FLEXIBLE APPEARANCE MODEL - 3D Face Processing: Modeling, Analysis and Synthesis - page 67

coefficients in equation 6.8 and obtain the approximated radiance environment
map.
Note that it is an under-constrained problem to determine all the 9 coefficients
from a single frontal image of a face according to [Ramamoorthi‚ 2002]. To
produce plausible illumination approximation results without conflicting with
the information provided by the frontal image‚ we make assumptions about
lighting in the back to constrain the problem. One of the assumptions that
we make is to assume a symmetric lighting environment‚ that is‚ the back has
the same lighting distribution as the front. This assumption is equivalent to
assuming for in equation (6.6). The
rest of the coefficients can then be solved uniquely according to [Ramamoorthi‚
2002]. One nice property about this assumption is that it generates the correct
lighting results for the front‚ and it generates plausible results for the back
if faces rotate in the lighting environment. For applications which deal with
only frontal lighting‚ the symmetric assumption produces correct results. If
we want to synthesize face appearance after the face is rotated in the lighting
environment‚ we need to make the assumption based on the scene. For example‚
in the cases where the lights mainly come from the two sides of the face‚ we
use symmetric assumptions. In the cases where the lights mainly come from
the front‚ we assume the back is dark.

2.2 Reduce person dependency based on ratio-image
technique
2.2.1 Ratio image
In Section 2.1.1‚ we have derived the formula (equation 6.4) for the intensity
of the neutral face point at After the face surface is deformed‚ the

intensity of is

We denote

It can be observed that called the ratio image‚ is independent of surface

reflectance property [Liu et al.‚ 2001a]. Therefore‚ can be used

to as a facial motion representation independent of face albedos.

2.2.2 Transfer motion details using ratio image
The albedo-independency of ratio image give a novel representation of facial
motion field which is less person dependent than the original image. Liu et
al. [Liu et al.‚ 2001a] use this property to map facial expressions from one
person to another and achieve photo-realistic results.