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where the face part
h
f
is now composed by the averaged face template
h
f
,the
eigenface though gain mapping matrix
ʾ
, and
l
is the number of faces. The OAC
transform for the entire image is
H
f
(
2
H
(
X
,
Y
)=
X
,
Y
)
|
H
b
(
X
,
Y
)
|
(7.36)
where
H
f
and
H
b
are the nonlinear mapping response in Hilbert space
H
of
h
f
and
h
b
, respectively,
T
denotes the complex conjugate operation, and
X
Y
are the two-
dimensional transform domain indices. The labeled graph (LG) generated by this
transform is the adaptive ratio of target (face) signal peak height to the standard
deviation of the clutter (non-face) background of the image. From the fact that the
background power spectrum
,
2
|
H
b
(
X
,
Y
)
|
is unknown, we instead estimate it from
the spectrum of the entire image
H
. So we can calculate the adaptive priori
for a given image. The OAC detector is defined as
(
X
,
Y
)
M
T
2
D
(
X
,
Y
)=
↗|
H
(
X
,
Y
)
|
(7.37)
where
M
is a 5
5 matrix.
We then use kernel canonical correlation analysis (KCCA) [
212
] to get the
nonlinear correlation between
D
×
(
X
,
Y
)
and
H
(
X
,
Y
)
. A pair of directions
ˉ
D
and
D
and
H
ˉ
H
are obtained, such that the correlation between the two projections
ˉ
ˉ
is maximized.
For a given normalized image, we can estimate the face candidates in the
segmented image by arguing the OAC value of
D
(
X
,
Y
)
and
H
(
X
,
Y
)
,
arg max
a
i
b
i
C
∗
=
(7.38)
where
a
i
and
b
i
are respectively the projections of the variables
ʦ
(
D
)
and
H
on
i
ʦ
(
i
H
, and
i
ʦ
(
i
H
i
the projection vector
ˉ
and
ˉ
{
ˉ
)
,
ˉ
}
1
is the
t
pair directions of
=
D
)
D
OAC.
i
ʦ
(
D
)
)
T
a
i
=(
ˉ
ʦ
(
D
)
(7.39)
i
H
T
H
b
i
=(
ˉ
)
(7.40)
where
ʦ
(
D
)
is the diagonal of
D
(
X
,
Y
)
in the Hilbert space
H
. The segmentation
image mask
m
(
x
,
y
)
for the original image
g
(
x
,
y
)
is then generated from the
correlation image
h
(
x
,
y
)
as
0
C
∗
Th
h
(
x
,
y
)
<
m
(
x
,
y
)=
(7.41)
C
∗
Th
h
(
x
,
y
)
≥
1
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