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where
k
k
cos
θ
⎛
⎞
⎛
⎞
ix
v
μ
⎜
⎜
⎝
⎟
⎟
⎠
⎜
⎜
⎝
⎟
⎟
⎠
k
=
=
(7)
i
k
k
sin
θ
iy
v
μ
Ψ
i
(
x
)
is a plane wave characterized by the vector
k
i
enveloped by a Gaussian
function, where
Each
is the standard deviation of this Gaussian. The center frequency of
i
th
filter is given by the characteristic wave vector
k
i
having a scale and orientation
given by (
k
v
,
σ
θ
µ
)
.
Convolving the input image with a number of complex Gabor filters
with 5 spatial frequencies (
v
0,...7
)
will capture the
whole frequency spectrums, both amplitude and phase as illustrated in [9].
According to equation 5, each image
I
q
of face train dataset is mapped to
40
images
I
q
'
v,µ
, where
v
0,...4
)
and
8
orientations (
µ
=
=
{
0,...7
}. Test Image
H
is also mapped to
H'
v,µ
. Now
orientation matching between each train image and the test image is gained using
equation 8.
∈
{
0,...4
} and
µ
∈
r
=
n
−
m
(8)
q
,
H
,
f
q
,
H
,
f
q
,
H
,
f
where
m
q,f
and
n
q,f
are extracted from equation 9.
q
[
m
,
n
]
=
arg
max
(
mean
(
I
'
(
x
)
−
H
'
(
x
)
))
(9)
q
,
H
,
f
q
,
H
,
f
f
,
m
f
,
n
m
,
n
x
∈
Center
where
Center
is a
9×9
square in the middle of the image, e.g. for image with size
80×40
, it is {
36,...44
}×{
16,...24
}. Now the orientation matched image denoted by
OMI
q
v',µ'
is defined as equation 10.
q
q
v
OMI
=
I
'
(10)
v
,
H
,
μ
'
,
μ
where
μ
'
= μ
(
+
r
)
mod
8
(11)
,
H
,
f
Now we define the similarity vector
sim
f
whose
i
th element indicates the similarity
between
i
th train image and the test image, according to equation 12.
1
7
∑
=
sim
f
(
H
)
=
mean
(
OMI
q
(
x
)
−
H
'
(
x
)
)
(12)
i
f
,
H
,
m
f
,
m
8
x
∈
C
m
0
4 Employed Classification
Let assume that there exist
n
training images and one test image. Also assume that the
training images are indexed as number one to
n
respectively and the test image
indexed as number
n+1
. The goal is to understand to which training image the test
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