3D Face Surface Analysis and Recognition Based on Facial Surface Features - 3D Face Modeling, Analysis and Recognition - page 57

Table 2.1 Relation between signs of curvatures and geometric shapes of local patches of the surface

κ 1 > 0 κ 1 < 0 κ 1 = 0 H > 0 H < 0 H = 0

κ 2 > 0 pit n.p. n.p. pit peak n.p. G > 0

κ 2 < 0 saddle peak ridge saddle valley saddle ridge minimal surface G < 0

κ 2 = 0 valley n.p. plane valley ridge flat G = 0

n.p. means that the combination is not possible.

in the surface when relaxing the requirement of fixed curvature), and flatness. The signs of
the curvatures along with (near) zero curvatures (determined using appropriate thresholding)
along with region growing algorithm have been widely used for segmentation (Akagunduz
and Ulusoy, 2007; Besl and Jain, 1988; Moreno et al., 2003). Table 2.1 maps the signs of
curvatures to the geometric types of local patches, see Figure 2.4 for an illustration of such
facial surface segmentation.
Alternatively, the values of curvatures or their ranges along with constraints on the segments
such as proximity, smooth perimeters of the patches, and their areas could be used for clustering
the points into segments. The use of hierarchical clustering or K -means algorithms is typical
with these approaches.
The curvature-based patch segmentation is closely related to many landmark detection
approaches (Akagunduz and Ulusoy, 2007; Dibeklioglu et al., 2008; Segundo et al., 2007), in
terms of using the curvatures to detect the landmarks on the basis of their resemblance to the
geometric shapes mentioned above. The location of the facial landmarks (or fiducial points)
makes it possible to segment the facial surface into parts (part-segmentations).

2.3.2 Bilateral Profile-based 3D Face Segmentation
The tip of the nose (which is an important landmark of the face) and the ridge of the noise
lie on the plane of symmetry. Finding the plane of symmetry or its intersection with the
facial surface (bilateral profile line) can assist in detecting those landmarks accurately. The
detection/localization of these landmarks can also assist in the detection of the remaining ones
(based on relative positions). The extraction of the symmetry plane starts by finding an initial
course estimate of the plane (based on the principal directions of the face) then the points
of the surface are mirrored across that plane from both sides. The actual and mirror facial
surfaces are then iteratively registered. In each iteration, the symmetry plane is adjusted on the
basis of the new poses of the two facial surfaces. Zhang et al. (2006) use the bilateral profile
in addition to the mean curvature to detect the nose tip and the lowest point on the ridge of
the nose.
In the work by Mian et al. (2007), the nose tip in near frontal facial scans is detected. Then,
the facial surface is segmented by dropping the 3D points that lie outside a sphere centered
at the tip of the nose with a radius r 80 mm. The pose of the segmented facial surface is

then corrected to the frontal view using the principal directions of the face. The frontal view
and the knowledge of the location of the tip of the nose enables the segmentation of the parts
of the facial surface using image masks. The detection of the tip of the nose starts by slicing
the facial surface horizontally from top to bottom. Each resulting line is then searched for the

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