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In-Depth Information
G
−
1
z
=
(
s
)
(7.31)
G
−
1
=
[
T
(
r
)]
(7.32)
Finally, LND is applied on the result image by assuming the gray values are
drawn form a normal distribution. The output image
h
(
x
,
y
)
is normalized using
Eq. (
7.33
),
G
−
1
(
)
−
μ
i
˃
i
s
h
(
x
,
y
)=
(7.33)
˃
i
are the mean and standard deviation of
G
−
1
where
μ
i
and
[
T
(
r
)]
over the whole
image.
This illumination compensation procedure can account for the effects of illumi-
nation variations, local shadowing and highlights for faces in the original image,
therefore, the procedure preserves the essential elements of visual appearances for
detection.
7.5.1.3
Candidate Selection
After illumination compensation, a modified OAC method [
211
] is applied to
the normalized image
h
to locate face candidates. Compared with common
automatic face detection algorithms, this method does not need to use a pyramid
of downscaled copies of the input image and thus speeds up the processing. The
normalized image has similar power spectra and can be efficiently implemented in
the spatial domain in a running window that approximately meets the requirements
of the OAC process. This algorithm is adaptive to the input normalized image, and
is designed to complete the segmentation in a single iteration in Hilbert space
H
,
through the kennel function
H
transform. The transform of the normalized image
is a correlation image with normalized values ranging from zero to one. The OAC
detector examines this image and segments it according to the range of correlation
values. The image is then split into two segments after the correlation examination
that corresponds to face candidates and background regions, which can be used
conveniently by the later fine classifier with Gabor and AdaBoost algorithm.
Assume we have a normalized image
h
(
x
,
y
)
(
x
,
y
)
with multiple faces part
h
f
(
x
,
y
)
and
complex background part
h
b
(
x
,
y
)
, i.e.,
h
(
x
,
y
)=
h
f
(
x
,
y
)+
h
b
(
x
,
y
)
(7.34)
The face part
h
f
and background part
h
b
can be modulated as uncorrelated
independent signals, so we have
l
k
=
1
ʾ
k
h
f
(
h
(
x
,
y
)=
↗
x
,
y
)+
h
b
(
x
,
y
)
(7.35)
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