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

ponent color. The semantic facial score of the set T on a face image I(u, v), SF S T ,
is defined by prior weights on facial components and component matching scores as
follows:
SF S T =
∑ N−1
i=0
wt(i) · MS(i)
∑ N−1
i=0 wt(i) − ρ · SD (MS(i)) , (5.3)
where N is the number of semantic components, wt(i) and MS(i) are, respectively,
the a priori weight and the matching score of component i, ρ is a constant used to
penalize the components with high standard deviations of the matching scores, and
SD(x) stands for standard deviation of x.
The matching score for the i th facial component is computed based on the coherence
of the boundary and the coherence of color content (represented by a component
map) by
(
)
MS(i) = 1 M∑
i −1 A
1 ∑ i −1
e(u k , v k ) ·
M i A
j=0 i
k=0
∣ cos(θ
G
i (u j , v j ) − θ(u j , v j )) ∣ + f(uj , v j )
2
, (5.4)
where M i and A i are, respectively, the number of pixels along the curve of component
i and those of pixels covered by the component i, θ G i
and θ i are the normal direction
of component curve i in a semantic graph G and the gradient orientation of the image
I, f is the edge magnitude of the image I, and e(u k , v k ) is the facial component map
of the image I at pixel k. The gradients are computed as follows:
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