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

ased on the skin cluster model obtained from a subset of the HHI database. The
model is specified by the centers (denoted as C b (Y ) and C r (Y )) and widths of the
cluster (denoted as W c b (Y ) and W c r (Y )) (See Fig. 3.5). The following equations
describe how this transformation is computed.
⎧
( ⎪⎨ Ci (Y ) − C i (Y ) ) W c · i
C i(Y ′ W c i (Y )
) =
+ C i(K h ) if Y < K l or K h < Y,
⎪⎩ C i (Y ) if Y ∈ [K l , K h ],
⎧
⎪⎨
W c i (Y ) =
⎪⎩
⎧
⎪⎨
C b (Y ) =
⎪⎩
⎧
⎪⎨
C r (Y ) =
⎪⎩
W Lc i + (Y −Y min)·(W c i −W Lc i )
K l −Y min
if Y < K l ,
W Hc i + (Y max−Y )·(W c i −W Hc i )
Y max −K h
if K h < Y,
108 + (K l−Y )·(118−108)
K l −Y min
if Y < K l ,
108 + (Y −K h)·(118−108)
Y max −K h
if K h < Y,
154 − (K l−Y )·(154−144)
K l −Y min
if Y < K l ,
154 + (Y −K h)·(154−132)
Y max −K h
if K h < Y,
(A.3)
(A.4)
(A.5)
(A.6)
where C i in Eqs. (A.3) and (A.4) is either C b or C r , W c b = 46.97, W Lc b = 23,
W Hc b = 14, W c r = 38.76, W Lc r = 20, W Hc r = 10, K 1 = 125, and K h = 188. All
values are estimated from training samples of skin patches on a subset of the HHI
images. Y min and Y max in the Y C b C r color space are 16 and 235, respectively. Note
that the boundaries of the cluster are described by two curves C i (Y ) ± W c i (Y )/2,
155