Graphics Reference
In-Depth Information
the fact that the shape of facial curves is used to match each other to compute the similarity
between faces.
A possible way to smooth the effect of the noise without losing the effectiveness of rep-
resentations based on facial curves is to consider aggregations of facial curves instead of
individual ones. In practice, this corresponds to extend
facial curves
to
facial surfaces
.In
fact, the use of extended surfaces of the face should permit the punctual influence of noisy
data to be reduced, thus making the representation extracted from the facial surfaces more
descriptive and reliable. Following this intuition, the approaches in Samir et al. (2006) and
Samir et al. (2009) can be extended to the case of
iso-depth surfaces
and
iso-geodesic surfaces
,
respectively. In particular, the idea to describe the face using iso-geodesic surfaces has been
originally proposed in Berretti et al. (2006), and then developed in Berretti et al. (2010), and
Berretti et al. (2012).
In the approach of Berretti et al. (2010), the structural information of a face scan is captured
through the 3D shape and relative arrangement of
iso-geodesic stripes
identified on the 3D
surface. Iso-geodesic stripes are defined by computing, for every surface point, the normalized
geodesic distance between the point and a reference point located at the
nose tip
of the face.
Normalized values of the geodesic distance are obtained dividing the geodesic distance by the
Euclidean
eye-to-nose
distance, that is the sum of the distances between the nose tip and the
two points located at the inner commissure of the left and right eye fissure, and the distance
between the two points at the inner eyes. The algorithm reported in Mian et al. (2007) is used for
the identification of the nose tip and of the two inner eye points. This normalization guarantees
invariance of the distance values with respect to scaling of the face scan. Furthermore, since
the Euclidean eye-to-nose distance is invariant to face expressions, this normalization factor
does not bias values of the distance under expression changes.
The fact that geodesic and Euclidean distances of the face are capable to characterize
individual morphological traits of the face is strongly supported by studies of face anthropom-
etry conducted by Farkas (Farkas, 1994). These studies have evidenced that relevant facial
information is conveyed by measuring the Euclidean and geodesic distances, and the angles
between 47 fiducial points. Figure 3.27
a
,
b
, illustrate some of the fiducial points and facial
measurements.
v
v-tr
tr
tr
sci
sa
n
en-ex
ex
en
t
t
ch-t
or
prn
al
sn
sba
go
ear inclination
ch
sto
ch
gn
gn
mentocervical angle
(a)
(b)
Figure 3.27
(a) Some of the fiducial points proposed by Farkas:
alare
(al);
cheilion
(ch);
endocanthion
(en);
exocanthion
(ex);
gnathion
(gn);
nasion
(n);
orbitale
(or);
pronasale
(prn);
subnasale
(sn);
tragion
(t);
trichion
(tr);
vertex
(v). (b) Some facial measurements (Farkas, 1994): geodesic distance (ch-t);
Euclidean distances (v-tr and en-ex); angular measures (mentocervical angle and ear inclination)
