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Figure 3.2.
The markers of the Microsoft data [Guenter et al., 1998]. (a): The markers are

shown as small white dots. (b) and (c): The mesh is shown in two different viewpoints.

3. Learning Holistic Linear Subspace

To make complex facial deformation tractable in computational models, peo-

ple have usually assumed that any facial deformation can be approximated by

a linear combination of some basic deformation. In our framework, we make

the same assumption, and try to find optimal bases under this assumption. We

call these bases
Motion Units
(MUs). Using MUs, a facial shape

can be

represented by

where

denotes the facial shape without deformation,

is the mean facial

deformation,

is the MU set, and

is the MU

parameter (MUP) set.

In this topic, we experiment on both of the two databases described in Sec-

tion 2. Principal Component Analysis (PCA) [Jolliffe, 1986] is applied to learn-

ing MUs from the database. The mean facial deformation and the first seven

eigenvectors of PCA results 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 Fig-

ure 3.3. 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 The remaining faces are deformed by the first four MUs scaled by a

constant (from left to right). The method for visualizing MUs is described in

Section 5. Any arbitrary facial deformation can be approximated by a linear

combination of the MUs, weighted by MUPs. MUs are used in robust 3D facial

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