reformulated the detection task as a problem of salient region
detection [9]. However, strong clutters could also be salient and
affect the detection results in some cases.
The second category is background-based method which con-
centrates on the prediction or preservation of backgrounds, and
then the target is achieved by calculating the residual between
the input image and the predicted background. Top-Hat transfor-
mation was widely applied in infrared small target detection
[10–12]. It was firstly utilized for small targets detection in [10],
but it was sensitive to noise. Afterwards, Bai et al. [13] eliminated
backgrounds with a new Top-Hat transformation constructed by
two different but relevant structuring elements. It obtained supe-
rior performance to the initial Top-Hat method; however, it was
sensitive to the structuring elements size. Two-dimensional least
mean square adaptive filters were applied to the detection in
[14]. The Max-Mean and Max-Median filters were investigated
for the detection problem in [15]. In their methods, the original
image was filtered to estimate the background, and then the fil-
tered image could be subtracted from the original image. Further-
more, kernel-based regression was presented to estimate the
background in [16]. However, the performance of these methods
which consider the background as relatively homogeneous or
self-correlated is usually limited when the clutters are strong or
complex.
The third category is the learning-based method. Liu et al. pro-
posed an improved template matching method involving principal
component analysis (PCA) and kernel method [17].In[18], PCA
was performed in the salient regions to detect the target. However,
the training samples were generated or simulated in these meth-
ods, and the changeable appearances of small targets could
degrade their performance. In [19], Gao et al. regarded the small
target and the background as a sparse component and a low-
rank component, respectively. In their approach, the detection
was converted into recovering the two components from a data
matrix. Some methods have applied sparse representation in
detection recently [20,21]. However, these methods were usually
time-consuming.
Different from traditional algorithms, according to the shape
information of the target, we characterize two local properties of
the small target from the perspective of intensity and gradient to
suppress background clutters and detect infrared small targets.
An infrared small target is shaped like an isotropic Gaussian inten-
sity function because of the optics point spread function of the
thermal imaging system at a long distance [9]. For intensity, the
brightness value of the target is larger than the value of its locally
neighboring pixels in infrared images. Additionally, for a two-
dimensional Gaussian function, almost all gradients of this func-
tion point to its center. Similarly, the corresponding gradients of
the infrared small target roughly point to the target center. These
two properties are regarded as the local intensity property and
the local gradient property respectively. The homogeneous back-
grounds can be suppressed by using the local intensity property
as their intensity values are nearly identical; for the backgrounds
with strong edges, their gradient directions are generally consis-
tent, hence, these gradients are different from the gradients of
the target in distribution. Therefore, by combining the two proper-
ties, background clutters can be effectively suppressed. First, we
calculate the local intensity and gradient (IG) map from the input
infrared image. Then, we obtain the targets from the IG map via
an adaptive threshold.
The remainder of this paper is organized as follows. Section 2
explicates the characteristics of local intensity and gradient (LIG)
and gives the details of our method. Section 3 presents the exper-
imental results on the real database. Finally, we draw the conclu-
sions in Section 4.
2. Analysis and methodology
This section describes the LIG properties of infrared small tar-
gets. Meanwhile, we present the computation process of the pro-
posed method.
2.1. Analysis of small target characteristic
Chan et al. proposed that the small target in infrared images
could be modeled by a Gaussian intensity function [22]:
Iðx; yÞ¼
c
e
1
2
ðð
x
r
x
Þ
2
þð
y
r
y
Þ
2
Þ
ð1Þ
where c is the peak value of the target pixels,
r
x
and
r
y
denote hor-
izontal and vertical standard deviation parameters, respectively.
Infrared small targets generally occupy a few pixels in images,
and lack texture and color information. However, an infrared small
target is usually considered to be brighter than its surrounding
background [23]. Therefore, we realize that the local intensity
information is valuable for detecting the small target. The compar-
atively dark or homogeneous backgrounds can be suppressed by
exploiting the local intensity information since their intensity val-
ues are small or nearly identical. We dub this property the local
intensity property.
Additionally, considering that almost all gradient vectors of a
two-dimensional Gaussian function point to its center, we realize
that the gradient vectors of the target also roughly point to the tar-
get center, which is presented in Fig. 1. Moreover, the gradient
directions of the backgrounds with strong edges are generally con-
sistent. This property is viewed as the local gradient property.
Accordingly, the local gradient property can be also used for
detecting the small targets. As is shown in Fig. 2, some back-
grounds, such as trees, have no local intensity property. Besides,
the background labeled by a blue bounding box or a red bounding
box is local orientated and has no local gradient property.
By virtue of the characteristics analyzed above, the intensity
and gradient information is valuable for infrared small target
detection.
2.2. Calculation of the LIG properties
Based on the analysis above, we give the computing process of
the LIG properties as follows. First, we present the calculation of
the local intensity property. Given an image patch of size n n,
the average value of the local surrounding area is denoted by
f ¼
1
1 N
m
f
0
X
n
i¼1
X
n
j¼1
f
ij
!
; ð2Þ
where N
m
is the pixel number in an image patch. f
ij
denotes the
value of each pixel in the patch, and f
0
represents the value of its
center pixel. Further, we can achieve the local intensity value of
an image patch by
I ¼ maxð0; f
0
f Þ: ð3Þ
For an infrared small target, its gray value is normally larger
than that of its surrounding pixels [23], thus I > 0. Whereas, the
clutter whose value of the center pixel is smaller than the local
mean can be suppressed.
After I is achieved, we divide the image patch into four parts
along the radial direction, and set the center of the patch as the ori-
gin to establish a polar coordinate system. Each part can be
expressed by
W
i
¼ð
c
; h
i
Þj
p
ði 1Þ
2
< h
i
6
p
i
2
; ð4Þ
H. Zhang et al. /Infrared Physics & Technology 89 (2018) 88–96
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