Learning 3D Face Deformation Model: Methods and Applications - 3D Modeling and Animation: Synthesis and Analysis Techniques for the Human Body - page 324

Learning Holistic Linear Subspace

To make complex facial deformation tractable in computational models, re-
searchers have usually assumed that any facial deformation can be approxi-
mated by a linear combination of basic deformation. In our framework, we make
the same assumption and try to find optimal bases. We call these bases Motion
Units (MUs). Using MUs, a facial shape s can be represented by

M

∑ =

s = s + ( c e + e )

(1)

0 0

i i

i 1

s e

where denotes the facial shape without deformation, is the mean facial

e

, e

e

c , c , …,

c deformation, { , ..., } is the MU set, and { } is the MU

M

parameter (MUP) set.
PCA (Jolliffe, 1986) is applied to learning MUs from the facial deformation of
the database. The mean facial deformation and the first seven eigenvectors are
selected as the MUs. The MUs correspond to the largest seven eigenvalues that
capture 93.2% of the facial deformation variance. The first four MUs are
visualized by an animated face model in Figure 4. The top row images are the
frontal views of the faces and the bottom row images are side views. The first

face is the neutral face, corresponding to s . The remaining faces are deformed
by the first four MUs scaled by a constant (from left to right). The method for

Figure 4. The neutral and deformed faces corresponding to the first four
MUs. The top row is the frontal view and the bottom row is the side view.