GEOMETRIC MODEL-BASED 3D FACE TRACKING - 3D Face Processing: Modeling, Analysis and Synthesis - page 30

(3) statistical shape and appearance models, such as ASM [Cootes et al., 1995]
and AAM [Cootes et al., 1998].

1.1 Parameterized geometric models

1.1.1 B-Spline curves

Blake et al. [Blake et al., 1993] propose parametric B-spline curves for con-
tour tracking. The tracking problem is to estimate the control points of the
B-spline curve so that the B-spline curve matches the contour being tracked as
closely as possible. However, without global constraints, B-spline curves tend
to match contours locally, resulting in wrong matching among contour points.
The robustness of the algorithm could be improved by employing constraints
on the possible solution subspace of the contour points [Blake et al., 1995].
Therefore, it prevents generating physically impossible curves. Instead of us-
ing grey-level edge information, Kaucic and Blake [Kaucic and Blake, 1998]
and Chan [Chan, 1999] utilize the characteristics of human skin color. They
propose using either Bayesian classification or linear discriminant analysis to
distinguish lips and other areas of facial skin. Therefore, the contours of the
lips can be extracted more reliably. It is well known that color segmentation
is sensitive to lighting conditions and the effectiveness of color segmentation
depends on the subject. This can be partially solved by training a color classi-
fier for each individual. Nevertheless, these two approaches do not handle 3D
rotation, translation and appearance changes of lips.

1.1.2 Snake model

Kass et al. [Kass et al., 1988] propose the snake for tracking deformable
contours. It starts from an initial starting point and deforms itself to match
with the nearest salient contour. The matching procedure is formulated as an
energy minimization process. In basic Snake-based tracking, the function to
be minimized includes two energy terms: (1) internal spline energy caused
by stretching and bending, and (2) measure of the attraction of image features
such as contours. B-Spline [Blake et al., 1993] is a “least squares” style Snake
algorithm. Snakes rely on gray-level gradient information for measuring the
energy terms of the snakes. However, it is possible that gray-level gradients
in images are inadequate for identifying the contour. Therefore, Terzopoulos
and Waters [Terzopoulos and Waters, 1990a] highlighted the facial features by
makeup to help Snake-based tracking. Otherwise, Snakes very often align onto
undesirable local minima. To improve Snakes, Bregler and Konig [Bregler and
Konig, 1994] propose eigenlips that incorporate a lip shape manifold into Snake
tracker for lip tracking. The shape manifold is learned from training sequences
of lip shapes. It imposes global constraints on the Snake contour shape model.