RETRACTED: An Infrared Small Target Detection Method Based on a Weighted Human Visual Comparison Mechanism for Safety Monitoring

: Infrared small target detection is a crucial technology in both military and civilian applications, including surveillance, security, defense, and combat. However, accurate infrared detection of small targets in real-time is challenging due to their small size and similarity in gray level and texture with the surrounding environment, as well as interference from the infrared imaging systems in unmanned aerial vehicles (UAVs). This article proposes a weighted local contrast method based on the contrast mechanism of the human visual system. Initially, a combined contrast ratio is deﬁned that stems from the pixel-level divergence between the target and its neighboring pixels. Then, an improved regional intensity level is used to establish a weight function with the concept of ratio difference combination, which can effectively suppress complex backgrounds and random noise. In the ﬁnal step, the contrast and weight functions are combined to create the ﬁnal weighted local contrast method (WRDLCM). This method does not require any preconditioning and can enhance the target while suppressing background interference. Additionally, it is capable of detecting small targets even when their scale changes. In the experimental section, our algorithm was compared with some popular methods, and the experimental ﬁndings indicated that our method showed strong detection capability based on the commonly used performance indicators of the ROC curve, SCRG, and BSF, especially in low signal-to-noise ratio situations. In addition, unlike deep learning, this method is appropriate for small sample sizes and is easy to implement on FPGA hardware.


Introduction
The use of unmanned aerial vehicles (UAVs) has become widespread and poses a significant threat to densely populated areas, as well as restricted areas such as airdromes [1,2].Thermal infrared (IR) imaging allows remote monitoring of drones in all weather circumstances.Thus, the anti-unmanned-drone technique based on a thermal infrared imaging system has received increasing attention from investigators [3,4], while the infrared acquisition of small targets is also an essential technology in military, civil, and other fields [5][6][7].This technology plays a crucial part in UAV target detection [8], control, and defense [9].Quick and exact identification and tracing of targets in each frame is crucial in infrared detection [10].However, it is challenging to correctly detect the genuine target without false alarms mainly because of the following reasons: (a) In images obtained by the infrared imaging machinery, the small target takes up only a handful of pixels in the entire image.
The distance between the infrared imaging system and the actual target is usually large, making the small target less noticeable in the overall image with no distinct features or texture [11].(b) Detecting small IR targets in infrared imaging is challenging due to irregular motion, occlusion, and blurring.The target may only occupy a couple of pixels, making it difficult to tell apart from the background [12].(c) Complex background edges and high brightness noise with single pixels in the image can often resemble small targets, leading to false positive detection results [13].Therefore, achieving accurate real-time detection of small IR targets continues to be a challenging task.
There are several existing methods for small IR target detection, including those based on the spatial domain [14], frequency domain [15], morphology [16], and background estimation [17].While traditional algorithms have been widely used, there is now an increasing interest in deep-learning-based techniques, both supervised [18] and unsupervised [19].The spatial local contrast formula employs the principle of human vision to prioritize the correlation between the target and its surroundings.It computes the local contrast between the target area and its neighboring background to detect the target.Examples of this method include the combination of filtering and morphology [20], the sub-block and contrast approach [21], the difference stemming from the Gaussian bandpass filter [22], the multi-scale local contrast method [23], the local contrast measure map [24], the minimum mean square means for backdrop estimation [25], and the matched filtering and three-layer windows [26].Three classifications can be applied to these methods: ratio, differential, and ratio-differential methods.From the discussion in the references, it is evident that ratio-based approaches can enhance the real target but cannot remove a prominent background.Difference-based methods can eliminate a prominent background, but they do not provide an effective way to strengthen the target.Ratio-differential methods can amplify the target while eliminating a high-brightness background.Complex backgrounds can lead to false alarms when using local basic contrast algorithms for detection.However, local contrast algorithms with weighting functions can improve detection performance by suppressing clutter.Some researchers have used local statistics, such as variance or similarity measures, as weighting functions.For example, in [27], a weighting function is created to address cloud edges; in [28], the variance of the central cell is utilized; in [29], the similarity of the target's pixels is combined with the differences between real objectives and their surrounding neighborhood; in [30], the higher signal-to-clutter ratio is applied.On the flip side, some researchers have preferred to design and compute the weighting function themselves.For example, Qi et al. [31] employed the differences between the real object and its neighborhood to create the weight in small image areas.Chen et al. [32] recommended a methodology based on top hat filtering and contrast.Bai et al. [33] improved the entropy formula and proposed a target measurement method of contrast.Nasiri et al. [34] introduced a target area model based on three-layer patches, which utilizes the variance difference between layers.Gao et al. [35] also utilized differences in variance.Liu et al. [36] considered the number of bright pixels in the surroundings.Lv et al. [37] defined a weight function using the regional intensity level between the target and its surrounding neighborhood.Weighted local contrast algorithms typically rely on either a ratio-based or a difference-based approach.While effective, these algorithms have certain limitations as they only consider the difference operation in their weighting function calculation, neglecting the ratio operation, which can result in weak enhancement of the true target.Additionally, some weighting functions may be overly sensitive to random noise, which can lead to the incorrect identification of random noise in a sub-block as a true target, even if it has the highest value.Therefore, a combination of ratio-based and difference-based approaches, known as the ratio-difference combined type, may be more effective.
Over the past decade, deep learning has witnessed remarkable advancements across various domains such as biology, images, speech, language, and more.Numerous researchers have endeavored to synergize local contrast algorithms with neural networks to attain enhanced detection outcomes.Dai and Wu [38] leveraged the scarcity of the target and the self-correlation of the background to effectively segregate the target from the surroundings, employing a tensor structure to design a weight function.In [39], the authors integrated partial tensors and kernel norms to jointly weigh the l1 norm.Gupta et al. [40] introduced a computationally efficient CNN framework and integrated lightweight networks for small target detection.Dai et al. [41] incorporated contrast features into the network feature layer and fused shallow and deep features to achieve target detection.In [42], the authors proposed a framework that combines handcrafted features and convolutional features to extract target features.Similarly, Du et al. [43] devised small anchors for capturing targets based on the shallow layer of the ResNet50 framework.Despite these advancements, FPGA implementation of deep-learning-based methods encounters challenges due to model complexity.Even if deep learning approaches are deployed on FPGA, ensuring real-time performance becomes arduous, thereby impeding the system's ability to provide prompt feedback.Furthermore, training neural network models necessitates substantial data volumes, and a multitude of parameters, and entails high time complexity, resulting in limited generalization capabilities.Considering these factors, the practical utilization of deep learning algorithms in real-world product applications remains limited.Consequently, this study primarily focuses on parsing algorithms that facilitate subsequent hardware processing.
Based on the human visual contrast mechanism, we propose a weighted contrast local contrast method.This algorithm effectively eliminates various clutter and point noise, making it suitable for detecting small targets amidst different background noises.It demonstrates robustness even when the size of the target changes.Furthermore, this algorithm does not require preprocessing and exhibits good robustness.It does not rely on extensive data for a specific network model and possesses the ability for parallel execution.This allows for real-time feedback in target detection systems and facilitates easy productization to address industry needs.
In summary, the main objectives of this study are as follows: (1) to design a contrast method that combines ratio and difference operations to inhibit background noise and enhance target detection; (2) to introduce a novel weighting function, to further restrain random noise; and (3) to design multi-scale operations to accommodate targets with varying sizes.

Proposed Method
We begin by analyzing the traits of the target and the different background types depicted in Figure 1.Subsequently, leveraging these characteristics, we present a weighted ratio-difference local contrast method, termed WRDLCM.images, moving targets tend to have higher pixel values compared to the stationary background.
(2) In an infrared image, a normal background typically appears in large quantities, characterized by relatively low pixel values.Conversely, the target pixels exhibit a significantly larger value, rendering it more prominent when contrasted with the normal background.(3) A high-brightness background often manifests as a largely connected area with substantial pixel values.While these pixel values may exceed those of the real target, the differences in pixel values between highlighted backgrounds are relatively small.Consequently, it becomes easier to distinguish the genuine target from the highlighted backdrop.(4) When dealing with backgrounds that contain edges, a significant difference is usually noticeable in a particular direction.However, real targets differ from their neighboring elements in all surrounding directions.(5) The pixel value of PNHB may closely resemble that of a real target.However, PNHB occupies a very limited number of pixels, often just a single pixel, whereas the pixels corresponding to the real target form a circular area with a similar appearance [45].
Based on the above observation results, contrast features can be designed to accurately capture real targets [46,47].

The Characteristics of the Target and Other Different Types of Backgrounds
An IR image containing a small dim target [44] is depicted in Figure 1, encompassing various components: True small target (TT), normal large area background (NB), background with relatively high brightness across the entire image (HB), background with an edge shape (EB), and pixel-sized noises with high brightness (PNHB).The 3D distributions provide a comprehensive visualization of the detailed pixel information for each component.Based on the characteristics observed in both the two-dimensional and three-dimensional images depicted in Figure 1: (1) A genuine infrared target typically exhibits a concentrated region where pixel values gradually diminish from the center outwards, with a relatively finite number of pixels distributed across the entire image.Leveraging the principles of thermal infrared images, moving targets tend to have higher pixel values compared to the stationary background.(2) In an infrared image, a normal background typically appears in large quantities, characterized by relatively low pixel values.Conversely, the target pixels exhibit a significantly larger value, rendering it more prominent when contrasted with the normal background.(3) A high-brightness background often manifests as a largely connected area with substantial pixel values.While these pixel values may exceed those of the real target, the differences in pixel values between highlighted backgrounds are relatively small.Consequently, it becomes easier to distinguish the genuine target from the highlighted backdrop.(4) When dealing with backgrounds that contain edges, a significant difference is usually noticeable in a particular direction.However, real targets differ from their neighboring elements in all surrounding directions.(5) The pixel value of PNHB may closely resemble that of a real target.However, PNHB occupies a very limited number of pixels, often just a single pixel, whereas the pixels corresponding to the real target form a circular area with a similar appearance [45].
Based on the above observation results, contrast features can be designed to accurately capture real targets [46,47].
On the basis of analyzing the above objectives and the characteristics of different types of backgrounds, we propose a weighted ratio-difference local contrast method(WRDLCM) consisting of two main components: a fundamental local comparison algorithm and a weight function.The first component entails a ratio-based and difference-based local contrast algorithm that facilitates target enhancement while suppressing the background.The second component involves a weight function, which incorporates the concept of ratio-difference combination.Additionally, to accommodate targets of different sizes, a multi-scale algorithm is devised.Notably, prior to calculating the weight function, we introduce the IRIL approach that suppresses random noise by utilizing the average value of the largest pixels instead of solely relying on the maximum value.This method has proven advantageous in detecting targets moving within complex environments.The proposed algorithm prioritizes a restricted number of pixels within the local small area during the calculation of each pixel, leading to a reduced computational load.Furthermore, the algorithm supports parallel processing techniques, thereby facilitating efficient realtime performance.

Design of the Detection Algorithm
Based on the preceding analysis, it is established that a truly small target within an infrared (IR) image exhibits notable significance within a limited vicinity of its surrounding neighborhood.Additionally, the pixel value of the target gradually diminishes from the center toward the periphery, while the normal background tends to be dark and featureless.Consequently, it is feasible to concentrate on the localized range encompassing the target and its surroundings, represented by a window (as depicted in Figure 2).We define this confined pixel range as an image block, comprising nine sub-blocks: a central sub-block 15, 2922 5 of 23 denoted as T and eight neighboring sub-blocks labeled as B1 to B8.By traversing the entire image using these image blocks, the central sub-block can effectively discern the presence of a genuine target, while the surrounding sub-blocks aid in determining background information.In situations where target measurements are inconclusive, the size of the subblock, denoted as N, should correspond to the dimensions of the largest small target [22].According to the international optical organization SPIE, small targets typically exhibit dimensions smaller than 9 × 9 pixels [48].
background information.In situations where target measurements are inconclusive, th size of the sub-block, denoted as N, should correspond to the dimensions of the large small target [22].According to the international optical organization SPIE, small targe typically exhibit dimensions smaller than 9 × 9 pixels [48].
The detailed process of the WRDLCM algorithm is depicted in Figure 3. Initially, fo the unknown target, the number of possible scales can be set first, and the contrast can b calculated at each scale, for example, at the pth scale, the local contrast methods of rat (RLCMp) and difference (DLCMp), as well as the weight function based on the local co trast method (WLCMp), are computed for the window.The RLCMp and DLCMp are the combined to form RDLCMp, which is multiplied by the weighting function to obta WRDLCMp.Finally, the maximum value across multiple scales is selected as th WRDLCM output.We will describe the multi-scale detection method in Section 2.2.5.B applying a threshold, precise target identification can be achieved.The detailed process of the WRDLCM algorithm is depicted in Figure 3. Initially, for the unknown target, the number of possible scales can be set first, and the contrast can be calculated at each scale, for example, at the pth scale, the local contrast methods of ratio (RLCMp) and difference (DLCMp), as well as the weight function based on the local contrast method (WLCMp), are computed for the window.The RLCMp and DLCMp are then combined to form RDLCMp, which is multiplied by the weighting function to obtain WRDLCMp.Finally, the maximum value across multiple scales is selected as the WRDLCM output.We will describe the multi-scale detection method in Section 2.2.5.By applying a threshold, precise target identification can be achieved.Traversing the image block through the entire image will ultimately result in a new matrix in which the target will occupy the highlighted pixel portion, and the pixel value of the remaining background portion is 0.

R E T R A C T E D
Traversing the image block through the entire image will ultimately result in a new matrix in which the target will occupy the highlighted pixel portion, and the pixel value of the remaining background portion is 0.

The Calculation of the Radio-Based Local Contrast Method (RLCM)
In many papers, it is common for authors to calculate contrast using the maximum pixel value.However, these approaches may not effectively suppress normal backgrounds or minor noise surrounding the target, leading to inaccurate small target detection.In this article, we propose a different method where contrast is calculated using average pixel values.This approach allows for the elimination of background and clutter, resulting in more accurate small target detection.
In the ith direction, the pixel contrast of RLCM i between the background sub-block Bi and the center sub-block T is identified as follows: where (2) here, ξ is a small value greater than 0. In the event that the denominator in the above formula is 0, ξ is set to 1. K 1 and K 2 represent the maximum number of grayscale values in the sub-block, Gray j T and Gray j Bi denote the jth maximal gray value of T and Bi, respectively.The inclusion of mean operations in M T and M Bi helps mitigate the interference of PNHB.Moreover, considering that the real target typically exhibits attenuation from the center, it is recommended to set K 1 to a value smaller than the pixel count of the target.This choice ensures a larger RLCM value, thereby enhancing the target.Additionally, for better results, it is advisable for K 2 to be slightly larger than K 1 .
In the context of the image block illustrated in Figure 2, there are eight directions surrounding the target.To counteract the impact of edge background, the RLCM is described as follows:

The Calculation of the Difference-Based Local Contrast Method (DLCM)
Based on the analysis presented in Section 2.1, it is observed that a high-brightness background typically manifests as a connected region with significantly larger pixel values, exhibiting similarity within the highlighted background area.Exploiting this characteristic, we can devise a differential form of contrast to counter the effects of the highlighted background.The contrast difference in the ith direction is defined as follows: where M T and M Bi are the same as in Formulas ( 2) and (3), respectively, and ξ is defined as in Formula (3).The absolute value in Formula (5) is used to avoid negative values.The final DLCM is obtained by selecting the largest DLCM value among the eight neighborhood directions, as expressed by the following equation:

The Calculation of the RDLCM
As discussed earlier, RLCM is effective in handling complex background edges, PNHB, and normal background, while DLCM is capable of eliminating a high-light background and PNHB.To enhance the real target more effectively, we propose a ratio-difference combined local contrast method (RDLCM) that combines the strengths of RLCM and DLCM.By calculating the Hadamard product of RLCM and DLCM, the calculation formula for RDLCM is as follows: 2.2.4.Definition of the WLCM (1) The Improved RIL In scenarios where the image contains multiple backgrounds and significant clutter, relying solely on RDLCM for detection may lead to false alarms.To address this challenge, this paper introduces a novel weighting function that comprises two components.The first component involves the introduction of the IRIL, which aims to mitigate the impact of clutter and enhance target detection accuracy.The second component focuses on the computation of the weighting function based on the ratio-difference combination.Together, these components contribute to improving the detection algorithm's overall effectiveness.
The RIL introduced by Lv et al. [41] is a valuable metric for evaluating the intricacy of a block.However, the initial RIL definition, sensitive to isolated random noise, is merely determined as the difference between the block's highest value and its mean value.To address this limitation, we propose the IRIL, which incorporates the mean value to mitigate the impact of isolated random noise.This improved definition applies to both the IRIL i of neighborhood sub-blocks Bi and the IRIL T of the center sub-block T.
where M T and M Bi are the same as Formulas ( 2) and (3), respectively.The subscript "mean" indicates the average value.The absolute value in Formula ( 10) is used to ensure nonnegativity.ξ is the same as in Formula (3).The results of M T and M Bi from Formula (2) and Formula (3) can be directly utilized without precomputation, which greatly enhances efficiency.The final IRIL value is obtained through the maximum pooling procedure.
(2) The WLCM In this paper, similar to the calculation method of the RDLCM, The WLCM is computed using both ratio and difference operations.IRIL T and IRIL are incorporated as weighting factors to calculate the ratio and difference, respectively.The weight value w(x, y) of a specific pixel (x, y) is obtained as follows: When defining WLCM, we take into consideration non-negative constraints to ensure that the weight function remains positive.The weighting function in this study is designed based on the similarities and differences between the target and background.Compared to existing weight function approaches, it incorporates a wider range of factors, providing a more comprehensive representation.Algorithm 1 shows the calculation steps of WRDLCM at the pth scale.

Multi-scale WRDLCM Calculation
The previous basic contrast algorithm and weight function are multiplied using the Hadamard product to form WRDLCM, as shown in Equation ( 13).This operation effectively enhances small targets throughout the entire image.The contrast calculation for each window is performed in parallel, improving the program's runtime speed and satisfying the real-time demands of the probing system.
Regarding the key parameter K in Formulas ( 2) and ( 3), achieving multi-scale target detection requires self-adaptive adjustment based on the target's size.By applying Formulas (1) to (13), the WRDLCM can be determined, and the WRDLCM values at different scales can be maximized.The formula is as follows: The range of p is 1 to L, representing the first scale, the second scale, and so on.L represents the number of scales.It is important to note that real targets are typically brighter than their surrounding objects.To further suppress clutter, non-negative constraints are applied.
The process of multi-scale WRDLCM calculation can be described as follows: (1) For the pth scale, suitable values of K 1 and K 2 are selected.In this paper, three scales are designed.For scale 1 (target size 3 × 3), the values of K 1 , K 2 , and N are configured to 2, 4, and 5, respectively; for scale 2 (target size 5 × 5), the values of K 1 , K 2 , and N are configured to 9, 18, and 7, respectively; for scale 3 (target size 7 × 7), the values of K 1 , K 2 , and N are configured to 16, 32, and 9, respectively.(2) For a given IR image, the output of the maximum WRDLCM at each pixel across different scales is determined using Formula (14).It can be easily demonstrated that performing multi-scale WRDLCM calculation yields the most appropriate detection results.Furthermore, this algorithm incorporates parallel operations during the contrast calculation, significantly optimizing the real-time performance of the detection system.
Algorithm 2 gives the main steps of the multi-scale WRDLCM calculation.

Performance Analysis and Threshold Manipulation 3.1. Analysis of Detection Performance
Figure 4 shows image blocks in various regions in the original IR image.The left side of each graphical block represents its 3D distribution.Specifically, Figure 4a illustrates a region containing a genuine small target, while the remaining sub-images showcase different types of backgrounds.

Threshold Operation
After the computation of WRDLCM, the target becomes highly prominent in the im age, while the majority of the background is filtered out.Subsequently, the employme of threshold operations enables the extraction of the genuine target.The formula for d termining the threshold value is as follows: where  is a given factor between 0 and 1.
During our analysis of experimental results, we determined that an appropria range for the threshold parameter  lies between 0.6 and 0.9.Utilizing the WRDLCM r sults, we solely extract the portion where the pixel value exceeds the threshold.To e hance the displayed outcome, we further apply an expansion operation to the extract region.The output result of the algorithm comprises the small target along with its e panded region.

Experimental Analysis and Results
To validate the algorithm proposed in this article, we conducted experiments usin A thorough observation of the 3D distribution map in Figure 4 reveals distinct characteristics for both the target and each background type.By employing the ratio and difference calculations in the algorithm, it can be deduced that only the WRDLCM of the real target yields the highest value.Consequently, this analysis demonstrates the capability to accurately detect small targets.

Threshold Operation
After the computation of WRDLCM, the target becomes highly prominent in the image, while the majority of the background is filtered out.Subsequently, the employment of threshold operations enables the extraction of the genuine target.The formula for determining the threshold value is as follows: where λ is a given factor between 0 and 1.
During our analysis of experimental results, we determined that an appropriate range for the threshold parameter λ lies between 0.6 and 0.9.Utilizing the WRDLCM results, we solely extract the portion where the pixel value exceeds the threshold.To enhance the displayed outcome, we further apply an expansion operation to the extracted region.The output result of the algorithm comprises the small target along with its expanded region.

Experimental Analysis and Results
To validate the algorithm proposed in this article, we conducted experiments using various infrared small target datasets.All experiments were conducted on a 2.70 GHz Intel Core i5-6400 PC with 8 GB of RAM under MATLAB environment.

Data and Performance Evaluation Indicators
In this paper, the number of scales we utilized is three, and the size distribution of N is set to 5 × 5, 7 × 7, and 9 × 9, respectively.We conducted tests on infrared images consisting of 1400 frames from multiple sequences.These sequences encompassed varying sizes of small targets and distinct backgrounds.Table 1 offers a general outline of the first frame image of each sequence.Some of these sequences were captured by HgCdTe infrared detectors, and depict floor plans near Wuhan Tianhe International Airport, while the remaining images were provided by our team.We use the common signal clutter ratio gain (SCRG) and background suppression factor (BSF) to evaluate the capability of the algorithm.Higher values of these performance indicators indicate better performance.SCR stands for signal-to-noise ratio.A small target with a higher SCR is more easily detectable.SCRG measures the level of enhancement of the input and output signals of a target in comparison to the background.It is also an indicator of the difficulty of detecting small targets.SCR and SCRG are established as follows: where µ t signifies the average pixel size of the target, µ b represents the pixel value size of the area around the target, and σ b is the standard deviation of pixel values around the target.SCRG in indicates the signal-to-noise ratio of the input image, and SCRG out epitomizes the signal-to-noise ratio of the output image.BSF indicates the efficacy of background attenuation, and the formula is as follows: where C in signifies the deviation from the mean of the original input image, and C out symbolizes the deviation from the mean of the output image after detection.

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C T E D

Experimental Outcomes Using the Proposed Method
In Figure 5a, we present samples from six sequences where the real target is not prominent in the entire image, occupying only a few pixels, with significant interference surrounding it.Figure 5b showcases the calculation output of RLCM (displaying a singlescale result with a block size of 5 × 5). Figure 5c displays the results of DLCM, while Figure 5d demonstrates the joint operation of RLCM and DLCM, resulting in RDLCM.Compared to Figure 5b, Figure 5d effectively filters out most of the background, making the infrared target more salient.The effect of the weight function WLCM, designed in this paper, is displayed in Figure 5e. Figure 5f showcases the combined performance of WLCM and WRDLCM.In Figure 5g, the target becomes more prominent, and the background is nearly suppressed due to the influence of the weight function.Finally, accurate detection of the actual target is achieved through threshold operations, as depicted in Figure 5h.To assess the adaptability of the proposed algorithm to the real-time motion of infrared targets, we conducted tests on randomly selected images from the aforementioned six sequences (excluding the images used in Figure 5).The results, presented in Figure 6, demonstrate that even with random image selection within the sequence, the algorithm reliably detects the real target.This further confirms the effectiveness of the algorithm and its ability to adapt to varying scenarios.To assess the adaptability of the proposed algorithm to the real-time motion of infrared targets, we conducted tests on randomly selected images from the aforementioned six sequences (excluding the images used in Figure 5).The results, presented in Figure 6, demonstrate that even with random image selection within the sequence, the algorithm reliably detects the real target.This further confirms the effectiveness of the algorithm and its ability to adapt to varying scenarios.

Comparisons with Popular Methods
The algorithms that were compared to our proposed algorithm include VAR-D [6], ILCM [21], NLCM [22], MPCM [24], RLCM [23], MDTDLMS [25], and WLDM [2 The VAR-DIFF algorithm incorporates a weight function in its contrast calculation, bu only utilizes a difference operation.ILCM and MPCM are sub-block-based methods w out weighting.The RLCM and MDTDLMS algorithms employ both difference and ra operations.The weight functions in WLDM and NLCM are designed based on spec characteristics of small targets.Our proposed algorithm, WRDLCM, introduces a no approach combining ratio-difference operations and a new weighting function.
Tables 2 and 3 present a thorough comparison of different algorithms using t widely adopted performance metrics: SCRG and BSF.Higher values of these performa indicators indicate better performance.Our algorithm demonstrates significant impro ment in enhancing genuine targets, leading to favorable SCRG and BSF values across m scenarios.

Comparisons with Popular Methods
The algorithms that were compared to our proposed algorithm include VAR-DIFF [6], ILCM [21], NLCM [22], MPCM [24], RLCM [23], MDTDLMS [25], and WLDM [27].The VAR-DIFF algorithm incorporates a weight function in its contrast calculation, but it only utilizes a difference operation.ILCM and MPCM are sub-block-based methods without weighting.The RLCM and MDTDLMS algorithms employ both difference and ratio operations.The weight functions in WLDM and NLCM are designed based on specific characteristics of small targets.Our proposed algorithm, WRDLCM, introduces a novel approach combining ratio-difference operations and a new weighting function.
Tables 2 and 3 present a thorough comparison of different algorithms using two widely adopted performance metrics: SCRG and BSF.Higher values of these performance indicators indicate better performance.Our algorithm demonstrates significant improvement in enhancing genuine targets, leading to favorable SCRG and BSF values across most scenarios.VAR-DIFF performs well from the perspective of SCRG and BSF in the second and third sequences but shows limited performance in the remaining sequences.The differential operation in VAR-DIFF can effectively eliminate backgrounds with large areas of similar pixel values and accurately detect genuine targets.However, it struggles to suppress complex backgrounds in the presence of bright backgrounds or clutter, resulting in a subpar performance in the other four sequences.ILCM, NLCM, MPCM, and RLCM all exhibit low SCRG and BSF values, as these methods do not employ weight functions to enhance targets.They simply rely on differential or ratio-difference combined contrast for target detection.WLDM, on the other hand, incorporates a weight function to enhance targets and demonstrates high SCRG values in the third, fifth, and sixth sequences, as its designed weight function effectively resists cloud edges.MDTDLMS combines the concepts of background estimation and difference ratio, and exhibits excellent SCRG performance in the first sequence due to the simplicity of the background, which allows for accurate estimation.However, its performance in other sequences is not as strong as that of our proposed method.Based on the calculation results, our proposed method demonstrated superior performance in comparison to most methods, consistently achieving outstanding SCRG and BSF values across all six sequences.Although the SBE method may have outperformed our algorithm in certain sequences, its algorithmic complexity surpasses that of our proposed method.

R E T R A C T E D
The receiver operating characteristic (ROC) curve is an important measure for evaluating the capability of an algorithm.It gives a graphical depiction of the relationship between the true positive rate and the false positive rate.Figure 7 presents the comparison of ROC curves for different algorithms.In addition to the aforementioned comparison algorithms, several additional methods are included in the ROC curve comparison, such as TLLCM [26], STLCM [49], TCF [50], STLCF [51], SBE [52], and WSLCM [53], which are popular algorithms of different types.From the ROC curve, it is evident that our proposed method outperforms most algorithms and is comparable to newer approaches developed in recent years.To evaluate the capability of the algorithm, we conducted tests on both a real dataset and a simulated dataset consisting of 200 infrared images containing small targets and complex backgrounds.The simulation parameters were set as follows: an image size of 256 × 320 pixels, a signal-to-noise ratio of 0.2, a background brightness of 100, a target brightness of 120, and a bright region in the upper left corner of the simulated image with a brightness value of 150.The initial target coordinates on the first frame were set to 80 on the vertical axis and 20 on the horizontal axis.The horizontal positions were incremented by 1 for each subsequent frame.The target's shape was generated using a two-dimensional Gaussian model.The target and background were combined to create the simulated image, and random noise with a noise intensity of 20 was added.

R E
Subsequently, the performance of the proposed algorithm was tested on this simulated dataset, and several comparative algorithms were also applied to assess the dataset and generate ROC curves.Figure 8 illustrates the challenges posed by the bright background and complex noise in the vicinity of the target, making target detection difficult.We tested the images from the 200 datasets and selected two random images to showcase the detection results.As depicted in Figure 8, small targets can be accurately detected even in the presence of complex bright backgrounds and noise.
Figure 9 presents the comparison results of the ROC curves for several popular algorithms on the simulated dataset.Our algorithm ranked second in terms of performance.The optimal MDTDLMS-RDLCM [25] algorithm, which combines background estimation and local contrast design, achieved the best performance.This demonstrates the practicality of our algorithm in real-world scenarios.In future work, we can explore the integration of background estimation to design local contrast more suited for target detection.Overall, our algorithm is applicable for detecting small targets in both real and simulated scenarios.To evaluate the capability of the algorithm, we conducted tests on both a real dataset and a simulated dataset consisting of 200 infrared images containing small targets and complex backgrounds.The simulation parameters were set as follows: an image size of 256 × 320 pixels, a signal-to-noise ratio of 0.2, a background brightness of 100, a target brightness of 120, and a bright region in the upper left corner of the simulated image with a brightness value of 150.The initial target coordinates on the first frame were set to 80 on the vertical axis and 20 on the horizontal axis.The horizontal positions were incremented by 1 for each subsequent frame.The target's shape was generated using a two-dimensional Gaussian model.The target and background were combined to create the simulated image, and random noise with a noise intensity of 20 was added.
Subsequently, the performance of the proposed algorithm was tested on this simulated dataset, and several comparative algorithms were also applied to assess the dataset and generate ROC curves.Figure 8 illustrates the challenges posed by the bright background and complex noise in the vicinity of the target, making target detection difficult.We tested the images from the 200 datasets and selected two random images to showcase the detection results.As depicted in Figure 8, small targets can be accurately detected even in the presence of complex bright backgrounds and noise.

R E T R A C T E D
Figure 9 presents the comparison results of the ROC curves for several popular algorithms on the simulated dataset.Our algorithm ranked second in terms of performance.The optimal MDTDLMS-RDLCM [25] algorithm, which combines background estimation and local contrast design, achieved the best performance.This demonstrates the practicality of our algorithm in real-world scenarios.In future work, we can explore the integration of background estimation to design local contrast more suited for target detection.Overall, our algorithm is applicable for detecting small targets in both real and simulated scenarios.

Experiments against Random Noise
Random noise is a significant factor that can degrade detection performance.To assess the robustness of our algorithm, we introduced different levels of noise to the original images from the sequence used in the previous experiments.Figure 10 illustrates the results where white noise with a variance of 0 and mean values ranging from 1 to 5 was added to the images.Subsequently, a performance test for target detection was conducted.From the ROC curve results presented in Figure 10, it is evident that our proposed algorithm performs well across all noise conditions.Regardless of the varying levels of noise, our algorithm consistently demonstrates reliable detection capabilities.

Experiments against Random Noise
Random noise is a significant factor that can degrade detection performance.To assess the robustness of our algorithm, we introduced different levels of noise to the original images from the sequence used in the previous experiments.Figure 10 illustrates the results where white noise with a variance of 0 and mean values ranging from 1 to 5 was added to the images.Subsequently, a performance test for target detection was conducted.From the ROC curve results presented in Figure 10, it is evident that our proposed algorithm performs well across all noise conditions.Regardless of the varying levels of noise, our algorithm consistently demonstrates reliable detection capabilities.Table 4 provides a comparison of the processing times between several deep learning methods and our proposed approach.The results demonstrate that our method is capable of processing a higher number of frames per unit of time, effectively meeting the real-time requirements.By contrast, deep learning methods such as RIPT [38], PSTNN [39], and MF-LWCNN [40] require more time for processing.Table 4 provides a comparison of the processing times between several deep learning methods and our proposed approach.The results demonstrate that our method is capable of processing a higher number of frames per unit of time, effectively meeting the real-time requirements.By contrast, deep learning methods such as RIPT [38], PSTNN [39], and MF-LWCNN [40] require more time for processing.

Testing of Multiple Targets
To further analyze the effectiveness of our proposed method, we conducted experiments using a sequence containing multiple frames to detect two infrared small targets.Specifically, we utilized Seq.7, which consists of 200 frames, with the background primarily comprising a sea scene.The small targets in the images represent ships, and the image size is 280 × 228.The target sizes range from 5 × 5 to 7 × 7.
Figure 11 illustrates the detection results for two targets.The experimental outcomes validate the capability of our proposed method in highlighting the targets amidst intricate backgrounds.The WRDLCM calculation enhances the visibility of the targets, and the subsequent weighted processing significantly filters out the majority of the background, further emphasizing the targets.By applying a threshold value, the actual targets can be accurately identified.Figure 12 showcases the detection results of Seq.7 with the addition of random noise.As depicted in Figure 12c, the original image becomes blurred, and the identification of small targets becomes more challenging.Despite the difficulty introduced by the noise, the ROC curve demonstrates the stable performance of our proposed algorithm.However, when the noise variance reaches 8, which is relatively strong, the ROC curve exhibits a slight decrease.This indicates that our algorithm maintains good performance even in the presence of severe noise interference.small targets becomes more challenging.Despite the difficulty introduced by the noise, the ROC curve demonstrates the stable performance of our proposed algorithm.However, when the noise variance reaches 8, which is relatively strong, the ROC curve exhibits a slight decrease.This indicates that our algorithm maintains good performance even in the presence of severe noise interference.
(e) (f) (g) (h) Figure 12 showcases the detection results of Seq.7 with the addition of random noise.As depicted in Figure 12c, the original image becomes blurred, and the identification of small targets becomes more challenging.Despite the difficulty introduced by the noise, the ROC curve demonstrates the stable performance of our proposed algorithm.However, when the noise variance reaches 8, which is relatively strong, the ROC curve exhibits a slight decrease.This indicates that our algorithm maintains good performance even in the presence of severe noise interference.Furthermore, we conducted performance tests on single-frame images sourced from the single-frame dataset [53] and the public SIRST dataset [54].These single-frame images Furthermore, we conducted performance tests on single-frame images sourced from the single-frame dataset [53] and the public SIRST dataset [54].These single-frame images allow us to assess the algorithm's capability when spatiotemporal information from consecutive frames cannot be utilized.As depicted in Figure 13, our method achieves accurate target detection even with single-frame images.allow us to assess the algorithm's capability when spatiotemporal information from consecutive frames cannot be utilized.As depicted in Figure 13, our method achieves accurate target detection even with single-frame images.

Detection of Small Inland UAV Targets Using Infrared Images
The accurate detection of small UAV targets holds great significance in both the military and civilian domains.This section focuses on evaluating the algorithm performance using inland UAV target datasets obtained from the reference [55].
As depicted in Figure 14, this paper employs five real UAV sequences for testing, representing diverse and complex scenes.Figure 14a displays the original IR sequences used for testing, while Figure 14b-f present the results of each step in the proposed The accurate detection of small UAV targets holds great significance in both the military and civilian domains.This section focuses on evaluating the algorithm performance using inland UAV target datasets obtained from the reference [55].
As depicted in Figure 14, this paper employs five real UAV sequences for testing, representing diverse and complex scenes.Figure 14a displays the original IR sequences used for testing, while Figure 14b-f present the results of each step in the proposed method.Figure 14g depicts the target detected after the threshold operation.Notably, Figure 14e showcases the outcome obtained through the application of the weight function, effectively filtering out most of the noise and significantly enhancing the visibility of the small target.Figure 14f represents the detection result obtained by combining RDLCM and WLCM.Finally, the threshold value is applied to filter the target region, resulting in the precise identification of the actual small target.Furthermore, to assess the performance of our method in the presence of noise, a certain level of noise with a mean value of 0 and a variance of 20 is added to the image in Figure 14. Figure 15 illustrates the detection results for images with added noise.As observed in Figure 15b, the image becomes considerably blurred after the introduction of random noise.However, as demonstrated in the final result depicted in Figure 15f Most of the aforementioned comparison algorithms do not consider the spatial and temporal dependencies between frames.By contrast, the method proposed in [56], referred to as MSLSTIPT, utilizes spatiotemporal information to extend image data to tensor domains.While this algorithm is novel and unique, it may not be effective for all small target detection scenarios.Figure 16 illustrates the comparison results between the MSLSTIPT algorithm and our proposed method on a small UAV target sequence, which is one of the five sequences mentioned in Figure 14.The first row shows the original images of the UAV sequence for the first six frames, while the second row presents the detection output of the MSLSTIPT algorithm.By contrast, the third row displays the detection output of our algorithm.It can be observed from the second row that the MSLSTIPT algorithm generates numerous false alarms and fails to achieve satisfactory detection performance.However, our algorithm demonstrates superior detection performance for these six sequential frames, as depicted in the third row.Most of the aforementioned comparison algorithms do not consider the spatial and temporal dependencies between frames.By contrast, the method proposed in [56], referred to as MSLSTIPT, utilizes spatiotemporal information to extend image data to tensor domains.While this algorithm is novel and unique, it may not be effective for all small target detection scenarios.Figure 16 illustrates the comparison results between the MSLSTIPT algorithm and our proposed method on a small UAV target sequence, which is one of the five sequences mentioned in Figure 14.The first row shows the original images of the UAV sequence for the first six frames, while the second row presents the detection output of the MSLSTIPT algorithm.By contrast, the third row displays the detection output of our algorithm.It can be observed from the second row that the MSLSTIPT algorithm generates numerous false alarms and fails to achieve satisfactory detection performance.However, our algorithm demonstrates superior detection performance for these six sequential frames, as depicted in the third row.

Conclusions
This paper presents a novel WRDLCM algorithm that combines the RDLCM a WLCM methods.The RDLCM algorithm leverages the benefits of both ratio-type and d ference-type local-contrast-based methods.It effectively suppresses various types of terference and enhances target objects without requiring any preconditioning algorithm Additionally, a new weighting function, WLCM, is proposed.This function calcula weighting factors using mean value arithmetic operations to mitigate single random noi By applying threshold filtering, the proposed algorithm accurately outputs the actual t get.The preliminary results demonstrate the effectiveness of our target detection a proach across various scenarios.Furthermore, our method is capable of detecting sm targets even when their scale changes.
Moreover, our approach offers advantages in FPGA hardware processing compar to deep learning methods.While deep learning methods exhibit good detection perf mance, their hardware implementation is challenging and may not meet the practical quirements of industrial applications, particularly in real-world product deployme Therefore, in future work, we aim to explore the integration of traditional algorithms w deep learning techniques to achieve real-time object detection for targets of different siz Additionally, we plan to focus on hardware implementation and production by levera ing FPGA technology, ensuring the wider applicability of our approach.

Conclusions
This paper presents a novel WRDLCM algorithm that combines the RDLCM and WLCM methods.The RDLCM algorithm leverages the benefits of both ratio-type and difference-type local-contrast-based methods.It effectively suppresses various types of interference and enhances target objects without requiring any preconditioning algorithms.Additionally, a new weighting function, WLCM, is proposed.This function calculates weighting factors using mean value arithmetic operations to mitigate single random noise.By applying threshold filtering, the proposed algorithm accurately outputs the actual target.The preliminary results demonstrate the effectiveness of our target detection approach across various scenarios.Furthermore, our method is capable of detecting small targets even when their scale changes.
Moreover, our approach offers advantages in FPGA hardware processing compared to deep learning methods.While deep learning methods exhibit good detection performance, their hardware implementation is challenging and may not meet the practical requirements of industrial applications, particularly in real-world product deployment.Therefore, in future work, we aim to explore the integration of traditional algorithms with deep learning techniques to achieve real-time object detection for targets of different sizes.Additionally, we plan to focus on hardware implementation and production by leveraging FPGA technology, ensuring the wider applicability of our approach.

Figure 1 .Figure 1 .
Figure 1.(a) A really small infrared target with other backgrounds; (b) a three-dimensional display of the target and four different types of backgrounds.On the basis of analyzing the above objectives and the characteristics of different types of backgrounds, we propose a weighted ratio-difference local contrast method(WRDLCM) consisting of two main components: a fundamental local comparison algorithm and a weight function.The first component entails a ratio-based and differencebased local contrast algorithm that facilitates target enhancement while suppressing the background.The second component involves a weight function, which incorporates the concept of ratio-difference combination.Additionally, to accommodate targets of differ-Figure 1.(a) A really small infrared target with other backgrounds; (b) a three-dimensional display of the target and four different types of backgrounds.

Figure 2 .
Figure 2. Local small image window used for WRDLCM calculation.

Figure 2 .
Figure 2. Local small image window used for WRDLCM calculation.

24 Figure 3 .
Figure 3.The detailed process of the WRDLCM algorithm.

Figure 3 .
Figure 3.The detailed process of the WRDLCM algorithm.

Algorithm 1
WRDLCM computation at the pth scale Input: Raw IR image and the parameters N, K 1 , and K 2 .Output: The result of the WRDLCMp calculation is a matrix called WRDLCMp.1: Create a patch consisting of 9 cells, as depicted in Figure 2. 2: Translate the patch horizontally in a left-to-right motion and vertically from top-to-bottom over the raw IR image.3: At every pixel, compute its corresponding RLCMp and DLCMp values using formulas (1)-(6).4: Once the calculation is completed for the entire image, create two new matrices RLCMp and DLCMp to store the results.5: Standardize the constituents in RFLCMp to the range (0, 1).6: Standardize the elements in DFLCMp to the range (0, 1).7: Compute the RDLCMp of the raw IR image by taking the Hadamard consequence of RLCMp and DLCMp: 8: Compute the WLCMp of the raw IR image using formulas (8)-(12).9: Standardize the parts in WLCMp to the range (0, 1).10: Determine the WRDLCMp of the raw IR image by performing the Hadamard outcome of RDLCMp and WLCMp.

Figure 4 .
Figure 4. Image blocks in different regions in the original infrared image: (a-f) represent the re small target, highlighted background, edge background, point noise, normal background, and pu noise in sequence, respectively.

Figure 4 .
Figure 4. Image blocks in different regions in the original infrared image: (a-f) represent the real small target, highlighted background, edge background, point noise, normal background, and pulse noise in sequence, respectively.

24 Figure 5 .
Figure 5.The result of contrast calculation at each step of the algorithm for the six sequences: (a) original infrared image; (b-f) calculation results of RLCM, DLCM, RDLCM, WLCM, and WRDLCM at the same scale, respectively; (g) results of maximizing WRDLCM at multiple scales; and (h) threshold screening and detection results after expansion.

Figure 5 .
Figure 5.The result of contrast calculation at each step of the algorithm for the six sequences: (a) original infrared image; (b-f) calculation results of RLCM, DLCM, RDLCM, WLCM, and WRDLCM at the same scale, respectively; (g) results of maximizing WRDLCM at multiple scales; and (h) threshold screening and detection results after expansion.

Figure 6 .
Figure 6.Step test results of sample images randomly selected from six sequences: (a) original frared image; (b,c) calculation results of RDLCM and WLCM at the same scale, respectively; (d) results of maximizing WRDLCM at multiple scales; and (e) threshold screening and detection sults after expansion.

Figure 6 .
Figure 6.Step test results of sample images randomly selected from six sequences: (a) original infrared image; (b,c) calculation results of RDLCM and WLCM at the same scale, respectively; (d) the results of maximizing WRDLCM at multiple scales; and (e) threshold screening and detection results after expansion.

25 Figure 8 .
Figure 8. Contrast calculation results at the main steps of the algorithm for the simulated images: (a) simulated images; (b,c) calculation results of RDLCM and WLCM at the same scale, respectively; (d) results of maximizing WRDLCM at multiple scales; and (e) threshold screening and detection results after expansion.

Figure 8 .
Figure 8. Contrast calculation results at the main steps of the algorithm for the simulated images: (a) simulated images; (b,c) calculation results of RDLCM and WLCM at the same scale, respectively; (d) results of maximizing WRDLCM at multiple scales; and (e) threshold screening and detection results after expansion.

Figure 8 .
Figure 8. Contrast calculation results at the main steps of the algorithm for the simulated images: (a) simulated images; (b,c) calculation results of RDLCM and WLCM at the same scale, respectively; (d) results of maximizing WRDLCM at multiple scales; and (e) threshold screening and detection results after expansion.

Figure 9 .
Figure 9. ROC curve of detection effect under different algorithms.

Figure 9 .
Figure 9. ROC curve of detection effect under different algorithms.

Figure 12
Figure12showcases the detection results of Seq.7 with the addition of random noise.As depicted in Figure12c, the original image becomes blurred, and the identification of

Figure 12 .
Figure 12.Performance at different noise levels: (a) the raw IR image; (b) Gaussian noise; (c) infrared image with Gaussian white noise (Variance: 8); and (d) ROC curves under different levels of random noise.

Figure 12 .
Figure 12.Performance different noise levels: (a) the raw IR image; (b) Gaussian noise; (c) infrared image with Gaussian white noise (Variance: 8); and (d) ROC curves under different levels of random noise.

Figure 13 .
Figure 13.The 3D graphs of the detection results of each step of our device for the single-frame image: (a) original; (b) RDLCM; (c) WLCM; (d) WRDLCM; and (e) output.

Figure 13 . 6 .
Figure 13.The 3D graphs of the detection results of each step of our device for the single-frame image: (a) original; (b) RDLCM; (c) WLCM; (d) WRDLCM; and (e) output.

Figure 14 .
Figure 14.The 3D graphs of the results of each mechanism step for the single-frame data: (a) original images; (b) image with noise added; (c) result of RLCM; (d) result of DLCM; (e) result of RDLCM; (f) result of WLCM; (g) result of WRDLCM; and (h) final output.

Figure 14 .
Figure 14.The 3D graphs of the results of each mechanism step for the single-frame data: (a) original images; (b) image with noise added; (c) result of RLCM; (d) result of DLCM; (e) result of RDLCM; (f) result of WLCM; (g) result of WRDLCM; and (h) final output.

Figure 16 .
Figure 16.Target sequence and contrast detection results: (a-f) the first to sixth frames of the quence; first row: original sequence image; second row: test results of MSLSTIPT method; third ro test results of our method.

Figure 16 .
Figure 16.Target sequence and contrast detection results: (a-f) the first to sixth frames of the sequence; first row: original sequence image; second row: test results of MSLSTIPT method; third row: test results of our method.

Algorithm 2 multi-scale WRDLCM determination Input:
Raw IR image and the parameters N, K 1 , K 2 , . . ., K L .for L scales.Output: The resulting matrix of the WRDLCM calculation is called WRDLCM.1: for p = 1,2, . . .,L do Compute the WRDLCM p using K p based on Algorithm 1. 2: end for 3: For each pixel, output the highest WRDLCM value across all L scales as the final multi-scale WRDLCM value, denoted as: WRDLCM = max max WRDLCM p , p = 1, 2, . . ., L , 0 (14) where (i, j) is the location of each pixel.

Table 1 .
Description of 6 real infrared sequences.

Table 2 .
The SCRG of different algorithms.

Table 2 .
The SCRG of different algorithms.

Table 3 .
The BSF of different algorithms.

Table 4 .
Processing frame time for different algorithms.

Table 4 .
Processing frame time for different algorithms.