by DoG, and filter them by key point filtering algorithm. Next, the
RoI is generated by these key points and represented by the BoW
model. At the same time, Non-RoI are also represented by the
BoW model. Finally, The visual words of RoI and Non-RoI are con-
nected to one visual word, which is used to represent the visual
features of the whole image.
Next we will introduce the RoI-BoW model in details.
Let the i-th image in the dataset be I
i
2R
N
1
N
2
; i ¼ 1; 2; ...; N,
the original image dataset is denoted as D as follows
D ¼fI
1
; I
2
; ...; I
N
g;
where N is the amount of images, N
1
and N
2
represent the size of
images. An input image can be seen as two variable function on
the rectangle
I
i
ðx; yÞ; ðx; yÞ2½1; 2; ...; N
1
½1; 2; ...; N
2
; i ¼ 1; 2; ...; N:
2.1. Key points filtering
For each image, initial key points are detected firstly by differ-
ence-of-Gaussian (DoG) algorithm [44]. The difference-of-Gaussian
[44] with the scale
r
and constant multiplicative factor k can be
computed by
Dðx; y;
r
; kÞ¼Lðx; y; k
r
ÞLðx; y;
r
Þ; ð1Þ
in which, Lðx; y;
r
Þ is the scale space of an input image Iðx; yÞ. It can
be obtained by (seen in page 94 in [44])
Lðx; y;
r
Þ¼
1
2
pr
2
e
x
2
þy
2
2
r
2
Iðx; yÞ: ð2Þ
In practice, the size is usually chosen as
r
¼ 1:6 and the constant
multiplicative factor is chosen as k ¼
ffiffiffi
2
p
.
One sampling pixel(except for border pixels) is selected as key
point only if the value of Dðx; y;
r
; kÞ is larger than all of these
neighbors (in 3 3 region, the sampling pixel is the central one
and its eight neighbors, example, if the geometry coordinate is
ði; jÞ of sampling pixel, the 3 3 region includes night points, they
are ði 1; j 1Þ; ði 1; jÞ; ði 1; j þ 1Þ; ði; j 1Þ; ði; jÞ; ði; j þ 1Þ;
ði þ 1; j 1Þ; ði þ 1; jÞ; ði þ 1; j þ 1Þ) or smaller than all of them.
After the DoG algorithm, the set of the initial key points of
image I
i
is obtained and denoted as
P
i
¼fP
i
1
; P
i
2
; ...; P
i
S
i
g;
where S
i
is the number of key points of image I
i
.
Since initial key points are too many, a filter algorithm is used to
remove some sparse points and retain the points distributed den-
sely. An example is illustrated in Fig. 3 and the filtering algorithm
is introduced as follows.
The filtering operator is denoted as h,
h : P
i
¼ P
i
1
; P
i
2
; ...; P
i
S
i
no
! Q
i
¼ Q
i
1
; Q
i
2
; ...; Q
i
T
i
no
; ð3Þ
where T
i
is the number of key points of image I
i
after filtering.
Each initial key point is judged by a boolean function as formula
(4),
bP
i
j
¼
1; lðP
i
j
Þ P L;
0; lðP
i
j
Þ < L;
(
ð4Þ
where b ¼ 1 means retaining the point, and b ¼ 0 means removing. l
is a statistic function to calculate the number of key points around
Fig. 1. The above two pictures show the similarity between salient regions detection and region of interest with difference-of-Gaussian. the below two pictures tell us that
there is significant difference. The first column is the original images. The middle column is the corresponding salient regions. The last column is region of interest with
difference-of-Gaussian (the keypoints are labeled with red points). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version
of this article.)
J. Zhang et al. / J. Vis. Commun. Image R. 26 (2015) 37–49
39
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