FLEXIBLE APPEARANCE MODEL - 3D Face Processing: Modeling, Analysis and Synthesis - page 68

Given two aligned images of person A's face and suppose is

the neutral face image and is the image of the deformed face. Based on

equation 6.11‚ we have

For a different person B‚ if we know its neutral face image we can compute
the deformed face image of B where B has the same motion as A. Similarly‚ we
can compute the ratio image for B as

We assume the images of A and B are aligned‚ that is‚ for every point on A‚
there is a corresponding point on B which has the same semantics (eye corners‚
mouth corners‚ etc). This alignment can be done using the techniques described
in Section 2.1.3. Since human faces have approximately the same geometrical
shapes‚ their surface normals at corresponding points are roughly the same‚
that is‚ We also assume that the deformation of the two

faces are roughly the same. Then we have Based on

equation 6.3‚ we can derive and

That leads to

From equations 6.12‚ 6.13 and 6.14‚ we can compute the unknown image as

Here the multiplication means pixel-by-pixel multiplication of the two images.
Besides computing novel face image for synthesis‚ ratio image can also be
used to design less person dependent appearance features for motion analysis.
This aspect will be discussed in more details in Chapter 7.

2.2.3 Transfer illumination using ratio image
The albedo-independency of ratio image also enables illumination effects
transfer across different surfaces. Wen et al. [Wen et al.‚ 2003] use this property
for face relighting from a single face image.
Following the derivation in Section 2.2.2‚ if the difference between and
is illumination effects instead of non-rigid motion‚ we can obtain the same
equation 6.15 for computing novel face appearance in the lighting envi-
ronment of More generally‚ A could be other objects such as the sphere
of radiance environment map. Then we can use the REM illumination model
together with equation 6.15 for modifying illumination effects in face images.