Face Detection and Modeling for Recognition - Biometrics Research ...

tw(i, j, k) = emw(i, j, k) · ow(i, j, k) · q(i, j, k); (3.15)
emw(i, j, k) = 1 (ew(i, j) + mw(k));
2
(3.16)
ew(i, j) = EyeMap(x i, y i ) + EyeMap(x j , y j )
;
2 · EyeMap(x m , y m )
i > j; i, j ∈ [1, N eye ]; (3.17)
mw(k) = MouthMap(x k, y k )
MouthMap(x m , y m ) ; k ∈ [1, N mth]; (3.18)
ow(i, j, k) =
2∏
e −3(1−cos2 (θ r (i,j,k))) ;
r=1
cos(θ r (i, j, k)) = ⃗u r · ⃗v r
‖⃗v r ‖ ;
‖⃗v r ‖ = 1. (3.19)
Eq. (3.17) describes the eye-pair weight which is the normalized average of the eye
map value around the two eyes, where EyeMap(x i , y i ) is the eye map value for the
i-th eye candidate (associated with an eye blob and a corresponding pixel in the
lowest level of the image pyramid). EyeMap(x m , y m ) is the eye map value for the
most significant eye candidate (having the highest response within the eye map). The
mouth weight, mw(k) in Eq. (3.18), is obtained by normalizing the mouth map value
at the k-th mouth candidate (i.e., a mouth blob), MouthMap(x k , y k ), by the mouth
map value at the most significant mouth candidate, MouthMap(x m , y m ). The faceorientation
weight, described in Eq. (3.19), is the product of two attenuation terms,
each of which is an exponential function of a projection (cosθ r ) of a vector (⃗v r ) along a
particular direction ( ⃗u r ), where r = 1, 2. As can be seen in Fig. 3.13, one term favors
a symmetric face, and it is a projection (cosθ 1 ) of the vector ⃗v 1 (from the midpoint of
the two eyes to the mouth) along a vector ( ⃗u 1 ) that is perpendicular to the interocular
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