Infrared time-sensitive weak and small target detection method based on density search and gradient decision

For detecting infrared time-sensitive weak and small targets in a complex air-ground background, it is easy to be interfered by low signal-to-noise ratio and strong noise. In this paper we proposed an infrared time-sensitive weak and small target detection method based on density search and gradient decision. First, we use adaptive wiener filtering to preprocess the infrared image to reduce noise interference; then, use the density peak search method to extract points of interest, and use the eight-directional gradient method to make decision-making judgments; finally, use the adaptive threshold segmentation method to extract true targets. The experimental results show that this method has good robustness and detection performance for single infrared time-sensitive weak and small target detection in the air-ground background.


Introduction
The infrared detection system has the characteristics of good concealment, long detection distance, strong anti-interference ability and all-weather work [1]. It has an extremely important position in target detection and is widely used in guidance, reconnaissance and early warning. In important applications such as infrared guidance or infrared early warning, people always hope to find timesensitive targets such as tanks and missiles in the distance as early as possible, so as to improve the performance of the guidance system or fight for more defense time to protect the safety of our targets. Generally, the distance between the target and the infrared detector is often tens or even hundreds of kilometers. After imaging by the optical system, the image of the target on the entire image is usually very small (less than 9×9 pixels). Therefore, the detection of infrared weak and small targets with high detection rate and low false alarm rate is the basic requirement for effective guidance and early warning, it has become one of the important factors that determine the success or failure of modern and future wars. So the detection of weak and small moving targets has become a research hot spot in recent years.
Through the research of a large number of scholars, infrared weak and small target detection can be divided into single-frame target detection and multi-frame target detection [2]. The main idea of singleframe detection is to model infrared weak and small targets, and separate the target from the background according to the characteristics of the small target; Multi-frame detection mainly relies on the inter-frame relationship between sequence images to learn and detect the motion characteristics of weak and small targets. Detection methods based on spatial filtering, such as median filter, averaging filter, high-pass filtering, morphological filtering, and their improved method [3][4][5][6], have a better effect of suppressing specific noise, but they have their own technical limitations. Based on the local contrast method, the most significant feature of the infrared weak and small target is that there is a significant contrast between the bright light central area and the dark light surrounding area. The central area often has a higher gray level distribution, but when facing a complex background The background clutter has strong edge characteristics, and their directional derivatives in a small local area are often flatter and stable. Chen et al. aiming at the characteristics of the local difference between the infrared dark image and the small target image, the difference between the dark target and the neighboring area is used for contrast measurement, but this method has limitations such as long calculation time and "expansion" effect [7]. This method are good for high SNR image detection, but are not satisfied with the complex background and low SNR image detection effect.
Based on the matrix factorization method, its central idea is similar to the idea based on local contrast. In the infrared weak and small target image, the small target is sparse with respect to the whole image, while the background image has a strong correlation and belongs to low rank. Based on this, Gao et al. proposed an infrared patch-image (Infrared Patch-Image, IPI) model, assuming that the background image and the target image meet the low-rank characteristics and the sparse characteristics respectively, so as to convert the infrared small target detection into a low-rank matrix and sparse matrix restoration problem [8].
In this paper we proposed an infrared time-sensitive weak and small target detection method based on density search and gradient decision. First, we use adaptive wiener filtering to preprocess the infrared image to reduce noise interference; then, we use the density peak search method to extract points of interest, and use the eight-directional gradient method to make decision-making judgments; finally, we use the adaptive threshold segmentation method to extract time-sensitive weak and small targets. Figure 1 shows the flow chart of the method in this paper. Figure 1 The method flow chart of this paper.

Infrared image preprocessing
Wiener filtering is a linear filter. For digital images, it can be designed according to the minimum mean variance criterion of the local area of the image, and it is a filtering method to estimate the current value of the signal mainly from all the previous observations and the current observations [9].
For a noisy image ( , ) f x y , the noise reduction model of the adaptive wiener filter for the image is expressed as follows: xy represent the position of the pixel, g represents the result after denoising,  is the average value of the neighborhood of the image, and w is an adaptive wiener filter based on the local stationary theory and the minimum mean square error criterion. w is calculated locally by the statistical value of the neighborhood signal of the pixel: where 2 n  is the noise variance, 2  is the local variance of the image f , which reflects the magnitude of the signal change in the local area of the image, and its value varies with the position of the pixel, so that the filter w is adaptive.

Extract points of interest
In the infrared weak and small target image, the relevant calculations are performed for each pixel, and the small target is finally extracted. Therefore, there is a problem that the detection takes a long time. In this paper, the method of density peak search is used to extract the points of interest in the infrared image. The basic idea is that weak and small targets are highlighting local areas, the gray scale value is much higher than the surrounding pixels; Weak and small targets generally exist in isolation, and they are far away from pixels with higher gray values. According to the literature [10], the density of pixel i is defined as: (3) where i g represents the gray value of pixel i , and ij d represents the distance between pixel i and a pixel with a higher gray value, usually expressed by Euclidean distance: The peak density  is when the density of both  and  reaches the maximum in the local area. In this section, we calculate the  of each pixel and arrange it from large to small, and then we select the largest 4 points as points of interest. Figure 2 Infrared weak and small target image gray value 3D map and density peak search results.

Decision-making judgments
According to the results of the 4 points of interest extracted in section 2.2, the real target cannot be judged only based on the density peak search results. Based on the large gray scale difference between the small infrared target and the surrounding background, the target is equivalent to a singular point in its local area, and has a large gray scale gradient in all directions. Therefore, this section used the eight-direction gradient method to detect and screen the candidate regions. Figure 3 shows the difference between the grayscale three-dimensional image and the gradient direction of the infrared small target and the background edge. It can be seen from Figure 3 that the gradient is a vector, indicating that the directional derivative of the function at a specific point moves along this direction and achieves the maximum value. If any pixel is set as ( , ) h i j , then the gradient of the point in any direction can be expressed as:  (8) represents the modulus of the gradient of ( , ) h u v along a certain direction, but for the processed infrared image, the calculation of hu  and hv  adopts an approximate difference method, so the eight-direction gradient can be approximately expressed as: where n is the step length, and its value is determined by the size of the time-sensitive and small target to be detected. The larger the n , the longer it takes. The target size in the experimental data set is 3×3 pixels, so 2 n  .

Adaptive threshold segmentation
Finally, this paper uses a simple adaptive threshold segmentation algorithm to effectively segment the time-sensitive weak and small targets in the eight-direction gradient detection image.
Tk  = +  (10) where  and  respectively represent the mean value and standard deviation of the image gray level, and k is a constant. According to experimental experience, k is generally set in the range of 0.4~0.8 for better detection results.

Results & Discussion
In order to verify the performance of this method, this section applies Top-Hat, ILCM [11], RLCM [12], LIG [13] and proposed method to five sets of real infrared weak and small target sequence images in the Windows 10 MATLAB 2020b environment. Table 1 introduces the data information of five sets of infrared image sequences. Figure 4 shows the processing results of two real infrared image sequences under each algorithm. Figure 5 shows the detection results of different algorithms. In order to further prove the superior performance of this method compared with the other six algorithms, and to quantitatively describe the dynamic relationship between the detection rate and the false alarm rate more clearly, by setting different thresholds, the corresponding reception is drawn for each sequence. Machine operating characteristic curve (ROC), which describes the relative relationship between true positives and false positives. The definition of detection rate and false alarm rate can be seen in equation (11) and (12).

Conclusions
To further improve the detection performance of infrared time-sensitive weak and small targets in the air-ground background, this paper developed an infrared time-sensitive weak and small target detection method based on density search and gradient decision. Through a pipelined process, we use adaptive wiener filtering to remove noise interference, and reduce interference for the next step of interest point extraction, then use the eight-directional gradient method to select interest points for decision-making, and perform adaptive threshold segmentation to extract true targets. Experimental verification shows that the method in this paper has good detection performance under complex cloud and ground background. Compared with other algorithms, it has a higher detection rate and a lower false detection rate. But because it is a pipeline structure, the real-time performance is not good, and we will make further optimizations in future work.