1. Introduction
Small infrared (IR) target detection has been widely used in airborne early warning, IR guidance, surveillance and tracking, and others. Usually, the earlier we detect a small IR target, the more time we get for dealing with it, and thus the more suitable decision can be made. However, factors such as low signal-to-noise ratio (SNR), variable target sizes, variable target intensity, less shape and texture information, blurred edges, and serious background clutters, cause small IR target detection to be a challenging task.
So far, many IR target detection algorithms have been developed ranging from recursive estimation techniques [
1] to partial sum of the tensor nuclear norm [
2]. Among them, morphology filtering such as the top-hat transform and its variants plays an important role [
3,
4]. Top-hat transforms are also combined with other techniques such as genetic algorithm [
5] to improve the detection performance. Though these methods can detect targets to a certain degree, their performance is greatly degraded under complex background clutters.
Over the last few years, it is widely shared that algorithms derived from visual attention mechanics work well for detecting a small target. The early work in 1998 made intellectuals pour attention into visual attention distribution [
6], and then saliency estimation methods corresponding to visual attention became popular in small IR target detection [
7]. Wang et al. are the early researchers to use the Difference of Gaussian (DoG) filters to get a saliency map for detecting real targets [
8]. However, due to problems like signal interference, a small target does not strictly obey the 2D Gaussian distribution, and thus cannot be successfully detected by merely adopting DoG filters. Further studies on visual attention focus on the relationship between a target and its neighborhoods. The local contrast method [
9,
10], the multiscale patch-based contrast measure [
11], weighted local difference measure [
12], human visual mechanism detectors [
13,
14], variance difference detector [
15], entropy-based contrast measure [
16], weighted local contrast detector [
17], local intensity and gradient detector [
18], visual saliency guided detector [
19], local difference adaptive measure [
20], the adaptive local measurement contrast, and salient region extraction and gradient vector processing [
21] are reported successively, demonstrating that the contrast between a target and its neighbor is helpful for small IR target detection.
Though many improved algorithms have been reported, it is still challenging to detect a small IR target in images with low SNR, low contrast, and serious background clutters. This paper presents an effective detection method based on the Mexican-hat distribution. A raw IR image is first processed by the modified top-hat transformation [
22] and the DoG filter, getting a filtered IR image. Then, the adjacent region around a pixel of the filtered image is radially divided into three sub-regions. Next, the pixels whose adjacent regions have the Mexican-hat distribution are determined as candidate targets. Finally, a small target is segmented out by locating the brightest pixel. Experimental results show that the adoption of the Mexican-hat distribution benefits our method with higher detection rate, lower false alarm rate, and faster detection speed than existing detectors. Though the existing detector in [
15] is resemble to our method, it performs on raw IR images and only compares the relationship between two regions. On contrast, we operate on the filtered image and detect an IR target based on the Mexican-hat distribution, and our experimental results show that such strategy can effectively enhance the small IR target and improve the detection rate.
The rest of the paper is organized as follows.
Section 2 analyzes the characteristics of the adjacent region of a target in a DoG-filtered image.
Section 3 describes the details of the proposed method.
Section 4 presents experimental results along with some analysis. Finally,
Section 5 gives some conclusions.
2. Mexican-Hat Distribution of the Adjacent Region around an IR Target
Let
I(
x,
y) be an image. Then its DoG-filtered image,
, is formed by (1) [
23]:
where
and
are the standard deviations of the two Gaussian kernels, ‘*’ is the convolution operation given by (2).
After careful observation, we find the pixel intensity of the adjacent region around an IR target shows a regular bright-dark-bright pattern along the radial direction. Specifically,
Figure 1 illustrates such bright-dark-bright pattern. The center pixel of a target patch is the brightest, and then the intensity decreases gradually along the radial direction until reaching the lowest value. After that, the intensity increases again. As shown in
Figure 1c, the profile of such bright-dark-bright pattern is like a Mexican hat, and thus we call it Mexican-hat distribution in this paper.
Based on the above observations, we propose to detect small targets in IR images via the Mexican-hat distribution. As shown in
Figure 2, we first divide the adjacent region of a small target into three sub-regions along the radial direction that are respectively termed as
,
, and
. For a small target positioned at (
r,
c),
is a (2
L + 1) × (2
L + 1) square image region centered at (
r,
c), and
is one-pixel square border just outside
, and
is one-pixel square border without four corner pixels outside
. According to the Mexican-hat distribution, we know that the intensity relationship between the three sub-regions of a target roughly meets the bright-dark-bright pattern, and thus have the following rule:
Rule 1: If the mean intensity of is both larger than and , and the mean intensity of is smaller than , then the center of can be a candidate target center.
3. The Proposed Method
As shown in
Figure 3, the proposed four-step method for detecting a small IR target is based on the Mexican-hat distribution. To increase the contrast between small targets and the background, the modified top-hat transformation [
22] is first applied to a raw IR image, followed by DoG filtering. Then, the Mexican-hat-distribution based
Rule 1 is applied to the DoG image, getting candidate targets. Finally, a small IR target is detected by locating the brightest pixel.
Here, to deal with the variable size of small IR targets, the following iteration strategy is adopted when applying
Rule 1 to a DoG image. First, let the half-width,
L, of region
ranges from 1 to 5, implying the size of region
varies from
to
that is consistent to the recognition that a small target usually occupies less than 80 pixels [
24]. Then for each
L,
Rule 1 is applied to the adjacent of each pixel of the DoG-filtered image. Those pixels that meet
Rule 1 are labeled as candidates, and their intensity is emphasized by the mean intensity of
. Meanwhile, the corresponding size of
, i.e., (2
L + 1) × (2
L + 1) are recorded as the target size.
Algorithm 1 presents the details for finding candidate targets as well as their sizes. Considering small IR targets are usually brighter than the background,
Rule 1 is merely applied to the patches whose center pixel is brighter than
with
and
being the mean intensity and the standard variance of the DoG-filtered image.
Algorithm 1 Candidate target detection. |
- 1:
Input: —the DoG-filtered image H,W—the height and the width of th—threshold - 2:
Output: —the image with enhanced candidate targets (, )—the coordinates of candidates s—the size of candidates inten—the mean intensity of candidates - 3:
for to do - 4:
for to do - 5:
if (r, c) > th then - 6:
for to 5 do - 7:
Locate sub-regions , and according to Figure 2; - 8:
mean intensity of , with , 1 and 2. - 9:
if , , and then - 10:
(, ) = (r, c) s(, ) = inten(, ) = (, ) = (, ) − - 11:
else - 12:
break; - 13:
end if - 14:
end for - 15:
end if - 16:
end for - 17:
end for
|
Next, to further remove false targets, the statistics of sub-regions
,
and
are calculated. For real small IR targets, their intensity might not strictly meet the Mexican-hat distribution. For example, the first row of
Figure 4 shows that the center pixel of a target is not the brightest, and the second row shows that nearly half of pixels in region
and in region
don’t meet the Mexican-hat distribution. Therefore, for a candidate target located at (
r,
c), (3) is adopted to calculate the ratio of the number of pixels in
being darker than the mean intensity of
to the total pixels of
.
where
is the mean intensity of
, and
represents the cardinality of a set.
Then the pixel by pixel differences between
and
are calculated along the row direction and the column direction, respectively, followed by the computation of the ratio of the number of pixels in
being darker than the corresponding pixels in
to the total pixels with (4) and (5).
where
and
represent pixels of the first and the last columns in
R1, and
and
are the pixels of the first and the last rows in
. Equation (5) indicates that each corner element in
has been compared two times, so the total number of pixels in (4) is given by
Card(
) + 4 rather than
Card(
).
Having the ratios of and , we compare them with two predetermined thresholds and , and use Rule 2 to detect a true small target. Finally, Rule 3 is applied to both target regions and non-target regions to further enhance targets while suppressing non-targets.
Rule 2: If and , then the corresponding pixel position (r, c) is the center of a small target.
Rule 3: If (
r,
c) is the center of a small target, then use (6) to enhance it; otherwise use (7) to suppress it.
where
,
and
represent the final enhanced IR image, the raw IR image, and the DoG-filtered image, max(.) and min(.) are the maximum and the minimum functions.
Since small targets in both a raw IR image and DoG-filtered image are usually brighter than their surroundings, the term
in (6) and (7) can enhance targets while suppressing backgrounds. Moreover, since both
and
are positive numbers smaller than 1, the term
in (6) is always bigger than the term
in (7). Therefore, by applying (6) and (7) to targets and non-targets, we can get a final image with salient targets. As a result, the target is easily detected by assigning the pixel with the maximum intensity as the target center. Algorithm 2 gives the details of our method for detecting small IR target.
Algorithm 2 Our method for detecting small IR target. |
- 1:
Input: I, —raw IR image and the corresponding DoG image , —thresholds H,W—the height and the width of - 2:
Output: (, )—target center - 3:
for to do - 4:
for to do - 5:
if is the center of a candidate target then - 6:
compute and with (3)–(5). - 7:
if and then - 8:
use (6) to get - 9:
else - 10:
use (7) to get - 11:
end if - 12:
end if - 13:
end for - 14:
end for - 15:
()
|
5. Conclusions
In this paper, we have proposed a new method for detecting small IR targets. Our method is based on that the adjacent region of a small target in a DoG-filtered image roughly holds the Mexican-hat distribution. Our experimental results on both real-world and synthetic IR images show that our method is quite effective in enhancing small IR targets while suppressing background clutters. In terms of SCRG, BSF, , and , our method outperforms both the traditional and state-of-the-art methods. Moreover, it runs faster than the RLCM, the LIG, the Max–median, and the Max–mean.
Our experimental results show that our method performs rather well in single target detection and can also be directly used for detecting multi-targets in simple background. However, such direct use degrades the detection performance when the background is very complicated. Thus, our future work will focus on detecting multi-targets in complex background via such a method.