Graphics Reference
In-Depth Information
The Nonrigidity of the Human Face
The 3D shape of the human face is highly deformable as a result of aging, weight loss/gain and
most prominently following variations in facial expressions. These variations pose challenges
to 3D face recognition as they can obscure those arising from identity variations (shape
variations among different individuals) on the basis of which individuals are recognized.
This is because the 3D shape variations of the human face among different individuals are
statistically small. In fact, some facial expressions, in addition to the geometric changes, can
induce topological changes to the 3D facial surface, such as those involving mouth opening.
Nevertheless, the nonrigidity of the human face is not arbitrary, particularly the one related to
facial expressions because the anatomical structure of the face remains unchanged. This factor
makes the modeling of the facial expressions or the extraction of expression-invariant features
for 3D face recognition possible. Another aspect of the nonrigidity due to facial expressions
is that some facial regions such as the nose and the forehead (called the semirigid regions) are
(to an extent) less affected by facial expressions. In addition, some facial regions (possibly
other than the semi rigid ones) may be less deformed than some others, depending on the
facial expression of the face. The two latter aspects have allowed for the development of
rigid
approaches to 3D face recognition (where the 3D face or some of its parts are treated as if they
are rigid) that are invariant to facial expressions.
The Symmetry of the Human Face
The 3D shape of the human face is bilaterally symmetric about a plane splitting the face
into two mirror, left and right, halves (to a large extent). Interestingly, facial symmetry holds
considerably not only for faces under neutral expression but also for most facial expressions,
especially those that naturally express emotional states or result from talking. The symmetry
of the face has been employed by many 3D face recognition systems for a number of tasks. It
was used for pose estimation and correction of 3D faces (e.g., Pan and Wu, 2005), whereby
they estimate the facial symmetry plane and define reference points on the symmetry profile
(i.e., the intersection between the symmetry plane and the 3D face). It was also used for feature
extraction or dimensionality reduction of the facial data (e.g., Gnanaprakasam et al., 2010;
Harguess et al., 2008). Other applications in which facial symmetry was exploited include,
and is not limited to, the interpolation of holes in raw facial data (for a better estimation of
the missing data), the localization of the fiducial points (for more robustness and accuracy),
the detection of the face (for an enhanced detection efficiency), and the normalization of
illumination of textured 3D faces. Nevertheless, the asymmetry of the human face can also be
of importance to face recognition as it may be person specific.
Fiducial Points of the Human Face
There are natural landmark points on the facial surface called the fiducial points, which can be
detected even when the face is deformed. Typical fiducial points include the eye corners, the mid
point between the eyes, the tip of the nose and its two lower corners, the furthest chin point,
and mouth corners. Sometimes, it is needed to establishing point-to-point correspondence
between two or more facial scans of the same person or of different people, as is the case
