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points. With a manually intensive procedure, they were able to generate highly
realistic face models. Fua and Miccio [Fua and Miccio, 1998] developed system
which combine multiple image measurements, such as stereo data, silhouette
edges and 2D feature points, to reconstruct 3D face models from images.
Because the 3D reconstructions of face points from images are either noisy
or require extensive manual work, researcher have tried to use prior knowledge
as constraints to help the image-based 3D face modeling. One important type
of constraints is the “linear classes” constraint. Under this constrain, it assumes
that arbitrary 3D face geometry can be represented by a linear combination of
certain basic face geometries. The advantage of using linear class of objects
is that it eliminates most of the non-natural faces and significantly reduces the
search space. Vetter and Poggio [Vetter and Poggio, 1997] represented an ar-
bitrary face image as a linear combination of some number of prototypes and
used this representation (called linear object class) for image recognition, cod-
ing, and image synthesis. In their representative work, Blanz and Vetter [Blanz
and Vetter, 1999] obtain the basis of the linear classes by applying Principal
Component Analysis (PCA) to a 3D face model database. The database con-
tains models of 200 Caucasian adults, half of which are male. The 3D models
are generated by cleaning up, registering the Cyberware TM scan data. Given a
new face image, a fitting algorithm is used to estimate the coefficients of the lin-
ear combination. They have demonstrated that linear classes of face geometries
and images are very powerful in generating convincing 3D human face models
from images. For this approach to achieve convincing results, it requires that
the novel is similar to faces in the database and the feature points of the initial
3D model is roughly aligned with the input face image.
Because it is difficult to obtain a comprehensive and high quality 3D face
database, other approaches have been proposed using the idea of “linear classes
of face geometries”. Kang and Jones [Kang and Jones, 1999] also use linear
spaces of geometrical models to construct 3D face models from multiple images.
But their approach requires manually aligning the generic mesh to one of the
images, which is in general a tedious task for an average user. Instead of
representing a face as a linear combination of real faces, Liu et al. [Liu et al.,
2001b] represent it as a linear combination of a neutral face and some number
of face metrics where a metric is a vector that linearly deforms a face. The
metrics in their systems are meaningful face deformations, such as to make the
head wider, make the nose bigger, etc. They are defined interactively by artists.
1.3 Summary
Among the many approaches for 3D face modeling, 3D range scanners pro-
vide high quality 3D measurements for building realistic face models. However,
most scanners are still very expensive and need to be used in controlled environ-
ments. In contrast, image-based approaches have low cost and can be used in
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