Information Technology Reference
In-Depth Information
•
Absolute value of the difference of the
y
-coordinate (
F
2
)
This is the normalized absolute value of the difference of the
y
-coordinate
y
ij
be-
tween
p
i
and
p
j
as shown in Fig. 2 (b). The absolute difference is divided by
d
for
the normalization. This facial feature is defined taking into consideration the ten-
dency that the
y
-coordinates of the facial feature points can be largely change when
a certain kind of facial expression (e.g., surprise or laughter) appears.
•
Ratio of the lengths of two line segments (
F
3
)
This is the ratio of the length of the line segment
l
ij
to that of the line segment
l
ik
as
shown in Fig. 2 (c). These line segments are formed by three facial feature points
p
i
,
p
j
,and
p
k
. This facial feature can represent the relative positional relationship
between three facial components.
•
Angle between two line segments (
F
4
)
This is the angle
between the line segments
l
ij
and
l
ik
.This
facial feature is shown in Fig. 2 (d). We attempt to make use of the shape of a facial
component using this feature value. For example, the shape of a corner of a mouth
is associated with this feature value obtained from the facial feature points near the
corner of a mouth.
θ
ij
,
ik
(
0
≤
θ
ij
,
ik
≤
π
)
•
Cosine of the angle between two line segments (
F
5
)
This facial feature value is defined as the cosine of
F
4
,thatis,cos
θ
ij
,
ik
.Itrepresents
the shape of a facial component from different aspect.
•
Area of a triangle (
F
6
)
This is the normalized area of the triangle
A
ijk
formed by three facial feature points
p
i
,
p
j
,and
p
k
as shown in Fig. 2 (e). The area is divided by
d
2
for the normalization.
This facial feature can be an approximation of the area of a facial component.
•
Ratio of the area of a triangle to the squared sum of the lengths of three sides
of the triangle (
F
7
)
This is the ratio of the area of the triangle
A
ijk
to the square of the sum of the lengths
of the three sides
l
ij
,
l
ik
,and
l
jk
. This facial feature is shown in Fig. 2 (f) and its value
is
A
ijk
/
(
2
. It is defined based on the shape of a triangle as well as the
+
l
ik
+
l
jk
)
l
ij
area of a triangle.
•
Internal angles of a triangle (
F
8
)
This feature value is based on the three internal angles
θ
ij
,
jk
,
θ
ij
,
ik
,and
θ
ik
,
jk
in the
|
θ
ij
,
jk
−
3
|
+
|
θ
ij
,
ik
−
triangle shown in Fig. 2 (g). It is computed by the equation
3
|
+
|
θ
ik
,
jk
−
3
|
. This feature value is associated with the shape of a triangle and it
is minimized (becomes zero) when the triangle is a regular triangle.
These facial feature values are defined for all the possible combinations of the
facial feature points. The number of
F
1
or
F
2
is 1711 (
=
59
C
2
), that of
F
3
,
F
4
,or
F
5
is
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