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

and are shown as blue-dashed lines in Fig. 3.5(a) for C b and in Fig. 3.5(b) for C r .
A.3 Skin Classifier
The elliptical model for the skin tones in the transformed C ′ b -C′ r space is described in
Eqs. (A.7) and (A.8), and is depicted in Fig. 3.6.
(x − ecx) 2 (y − ecy)2
+ = 1, (A.7)
⎡ ⎤
a 2
⎡
b 2 ⎤ ⎡ ⎤
⎢
x
⎥
⎣ ⎦ = cos θ sin θ
C
b ′ ⎢
⎥ ⎢
− cx
⎥
⎣
⎦ ⎣ ⎦ ,
(A.8)
y − sin θ cos θ C r ′ − cy
where cx = 109.38, cy = 152.02, θ = 2.53 (in radian), ecx = 1.60, exy = 2.41,
a = 25.39, and b = 14.03. These values are computed from the skin cluster in the
C ′ b -C′ r space at 1% of outliers.
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