Graphics Reference
In-Depth Information
in some approaches to expression modeling and expression invariant face recognition. For
rigid surfaces, an accurate point-to-point correspondence is possible (e.g., by using the ICP
algorithm). However, for deformable surfaces, the establishment of such correspondences is
more difficult. The problem can be undermined by first establishing correspondences between
the fiducial points of the facial scans. The fiducial points are also used as standard locations
from which local features can be extracted for 3D face recognition. Additional features can be
extracted from their relative locations for further enhancement of the recognition.
Self-Occlusions of the Human Face
Depending on the pose of the 3D face relative to the viewpoint of the 3D digitizer, parts of the
scanned facial surface can be self-occluded because some of the visible regions block the line
of sight between the 3D digitizer and the occluded regions. As a result, the occluded facial
surface regions cannot be digitized and will appear as holes in the single view scan (often
referred to as 2.5D scan). In profile facial scans, where the face is scanned from roughly either
the left or right side, all or large parts of the opposite side can be self-occluded. The side
of the nose, which is considered to be a highly discriminative region of the face, is easily
occluded even for a moderate side pose. On the other hand, facial scanning from frontal or
near frontal viewpoints is least affected by self-occlusions. In this case, all or nearly all of
the facial regions are visible to the 3D digitizer. Additionally, near frontal scanning is less
susceptible to occlusions by hair and clothing.
On that basis, the frontal facial pose is the choice of most recognition systems that match
2.5D probes scans against a gallery of 2.5D scans. The recovering of occluded regions is
possible by performing a scan from different viewpoints. From these multiple scans of the
face, a complete facial model can be generated from ear to ear. The online generation of
complete models (as probes) is not practical for most applications (complete against complete
model matching). However, matching 2.5D probes against complete gallery models is more
practical (offline model completion) and reduces the effects of occlusions (limited to the
probes) and allows for the matching of both frontal and profile 2.5D probes.
2.2 Curvatures Extraction from 3D Face Surface
3D facial surface curvatures (or curvature-like quantities) have been widely used in 3D face
recognition systems. Some 3D face preprocessing approaches (e.g., surface smoothing), 3D
face or subregion segmentation, feature extraction, and the detection of facial fiducial points
rely on some (or all) of the different types of surface curvatures. This section first discusses
the concepts and mathematical definitions of 3D curvatures and then covers some practical
methods for their extraction. For further information on this topic, the reader is referred to
textbooks on differential geometry such as those by O'Neill (2006) and Bar (2010).
2.2.1 Theoretical Concepts on 3D Curvatures
Curvature of 3D Curves
The curvature is a measure of how much a curve is bent. In other words, the curvature at a
point on the curve is the extent at which the curve locally deviates from the tangent at the
