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In-Depth Information
(
,
)
(
,
)
=
.
=
where
S
2 are used to
adjust the relative compactness of the saliency values. Equation (
5.3
) results in the
concentration of the activation into a few key locations.
i
j
is the saliency map at location
i
j
,
a
0
1 and
b
5.3
Saliency-Aware Local Descriptor
The SIFT descriptor aims at detecting and describing local visual features in two
steps. In the first step, the key points are localized, while in the second step,
local descriptors are built for each key point. A given image is decomposed into
a set of key points
X
=
{
x
1
,...,
x
n
}
with their corresponding SIFT descriptors
S
=
{
. In the process of obtaining the descriptors, the gradient vector
for each pixel in the key point's neighborhood is computed and the histogram
of gradient directions is built. Thus, the descriptor can be represented as a set
of gradient histograms, and can be denoted by
s
s
1
,...,
s
n
}
(
m
,
n
,
o
)
, where
m
,
n
and
o
are
respectively the indexes of the spatial bins and orientation channels.
A16
4 pixels each.
For each pixel within a sub-region, the pixel's gradient vector is added to a histogram
of gradient direction by quantizing each orientation to one of eight directions. Each
entry of a bin is further weighted by 1
×
16 neighborhood is partitioned into 16 sub-regions of 4
×
d
, where
d
is the geometric distance from
the sample to the bin center. This reduces boundary effects as samples move between
positions and orientations.
In order to incorporate the saliency information into the descriptor, when
calculating the histogram, each entry of a bin is weighted by the saliency weights:
−
1
M
o
(
i
,
j
)(
1
−
d
(
i
,
j
))
S
(
i
,
j
)
)=
∑
d
B
(
i
,
j
)
<
s
(
m
,
n
,
o
(5.4)
∑
d
B
(
i
,
j
)
<
1
S
(
i
,
j
)
where
M
o
(
i
,
j
)
represents the gradient magnitude at the location
(
i
,
j
)
in the
o
-th
orientation plane,
d
B
(
i
,
j
)
is the distance between the sample at
(
i
,
j
)
and the center
of the bin
B
(
m
,
n
)
,1
≤
m
,
n
≤
4, and 1
≤
o
≤
8.
16 pixels, chosen for obtaining the descriptor
s
.
The saliency value associated with the descriptor is obtained by weighting the
saliency map
S
Let
R
denote a region of size 16
×
(
i
,
j
)
discussed in Eq. (
5.3
) by a Gaussian of scale
˃
as follows:
exp
2
2
−
(
i
−
R
x
)
+(
j
−
R
y
)
∑
w
=
S
(
i
,
j
)
(5.5)
2
2
˃
(
i
,
j
)
∈
C
where
(
R
x
,
R
y
)
is the center of the region
R
.
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