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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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