3‚ 4 components are less than 6% of the constant coefficient.
2.1.3 Approximating a radiance environment map from a single image
Given a single photograph of a person's face‚ it is possible to compute its
3D geometry [Blanz and Vetter‚ 1999‚ Zhang et al.‚ 2001]. Alternatively‚ we
choose to use a generic geometric model (see Figure 8.2(a)) because human
faces have similar shapes‚ and the artifacts due to geometric inaccuracy are not
very strong since we only consider diffuse reflections.
Given a photograph and a generic 3D face geometry‚ we first align the face
image with the generic face model. Details of the 2D-3D alignment is discussed
in the implementation Section 1.3 of Chapter 8. After the photograph is aligned
with the 3D geometry‚ we know the normal of each face pixel and thus can
compute the
term in equation 6.8. Next‚ we can solve for the lighting
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