Digital Signal Processing Reference
In-Depth Information
m
i
(
i
)
(
i
)
1
c
=
j
}
x
k
=
=
1
(3)
i
m
i
(
i
)
1
c
=
j
}
=
1
Where m is the number of clusters to be found, i iterates over the all the intensities, j
iterates over all the centroids.
Now for every image can be segmented into several regions.
3.2
Region Similarity Measure
A region can be described in many aspects, such as the color, texture, shape and size
of the region. Among them the color histogram computed with the RGB color space is
an effective descriptor to represent the object color feature statistics. We uniformly
quantize each color channel into16 levels and then the histogram of each region is
calculated in the feature space of 16×16×16 = 4096 bins.
Bhattacharyya coefficient is a divergence-type measure which has a straightforward
geometric explanation, so we choose to use the Bhattacharyya coefficient
τ
(
R
,
Q
) to
measure the similarity between two regions
R
and
Q
. If two regions have similar
contents, their histograms will be very similar, and hence their Bhattacharyya
coefficient will be very high.
4096
=
τ
(
R
,
Q
)
=
Hist
u
R
⋅
Hist
u
Q
(4)
u
1
Where HistR and HistQ are the normalized histograms of R and Q, and the superscript
u represents the uth element of them.
The region histograms are local histograms and they reflect the local features of
images, hence such cases that two perceptually very different regions may have very
similar histograms are rare, and the higher the Bhattacharyya coefficient between
R
and
Q
is, the higher the similarity between them is.
τ
The score of
(
R
,
Q
) can be normalized into a range of 0 and 1 as follow:
sim
(
R
,
Q
) = 1-norm(
τ
(
R
,
Q
))
(5)
3.3
The Correlation between Regions with Keywords Measure
Given images of a training collection
T
, we should first segment them into region sets
R
={R
1
, R
2
,
⋯
, R
m
} using the image segmentation algorithm proposed in section 3.1,
next manually assign keywords to every region of R in order to establish the
correlation between regions and keywords. Let
W
be the annotation vocabulary,
W
= {
w
1
, w
2
,
⋯
, w
n
}, where w
1
, w
2
,
⋯
, w
n
is co-occurrence keyword corresponding to every
region in the set of regions
R
={R
1
, R
2
,
⋯
, R
m
}.
