LEARNING GEOMETRIC 3D FACIAL MOTION MODEL - 3D Face Processing: Modeling, Analysis and Synthesis - page 22

motion analysis presented in Chapter 4, and facial motion synthesis presented
in Chapter 5.
Figure 3.3. The neutral face and deformed face corresponding to the first four MUs. The top
row is frontal view and the bottom row is side view.
4. Learning Parts-based Linear Subspace
It is well known that the facial motion is localized, which makes it possible
to decompose the complex facial motion into smaller parts. The decomposition
helps: (1) reduce the complexity in deformation modeling; (2) improve the ro-
bustness in motion analysis; and (3) flexibility in synthesis. The decomposition
can be done manually based on the prior knowledge of facial muscle distri-
bution, such as in [Pighin et al., 1999, Tao and Huang, 1999]. However, the
decomposition may not be optimal for the linear combination model used be-
cause of the high nonlinearity of facial motion. Parts-based learning techniques,
together with extensive motion capture data, provide a way to help design parts-
based facial deformation models, which can better approximate real local facial
motion. Recently several learning techniques have been proposed for learning
representation of data samples that appears to be localized Non-negative matrix
Factorization (NMF) [Lee and Seung, 1999] has been shown to be able to learn
basis images that resemble parts of faces. In learning the basis of subspace,
NMF imposes non-negativity constraints, which is compatible to the intuitive
notion of combining parts to form a whole in a non-subtractive way.
In our framework, we present a parts-based face deformation model. In the
model, each part corresponds to a facial region where facial motion is mostly
generated by local muscles. The motion of each part is modeled by PCA as
described in Section 3. Then, the overall facial deformation is approximated