Projection of face images in 9-D spherical harmonic
The multiplication of two spherical harmonic basis satisfies the following relation according
to [Cohen-Tannoudji and et al., 1977]:
where is the Clebsch-Gordan coefficients. The coefficient of
in the righthand side is non-zero if and only if
and is even.
We then look at the second term of the righthand side in equation 6.7. Suppose
comes from and comes from the factor corresponding to lighting. For any
we have If for any we have That
proves the claim that if does not have the first four order components, the
second term of the righthand side in equation 6.7 contains components with orders equal to or
higher than 3.