Infrared Small Target Detection Based on Density Peak Search and Local Features

Zhang, Leihong; Yang, Hui; Zheng, Qinghe; Zhang, Yiqiang; Zhang, Dawei

doi:https://doi.org/10.1049/2024/6814362

IET Signal Processing

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Abstract Introduction Conclusion Data Availability Conflicts of Interest Acknowledgments References Copyright Related Articles

Research Article | Open Access

Volume 2024 | Article ID 6814362 | https://doi.org/10.1049/2024/6814362

Infrared Small Target Detection Based on Density Peak Search and Local Features

Leihong Zhang,¹Hui Yang,¹Qinghe Zheng,²Yiqiang Zhang,¹and Dawei Zhang^1,3

Academic Editor: Junmo Kim

Received02 Jan 2024

Revised12 Apr 2024

Accepted07 May 2024

Published27 May 2024

Abstract

The detection of small infrared targets is still a challenging task and efficient and accurate detection plays a key role in modern infrared search and tracking military applications. However, small infrared targets are difficult to detect due to their weak brightness, small size and lack of shape, structure, texture, and other information elements. In this paper, we propose a target detection method. First, to address the problem that the proximity of targets to high-brightness clutter leads to missed detection of candidate targets, a Gaussian differential filtering preprocessed image is used to suppress high-brightness clutter. Second, a density-peaked global search method is used to determine the location of candidate targets in the preprocessed image. We then use local contrast to the candidate target points to enhance the gradient features and suppress background clutter. The Facet model is used to compute multidirectional gradient features at each point. A new efficient surrounding symmetric region partitioning scheme is constructed to capture the gradient characteristics of targets of different sizes in eight directions, followed by weighting the candidate target gradient characteristics using the standard deviation of the symmetric region difference. Finally, an adaptive threshold segmentation method is used to extract small targets. Experimental results show that the method proposed in this paper has better detection accuracy and robustness compared with other detection methods.

1. Introduction

The infrared small target detection is a key technology in the design of infrared search and tracking systems. Due to the distance of the target from the detection system and its heavy atmospheric attenuation, real infrared small targets occupy only a few pixels in the image field, which makes it lack local structural information. In addition, they are often submerged in complex background clutter and heavy noise and result in low signal-to-noise ratios, making it difficult to distinguish small targets from background clutter and noise. Therefore, it is a challenging problem to separate small targets in IR images from complex backgrounds.

Over the last three decades, many methods have been proposed to implement infrared small target detection. Depending on the different characteristics of the small targets used by the algorithms, they can be divided into two main categories based on small target local information features and global information features. The method based on local information features is developed based on the obvious difference between the target and the background. One of the frequency domain-based Gaussian filters was applied to IR target detection. Wang et al. [1] proposed a bidirectional high-pass filter template and Kim [2] decomposed the Laplace Gaussian filter into four filters and applied the minimum filter to obtain the final spatially filtered image. These methods focus on removing low-frequency clutter but fail to filter out noise and strong clutter in the high-frequency component. Inspired by the human visual system (HVS), HVS-based methods are commonly used for single-frame small target detection. These include establishing a local contrast detection method (LCM) for an eight-directional dual-window filter template [3]. A relative local contrast detection method (RLCM) of differential ratio type local contrast is established [4]. A multiscale contrast detection method (MPCM) is established to calculate the local contrast of each pixel at multiple scales [5]. The established image patch is divided into four parts to calculate the local contrast of the target gradient direction and the gradient detection method (LCG) [6]. These methods quickly localize and extract regions of interest by enhancing the contrast between the target and the background. Usually, HVS-based methods can be implemented with low complexity. However, the algorithm is less robust and less effective in detecting weak targets with complex backgrounds.

Based on global information features from the image as a whole, one class focuses on the prediction or preservation of the background and then achieves target detection by calculating the residuals between the input image and the predicted background. Among such detection methods, top-hat filters [7], the max-mean/max-median filter [8], wavelet filters [9], the two-dimensional adaptive LMS (TDLMS) filter [10], and mathematical morphological top-hot filters [11] are widely used. However, the performance of these methods, which treat the background as relatively homogeneous or autocorrelated, is usually limited and detection is poor when the background is heavily cluttered and the target signal-to-noise ratio is low. There is also a class of mathematical optimization problems that use the low-rank nature of the background and the sparsity of the target to transform the detection problem of the target into one of recovering the low-rank and sparse components. Gao et al. [12] first proposed a method using local region construction to generalize the traditional infrared image model to a new infrared patch image model (IPI). Dai et al. [13] replaced the globally constant weights in the IPI model with adaptive weights for each column in the weighted IPI (WIPI). Guo et al. [14] proposed ReWIPI, which introduces a reweighted l₁ paradigm to enhance the sparsity of the target and uses a reweighted kernel norm to constrain the background. Zhang et al. [15] proposed (NLOC) uses the Lp paradigm to enhance the constraints on the sparse terms and the low-rank term constraints. This type of algorithm is useful for images with low signal-to-noise ratios and complex heterogeneous backgrounds, but it is prone to misdetection of strong luminance edges and greatly increases the computational volume of the algorithm. Inspired by the idea of density peak clustering (DPC) [16] in cluster analysis in recent years, Huang et al. [17] proposed DPS-GVR with pixel intensity as the density, which searches for density peaks in the whole image and then uses local features to identify real targets. However, the density is defined based on isolated pixels in DPS-GVR, which ignores the correlation between neighboring pixels of the small targets. Zhu et al. [18] proposed a local feature-based density peak search method (LF-DPS), which consumes more time for the computation of LTRP features, although LF-DPS is better adapted to clutter compared to DPS-GVR. Wu et al. [19] proposed modified density peak search and local grey difference (MDPS-LGD), which suppresses high-brightness clutter by using a local heterogeneity metric as the density, and then extracts the maximum response of the local minimum gray difference element as the density peak by a random-walk (RW) algorithm through a local gray difference metric, which can better extract candidate targets, but in subsequent segmentation processing the effect is not good.

In addition, with the continuous development of deep learning, deep learning is widely used in various field directions [20, 21, 22, 23]. Feature extraction is achieved by repeatedly applying operations such as convolution, pooling, and downsampling to achieve the detection of infrared small targets [24, 25, 26, 27, 28]. However, due to the small infrared targets in the image features are not obvious, in the neural network feature extraction is inevitable to lose the target feature information. Wang et al. [29] use generative adversarial networks to balance the leakage detection rate and false alarm rate in image segmentation, but do not reasonably use the underlying feature information and deep semantic information, and the detection accuracy is limited. Dai et al. [30] designed an asymmetric modulation structure fusing the underlying features and remote context information with FPN or UNet as the backbone, which improves the detection accuracy, but the target contour is seriously missing. Li et al. [31] designed a dense nested interaction module (DNIM) with UNet as the backbone, which realizes the high-level and low-level feature progressive interaction, but it also brings a large number of parameters and FLOPs. Compared with traditional methods, deep learning-based detection methods have limited training datasets, which limits the improvement of detection performance and robustness to some extent. Coupled with the high hardware requirements for deep learning builds, traditional detection methods are still dominant in practical applications.

To enhance and detect infrared dim small targets embedded in clutter background simply and efficiently. In this paper, we study the global and local information features of weak targets in IR images and propose a weak target detection model based on density peak search and local features in IR images. A simple Gaussian differential filtering is applied before searching for candidate target points from the image. The “concentration effect” is avoided and the probability of correct target detection is greatly improved. Then, based on the local feature differences between the small target and the background, the candidate target points are first contrasted locally to enhance the gradient characteristics and suppress background clutter. The Facet model is used to compute multidirectional gradient features at each point. A new efficient symmetric perimeter segmentation scheme is constructed to capture the gradient features in eight directions for different sized targets, followed by weighting the candidate target gradient features using the standard deviation of the symmetric region difference. Finally, adaptive segmentation is used to extract small targets. The validity of the model was verified on a real infrared image dataset. The model has better background suppression and target detection performance than the compared methods.

2.1. Difference of Gaussian

The DoG filter is a commonly used band pass filter that is widely used in image segmentation, edge detection, interest point detection, and other fields [32]. Therefore, the image is analyzed according to the target features and noise features, this article passes the image through Gaussian differential filtering to obtain the response value image of DoG, which can enhance the target signal and suppress the influence of large range of bright background clutter on candidate target detection.

The 1D Gaussian function is defined as as follows:where σ is the standard deviation of the Gaussian function.

The 2D Gaussian function is defined as follows:

Therefore, the DoG filter template is obtained by the difference between two Gaussian functions, which can be defined as follows:where σ₁ and σ₂ are standard deviations of the Gaussian functions.

The raw image is convolved with the DoG filter template to obtain the result after Gaussian differential filtering:where I is the raw image and I′ is the preprocessed image.

2.2. Density Peaks Searching

Inspired by the principle of DPC method, the density ρ and δ distance of each pixel in infrared image are defined as follows:where the gray value of the pixel I is defined as the density ρ of the pixel, the δ_i table is the minimum distance (d_ij) between the pixel I and any pixel with higher gray value, and the coordinates of the two-pixel points I and J are represented by (x_i, y_i) and (x_j, y_j), respectively.

For the image pixels with large ρ and δ, there is the maximum density in the local area, and because the infrared small target conforms to the maximum density characteristics in the local area in the infrared image, the density peak value γ can be defined to search for possible infrared small target punctuation points:

The peak density γ of each pixel in the image is calculated according to Equation (8), and then each pixel’s γ is ranked from largest to smallest, and the top n larger density peaks are considered as candidate targets:where is the set of the top n candidate target coordinate positions.

2.3. Multidirectional Gradient Characteristics

In order to enhance the gradient characteristics of the small target, this paper takes advantage of the difference between the area where the small target is located and the adjacent area and adopts a simple and effective local comparison measure, which can suppress the background clutter while enhancing the target and significantly improve the gradient characteristics of the target. Use the 3 × 3 image patch slider to slide the local area established with the candidate target point as the center (Figure 1), where 0 represents the area where the target may appear, and calculate the gray average value m_i of pixels in each area of areas 1–8, respectively:where i represents the serial number of regions 1–8, N_i represents the number of pixels in the ith cell, and represents the grayscale value of the jth pixel in the ith cell. Therefore, the contrast between the center cell and the ith surrounding cell is defined as , and L_n represents the maximum gray value of the center cell of the nth image block.

The visual brightness of the small targets in IR images is usually greater than that of their neighbors. Therefore, the gradient significance of candidate targets can be further improved by the following formula:

The gradient feature is an important feature attribute of the small target, and using Facet model to calculate the multidirectional gradient of each point can provide more comprehensive feature information. When compared with the direct calculation way, the facet model is a polynomial function based on all pixels in any small neighborhood of image pixels, which can fully consider the gray influence of each point and reflect the gray change of the image more fully, and the calculation result is more accurate. By using a bivariate cubic function to fit the neighborhood S_5 × 5, if r and c are the row and column coordinates of the domain S_5 × 5, the intensity function f (r, c) of the neighborhood r × c in the Facet model can be expressed as follows:where consists of a series of discrete orthogonal polynomials and is represented as . is the fitting coefficient, which can be obtained by least square fitting, and is expressed as follows:

From Equation (13), can be directly obtained by convolution operation of f (r, c) using a fixed filter, and the corresponding filter is expressed as follows:

If is brought into Equation (14), each expression of can be obtained. Furthermore, the first-order derivative of f (r, c) at each point in the α-direction can be expressed as follows:

Then, after processing Equation (15), the first-order derivatives at points in the α-direction can be expressed as follows:

Finally, based on the filter , the gradient characteristic map of the infrared image can be quickly obtained using Equation (16). By changing the value of α, the intensity change of a point in any direction can be obtained. In this paper, the directional derivatives in eight directions (α = 0°, 45°, 90°, 135°, 180°, 225°, 270°, 315°) are utilized to analyze the gradient characteristics of small targets.

3. Proposed Method

The target detection methods-based unilaterally on local features are less robust due to the weak brightness and lack of local features, such as shape, texture, and structure of weak infrared targets. In this paper, we propose an infrared small target detection model DPS-LMD based on density peak search and local features for the characteristics of infrared weak and small targets. This method makes full use of the global features of infrared small targets as a priori, and further uses local contrast and multidirectional gradient features. In the face of complex scenarios, the DPS-LMD model compensates for the problems of undetectability and high false alarm rate in the detection of weak targets. At the same time, the algorithm achieves better detection results after verification of detection in different backgrounds, which proves the excellent robustness of the algorithm. Figure 2 shows the whole flowchart of the method proposed in this paper. The specific steps are as follows: (1) preprocess the image with DoG filter; (2) using DPS to determine the candidate target; (3) local contrast is used to enhance the significance of candidate target gradient; (4) calculation and fusion of multidirectional gradient characteristics; and (5) threshold segmentation is used to determine the target position.

3.1. Determination of Candidate Targets

DPS is often effective in selecting candidate targets by exploiting the fact that small infrared targets have both a relatively high global density and a relatively large distance to higher density pixels. However, when the target is close to background clutter of higher luminance, this results in smaller δ values for the target pixels and thus smaller calculated density peaks, with the possibility of missing the first n larger density peaks when extracting them as candidate target points. Figure 3(a) shows the missed detection of DPS on some infrared images. In order to solve the possibility of missing detection by DPS, we first carry out Gaussian differential filtering on infrared images and then use DPS to detect candidate target points in the filtered images. Figure 3(c) is the result of redetection after filtering. Compared with the original image, the image filtered by DOG can increase the δ value of the target pixel without affecting the ρ value of the target pixel, which improves the accuracy of real target detection. Then, we use the conditional function p to further screen the candidate target pixels and narrow the candidate target range. When the image boundary is indented by 3 pixels, the probability that the target still appears in the image field of view is 99.38% [33]. Therefore, the conditional function p is expressed as follows:where M and N are the rows and columns of the IR image. (x_i, y_i) are the coordinates of the candidate target points. is the set of the top m candidate target coordinate positions.

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3.2. Local Contrast Gradient Enhancement and Multidirectional Gradient Calculation

As can be seen from the definition, local contrast can enhance the gradient saliency of candidate target objects and suppress the background. In this paper, local contrast is used to calculate the local area of candidate target points, which greatly reduces the influence of background clutter on target detection compared with the global contrast calculation of images. The gradient saliency of the candidate target points is enhanced and the background attached to the target points is suppressed after the local contrast calculation. Then, the Facet model is used to calculate the multidirectional gradients of the candidate target points, and the 3D mesh distribution of the gradient features in the eight directions is shown in Figure 1. The gradient features of the small target have a large response in each direction (marked by the red circles) and respond only in individual directions (marked by the green circles) for the high intensity background edge clutter. As shown in Figure 4, the gradient response strength sets of different sized targets in eight directions are located in the range of different sizes, such as Figure 4(a) for the target larger than 3 × 3, the gradient response has a larger response in the range of 9 × 9 of the candidate target points, and Figure 4(b) for the target smaller than 3 × 3, the gradient response has a larger response only in the range of 5 × 5 of the candidate target points. In order to better capture the gradient characteristics of the fused small targets in eight directions and to adapt to the gradient distribution of the small targets of different sizes, this paper designs image symmetric patches in eight directions around the candidate target points (x_s, y_s), as shown in Figure 5. For the horizontal gradient characteristics of the target point (α = 0°), the image symmetric patches d₁, d₂, D₁, and D₂ are segmented by the following formula:

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For the diagonal gradient characteristics of the target point (α = 45°), the image symmetric patches d₁, d₂, D₁, and D₂ are segmented by the following formula:

Symmetric patches of the image in other directions can also be obtained according to Figure 5. Therefore, we construct a calculation based on the symmetry of the gradient features of the target points. Further suppression of background clutter and adaptation to different sized targets are achieved by the following equation:

To better distinguish the target points from the various noises, we used the standard deviation of the differences by symmetric patch blocks for weighting the gradient responsiveness:

Therefore, the gradient response value of the point (x_s, y_s) in a certain direction can be obtained by the following formula:

The final gradient response of the target point is constructed by fusing the gradient features in eight directions:

The gradient fusion shown in Figure 1 is a 3D map of the candidate target points after multidirectional gradient fusion.

3.3. Threshold Segmentation

To distinguish between real target points, an adaptive threshold T is used to extract real small targets:

are the eight-directional gradient characteristic fusion response values of candidate target points , respectively. Where and denote the mean and variance of the gradient response at the target point, respectively, and k is a given parameter with an optimal range of 1.2–1.8.

3.4. Detection Ability Analysis

Small infrared targets are usually of varying shapes and have no distinct textural features. The real target is concentrated in a homogeneous and compact area, which is represented by a Gaussian-like spot. They tend to appear as heterogeneous and compact regions when compared with the surrounding background pixels. Gradient response values for each direction when the current pixel (x^T, y^T) belongs to the target.

When the pixels of the target are larger than 3 × 3, we have the following equation:

When the pixels of the target are less than 3 × 3, we have the following equation:

Therefore, for different sized targets, we have the following equation:

When the pixel (x^E, y^E) belongs to the high-intensity background edge, there are gradient response values only in individual directions, and the gradient response values in the rest of the directions are 0. For most of the directions, the gradient response values are as follows:

Therefore, we have the following equation:

In general, pixel sized high-brightness noise (PNHB) with higher brightness. The effective areas are all smaller compared to the real target. When the pixel (x^P, y^P) belongs to PNHB, for the gradient response values in all directions, we have the following equations:

Thus:

In summary, our proposed method can achieve effective background suppression and target enhancement. The real target can be clearly segmented from a complex background.

4. Experiments Evaluation

In this paper, the dataset SIRST [30] is used to verify the superiority of the method proposed in this paper. The dataset SIRST contains 427 single-frame HD images extracted from infrared image sequences of different scenes. In order to show more intuitively the reasonableness of each step of our proposed algorithm, we selected five representative types of images in the dataset to analyze the operation results of each module. Then, we systematically compare our proposed method with other detection algorithms through commonly used evaluation indexes. The experimental data analysis and detection results show that the method proposed in this paper has better detection accuracy and robustness. All test results and experimental comparisons are performed on a PC equipped with a 2.3-GHz Intel i5-12500H CPU and 16.0-GB RAM, and the code is implemented in MATLAB 2021b software.

4.1. Evaluation Index

In order to objectively evaluate the performance of various small target detection algorithms, this paper uses the commonly used evaluation metrics signal-to-noise ratio gain (SCRG), BSF, detection rate (Pd), and false alarm rate (Fa) to quantitatively analyze the detection algorithms.

We use SCRG to indicate the ability to enhance the signal strength, if an algorithm has a high SCRG score, it means that the algorithm is more capable of improving the small target and the contrast of the small target is more obvious after the operation. SCRG calculation formulas are as follows:where and are the maximum gray value of the target neighborhood and the average gray value of the whole image, respectively. SCRin is the signal clutter ratio of the original image. SCRout outputs the signal clutter ratio of the image.

We use the background suppression factor (BSF) to assess the ability of background suppression. If an algorithm has a high BSF score, it means that the algorithm has strong background rejection and that there is less interference from background clutter after running the algorithm. BSF calculation formulas are as follows:where denotes the gray standard deviation of the original IR image and denotes the gray standard deviation of the detected image. The background rejection effect of the target is proportional to the BSF.

In addition, the detection rate (Pd) and false detection rate (Fa) are used to compare the detection performance of each algorithm. They are defined as follows:

P_d and F_a are key metrics for evaluating test results, with larger P_d values and lower F_a values indicating better detection performance of the algorithm.

4.2. Analysis of Test Results

In order to visually evaluate the detection performance of the detection algorithm proposed in this paper for weak targets in infrared images, real infrared images under five different background conditions in the dataset are selected as columns in Figure 6(a) in this section. Among the scenes included are (1) backgrounds with sharp and complex cloud edge structures, (2) complex ground-level building background images, (3) background images with high brightness large area edge sea surface, (4) background images with strong disturbed ground and complex cloud structures, and (5) backgrounds with high brightness buildings and clouds. The 3D image of each image is given in column b of the figure. Five types of images are used to verify the robustness and reliability of the detection algorithm proposed in this paper for detecting infrared targets in different backgrounds. The results of the experiment are shown in Figure 6. Figure 6(c) shows the results of the improved density peak search. Figure 6(d) shows the 3D plot after fusion of the gradients in the eight directions of the candidate target points. Figure 6(e) shows the 3D map after threshold segmentation of the candidate target points. Figure 6(f) shows the final localized small targets to be detected, where the red circles are the detected small targets. For real IR images with five different complex backgrounds, the detection algorithm proposed in this paper accurately detects the small targets. From Figure 6(d), it can be observed that the gradient response values of the real small targets after contrast enhancement are much higher than those of the other candidate target fusion gradients in the eight directions of fusion, and the real target points can be accurately detected after adaptive threshold segmentation.

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4.3. Comparative Analysis with Other Algorithms

4.3.1. Comprehensive Evaluation of Different Algorithms

In order to further verify the effectiveness of the proposed method, we use different target detection algorithms for comparison. Four existing methods (MPCM, AAGD, LIG, and TLLCM) with high citation rate are selected to compare and analyze the detection performance. They are multiscale patch-based contrast measure for small infrared target detection (MPCM) [5], small infrared target detection using absolute average difference with cumulative directional derivative weighting (AAGD) [34], a local contrast method for infrared small-target detection utilizing a trilayer window (TLLCM) [35], and infrared small target detection based on local intensity and gradient properties (LIG) [36]. For complexity analysis, we add the infrared small target detection by density peaks searching and maximum-gray region growing (DPSMRG) [19]. For each method, we choose appropriate threshold segmentation values to process images in five different backgrounds, respectively, to verify the robustness of different methods. As shown in Figure 7, the detection results of five methods in different backgrounds are shown. Red squares are marked as small targets correctly detected, and green marks represent targets with detection errors. With a sharp and complex cloud edge structure background, several of the selected methods had good detection rates due to the large intensity of the small target as well as not being affected by the high intensity background. The MPCM algorithm is based on multiple scale gray scale local contrast and responds significantly to isolated PNHB noise, so false detections occurred. For complex ground-level building background images, in which the buildings have highlighted local protrusions, there is a significant contrast gap with the attachments, so both contrast-based MPCM and gray-scale differential AAGD show false detections. For high-brightness large-area edge sea background images, small targets are located in the lower-brightness sea background with significant contrast and are well detected by several methods. For background images of ground and complex cloud structures with strong interference, where there is a significant contrast and partial directional gradient difference between the ground and cloud background effects, combined with the low brightness of the small target, several of the methods compared did not detect the target correctly. For backgrounds with high-brightness buildings and clouds, the three-layer template local difference measure (TLLCM) responds significantly to the high-brightness regions at the edges of the image, resulting in false detection. The method proposed in this paper first performs local enhancement on weak targets, and then extracts gradient features in eight directions as contrast segmentation factors, and for background noise with strong gradient features in some directions, the method in this paper has a clear distinction. In conclusion, based on the above phenomena, it can be concluded that the proposed detection model achieves the most satisfactory test results among the five test methods.

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4.3.2. Comparison of Different Algorithms SCRG and BSF

In infrared dim target detection, the interference of complex background is the biggest problem in detection. Serious background clutter will increase the false alarm rate of detection and cover up weak targets. Therefore, this paper makes a quantitative analysis of the dataset by SCRG and BSF. The algorithm proposed in this paper is compared with the above four detection algorithms (Table 1). The test results of each method are normalized to ensure the accuracy of the experimental data. It can be seen from Table 1 that (1) MPCM has the lowest BSF. Especially when the background is more complex, some interference will be enhanced, and the effect of background suppression is poor; (2) when detecting images of different scenes, the algorithm proposed in this paper achieves high results on all evaluation indexes; and (3) compared with other methods, the TLLCM method has a better background suppression effect, but it is not particularly good for small targets, which may lead to false detection in segmentation.

4.3.3. Comparison of Different Algorithms Pd and Fa

To further demonstrate the advantages of the proposed algorithm in terms of detection performance, for the dataset used in this paper, we present the detection and false detection rates for each detection algorithm, as shown in Table 2. It can be seen that the proposed algorithm has the highest detection rate and the second lowest false detection rate, indicating that our method outperforms other methods in terms of detection performance.

4.3.4. Algorithm Complexity Analysis

For the complexity of the detection, the main calculation of our method comes from the calculation of the δ-distance in the DPS, and the subsequent calculation of the features is only for the candidate target points, which greatly reduces the complexity of the algorithm. We tested 400 images from the dataset and Table 3 shows the average time taken to process each image by the different methods. As can be seen from Table 3, the filter-based detection method is less complex and has a faster detection time, but due to its lower detection rate and higher false alarm rate it can only be applied to less complex background situations. Compared to the better detection methods LIG, TLLCM, and DPSMRG, our method takes less time.

4.4. Noise Attack Analysis

Noise is also a key factor affecting the detection results of infrared dim and small targets. The infrared imaging system mainly includes three parts: optical–mechanical structure, infrared detector, and electronic system. Therefore to measure the noise immunity of the algorithm, 266 images were randomly selected from the dataset and Gaussian noise was added to these images (mean value 0, variance 0.001, 0.005, 0.01). Figure 8 shows the detection rate and false alarm rate of the proposed algorithm and other algorithms for Gaussian noise with different variances. The Gaussian differential filtering in the proposed algorithm can have some suppression effect on Gaussian noise. As can be seen from the figure, when the effect of added noise is small (variance of 0.001, 0.005) our proposed method has better detection rate and false alarm rate than the compared methods, while when the noise effect is large (variance of 0.01), the false alarm rate of the proposed method in this paper is slightly larger than the AAGD method when the noise effect is large because the larger Gaussian noise will affect the search process of the density peak.

5. Conclusion

For the difficulty of detecting weak infrared targets in complex backgrounds, this paper makes use of the global feature information and local feature information of small infrared targets. An infrared target detection algorithm based on density peak search and local features is proposed. We improve density peak accuracy by adding Gaussian differential filtering. Based on the multidirectional derivative characteristics, an effective gradient feature extraction framework is proposed, which can effectively extract the gradient features of candidate target points after local contrast enhancement and suppress background clutter. Then, the standard deviation of symmetric regional difference is used to weigh the gradient characteristics of candidate targets, and the gradient response value of targets is further enhanced. Compared with existing infrared small target detection methods, the algorithm proposed in this paper has good robustness to various scenes, background suppression effect, and detection effect for complex scenes while being faster in computation and can effectively detect small infrared targets.

Data Availability

Data availability is not applicable to this article as no new data were created or analyzed in this study.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Nos. 62275153, 62005165), the Shanghai Industrial Collaborative Innovation Project (HCXBCY-2022-006), the Development Fund for Shanghai Talents (No. 2021005), and the Shandong Provincial Natural Science Foundation under Grant ZR2023QF125.

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Copyright © 2024 Leihong Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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IET Signal Processing

Infrared Small Target Detection Based on Density Peak Search and Local Features

Abstract

1. Introduction

2. Related Principles

2.1. Difference of Gaussian

2.2. Density Peaks Searching

2.3. Multidirectional Gradient Characteristics

3. Proposed Method

3.1. Determination of Candidate Targets

3.2. Local Contrast Gradient Enhancement and Multidirectional Gradient Calculation

3.3. Threshold Segmentation

3.4. Detection Ability Analysis

4. Experiments Evaluation

4.1. Evaluation Index

4.2. Analysis of Test Results

4.3. Comparative Analysis with Other Algorithms

4.3.1. Comprehensive Evaluation of Different Algorithms

4.3.2. Comparison of Different Algorithms SCRG and BSF

4.3.3. Comparison of Different Algorithms Pd and Fa

4.3.4. Algorithm Complexity Analysis

4.4. Noise Attack Analysis

5. Conclusion

Data Availability

Conflicts of Interest

Acknowledgments

References

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