Multi-directional prediction and high-order statistics target detection method for airborne air-to-air imaging

Abstract

The present application belongs to the technical field of target detection, and particularly relates to a multi-direction prediction and high-order statistics target detection method for airborne air-to-air imaging. The method comprises the following steps: S1: obtaining an original infrared image dataset, performing linear fitting filtering on the qth original infrared image to obtain a residual image; S2: selecting a candidate point in the residual image corresponding to the qth original infrared image based on a target threshold; S3: calculating the statistical fourth moment and local gradient level of each candidate point under a multi-scale window, and screening a small target based on the calculation result; S4: replacing the qth original infrared image with the q+1th original infrared image, repeating steps S1-S3, and obtaining the small targets in each original infrared image contained in the original infrared image dataset. The present application does not require target window priori and does not depend on a specific distribution model, can stably operate in a complex and changeable background, and has high engineering practicability and universality.

Description

Technical Field

[0001] This invention belongs to the field of target detection technology, and in particular relates to a multi-directional prediction and high-order statistical target detection method for airborne airborne imaging. Background Technology

[0002] Currently, infrared weak target detection technology has been widely used in airborne photoelectric detection, infrared search and track (IRST) systems, and high-altitude reconnaissance imaging. However, in engineering practice, due to the complex air-to-air imaging environment, significant background non-uniformity, extremely small target size, and low signal-to-noise ratio, traditional weak target detection algorithms often struggle to balance detection accuracy, stability, and real-time performance. Existing technologies can be broadly categorized into four types: traditional filtering methods, background prediction methods, local contrast enhancement methods, and low-rank sparse decomposition methods. However, existing technologies generally face two core difficulties: First, weak background modeling capabilities. In air-to-air infrared imaging, background brightness is affected by multiple factors such as atmospheric radiation, cloud structure, sky layering, and detector non-uniformity, exhibiting significant non-uniformity and complex gradient changes. Existing methods are generally based on the assumption of a stable or slowly changing background, leading to inaccurate prediction, insufficient suppression, and frequent false alarms in complex backgrounds. Second, limited target discrimination capabilities. Most traditional methods rely on low-order statistical features such as mean, variance, and contrast. These features have limited discriminative power in non-Gaussian noise and backgrounds with localized anomalies, making it difficult to effectively distinguish real small targets from background textures, noise impulses, or gradient abrupt changes. In summary, existing infrared small target detection methods still cannot simultaneously satisfy robustness, accuracy, and real-time performance under complex background conditions. There is an urgent need for a detection method with strong background suppression capabilities, high discriminative ability, and suitability for engineering applications. Summary of the Invention

[0003] In view of this, the present invention aims to provide a multi-directional prediction and high-order statistical target detection method for airborne airborne imaging, in order to solve the problem that the existing technology relies on low-order statistical quantities such as mean and variance, which makes it impossible to stably distinguish between "brightness gradient abrupt change" and "weak target". The present invention does not require target window prior, nor does it rely on a specific distribution model. It can operate stably in complex and variable backgrounds and has high engineering practicality and versatility.

[0004] To achieve the above objectives, the technical solution created by this invention is implemented as follows:

[0005] A method for multi-directional prediction and high-order statistical target detection for airborne airborne imaging includes the following steps:

[0006] S1: Obtain the original infrared image dataset, perform linear fitting filtering on the q-th original infrared image, and obtain the residual map corresponding to the q-th original infrared image;

[0007] S2: Set the target threshold corresponding to the q-th original infrared image, and select candidate points in the residual map corresponding to the q-th original infrared image based on the target threshold;

[0008] S3: Construct a multi-scale window, calculate the statistical fourth moment and local gradient level of each candidate point under the multi-scale window, and filter weak targets in the q-th original infrared image based on the calculation results;

[0009] S4: Replace the q-th original infrared image with the (q+1)-th original infrared image, and repeat steps S1-S3 to obtain the weak targets in each original infrared image contained in the original infrared image dataset.

[0010] Furthermore, step S1 specifically includes:

[0011] S11: Obtain the q-th original infrared image, and set the position coordinates in the q-th original infrared image as... Using the pixels to be detected as the pixels, a weighted background estimation optimization model is constructed:

[0012] ;

[0013] Where k is the extraction direction, k∈{0°,45°,90°,135°}. Optimize the weighted background estimation model for the pixels to be detected; Let k be the weighting factor corresponding to the pixel to be detected in the k direction. For background estimation of the pixel to be detected, These are the weighting coefficients of the local variance constraint term. These are the weighting coefficients for the directional gradient strength constraint term. Let be the directional gradient intensity of the pixel to be detected in the k-direction. Let K be the local variance of the pixel to be detected in the k-direction. This is the orientation prediction model for the pixel to be detected in the k direction;

[0014] S12: Calculate the partial derivative of the weighted background estimation optimization model and make the partial derivative result zero to obtain the weighting factor corresponding to the current pixel to be detected.

[0015] ;

[0016] in, This is the adjustment coefficient for the directional gradient intensity term. To stabilize the term and prevent the denominator from being zero;

[0017] S13: Replace the current pixel to be detected with the next pixel to be detected, and repeat steps S11-S12 until the weighting factors corresponding to all pixels of the qth original infrared image are obtained.

[0018] S14: Calculate the estimated grayscale image of the background corresponding to the q-th original infrared image based on the solution result of step S13. :

[0019] ;

[0020] S15: Solve for the residual image corresponding to the qth original infrared image using the following formula. :

[0021] ;

[0022] in, This is the qth original infrared image.

[0023] Furthermore, the orientation prediction model for the pixel to be detected in the k-direction. The expression is:

[0024] ;

[0025] in, To obtain the position coordinates in the q-th original infrared image The pixels are taken as the pixels to be detected, and the pixel sequence of the pixels to be detected in the 0° direction. This is the direction prediction model parameter vector for the pixel to be detected in the k direction.

[0026] Furthermore, the expression for the direction prediction model parameter vector corresponding to the pixel to be detected in the k direction is:

[0027] ;

[0028] in, Let be the prediction model coefficient matrix composed of the neighborhood samples of the pixel to be detected in the k-direction. To obtain the position coordinates in the q-th original infrared image The pixels are taken as the pixels to be detected, and the gray-level prediction vectors of the pixels to be detected in each direction are given.

[0029] Furthermore, the expressions for the grayscale prediction vectors of the pixel to be detected in each direction are:

[0030] ;

[0031] in, Let be the prediction model coefficient matrix composed of the neighborhood samples of the pixel to be detected in the k-direction. Let be the direction prediction model parameter vector corresponding to the pixel to be detected in the k direction. This represents the prediction residual of the direction prediction model for the pixel to be detected in the k direction.

[0032] Furthermore, in step S2, the target threshold corresponding to the qth original infrared image The expression is:

[0033] ;

[0034] in, Let be the mean of the residual image corresponding to the q-th original infrared image. Let be the standard deviation of the residual plot corresponding to the q-th original infrared image.

[0035] Furthermore, in step S2, the formula used to select candidate points in the residual map corresponding to the q-th original infrared image based on the target threshold is:

[0036] ;

[0037] ;

[0038] in, For the qth original infrared image, the th A connected region, Let q be the target threshold corresponding to the q-th original infrared image. Let be the total number of connected regions obtained after target thresholding in the q-th original infrared image. For the candidate point set, For the qth original infrared image, the th The pixel coordinates corresponding to the pixel maxima of each connected region. The residual map obtained after multi-directional prediction and higher-order statistical processing of the q-th original infrared image is shown in pixel coordinates. The response value at that location.

[0039] Furthermore, in step S3, the multi-scale window includes a 10×10 window, a 14×14 window, and an 18×18 window.

[0040] Furthermore, step S3 specifically includes:

[0041] S31: Calculate candidate points Statistical fourth moment under multi-scale windows:

[0042] ;

[0043] in, ( ) is the statistical fourth moment calculation function. For a 10x10 window, For 14x14 windows, For 18x18 windows, For the qth original infrared image, the th A connected region, The statistical fourth moment value corresponding to the candidate point within a window of scale s(t);

[0044] S32: Calculate candidate points Local gradient level:

[0045] ;

[0046] in, Let be the gradient magnitude distribution of the residual map corresponding to the q-th original infrared image;

[0047] S33: Based on candidate points The local gradient level is calculated using the following formula for candidate points. Gradient compensation threshold:

[0048] ;

[0049] in, Candidate points The corresponding gradient compensation threshold, The basic threshold is obtained based on the global statistical characteristics of the residual map. These are the gradient compensation coefficients. It is the numerical stability constant;

[0050] S34: Define candidate points Statistical fourth-order moment scoring function :

[0051] ;

[0052] S35: If Then the candidate points Add the candidate point to the target point set as the target point; otherwise, remove the candidate point. ;

[0053] S36: Replace the current candidate point with the next candidate point, and repeat steps S31-S35 until all candidate points in the candidate point set have been filtered to obtain the target point set. ;

[0054] S37: Output the weak targets in the q-th original infrared image using the following formula. :

[0055] .

[0056] Compared with the prior art, the present invention can achieve the following beneficial effects:

[0057] (1) The multi-directional prediction and high-order statistical target detection method for airborne airborne imaging described in this invention is a complete detection process for engineering applications. It achieves background suppression through multi-directional background prediction, target highlighting through high-order statistical fourth moments, and false alarm suppression through local gradient compensation. The modules work together to achieve accurate extraction of weak targets. This invention is specifically designed to address the challenges of complex cloud textures, sharp brightness gradients, and significant noise interference in airborne infrared imaging. It does not require prior target window information or rely on a specific distribution model, and can operate stably in complex and variable backgrounds, demonstrating high engineering practicality and versatility.

[0058] (2) The multi-directional prediction and high-order statistical target detection method for airborne airborne imaging described in this invention provides a detection method (MBFOM) that combines a linear front-end and a standardized fourth-order moment back-end. In the front-end, a linear gradient fitting model along four main directions is constructed based on multi-directional background prediction, and a weighted fusion scheme with joint constraints of gray-level variance and directional gradient is proposed to balance computational efficiency and background suppression capability while retaining target features. In the back-end, a method based on block image statistical fourth-order moments is proposed, which does not require separating the target from the background. It achieves accurate target representation by utilizing statistical distribution characteristics. In order to reduce the interference of background gradient on statistical fourth-order moments, a local gradient compensation algorithm is designed to represent the complexity of the block region and achieve adaptive adjustment of the threshold. This can achieve efficient suppression of large gradient and complex background interference, stable highlighting of weak targets, improved target detection rate, reduced false alarm rate, and meet the real-time requirements of airborne platforms. Attached Figure Description

[0059] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments and descriptions of the invention are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0060] Figure 1 A flowchart illustrating the multi-directional prediction and high-order statistical target detection method for airborne airborne imaging as described in the embodiments of the present invention;

[0061] Figure 2 A schematic diagram of the structure of the multi-directional prediction and high-order statistical target detection method for airborne airborne imaging as described in the embodiment of the present invention;

[0062] Figure 3 Schematic diagrams of infrared images of the four test sequences and target detection results of different methods described in the embodiments of the present invention;

[0063] Figure 4 ROC curves for the four test sequences described in the embodiments of this invention;

[0064] Figure 5 The processing results of different algorithms described in the embodiments of the present invention;

[0065] Figure 6 The processing results of different methods described in the embodiments of the present invention. Detailed Implementation

[0066] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not constitute a limitation thereof.

[0067] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0068] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on this invention. Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, features defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0069] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0070] The invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0071] like Figures 1 to 2 As shown, this invention proposes a multi-directional prediction and high-order statistical target detection method for airborne airborne imaging, which specifically includes the following steps:

[0072] S1: Obtain the original infrared image dataset, perform linear fitting filtering on the q-th original infrared image, and obtain the residual map corresponding to the q-th original infrared image;

[0073] S2: Set the target threshold corresponding to the q-th original infrared image, and select candidate points in the residual map corresponding to the q-th original infrared image based on the target threshold;

[0074] S3: Construct a multi-scale window, calculate the statistical fourth moment and local gradient level of each candidate point under the multi-scale window, and filter weak targets in the q-th original infrared image based on the calculation results;

[0075] S4: Replace the q-th original infrared image with the (q+1)-th original infrared image, and repeat steps S1-S3 to obtain the weak targets in each original infrared image contained in the original infrared image dataset.

[0076] It should be noted that this invention is a multi-directional prediction and high-order statistical target detection method for airborne airborne imaging. Through a comprehensive technical approach that closely integrates "multi-directional background prediction" and "statistical fourth-order moment discrimination," it achieves dual optimization of front-end background suppression and back-end target saliency enhancement. The overall method follows the principle of "suppressing the background first, then enhancing the target," and is designed with engineering feasibility, real-time performance, and adaptability to complex backgrounds as core considerations. It achieves stable extraction of small targets without relying on prior knowledge of target size or shape.

[0077] In the overall technical framework, the first step is multi-directional background prediction. This step, as the front-end processing stage of the entire algorithm, undertakes the main task of suppressing complex and non-uniform backgrounds. To address the challenges of strong directional changes in background structure, complex gradients, and obvious layering characteristics in aerial imaging, this invention constructs multi-directional neighborhood sequences using four typical directions (0°, 45°, 90°, and 135°). In each direction, least-squares linear fitting is performed on the gray-level sequences of adjacent pixels to obtain a trend estimate of the background brightness distribution. This directional fitting method can more effectively capture the local structure of background changes, especially at cloud edges or in areas of abrupt brightness changes. The residuals from the fitting can significantly highlight non-linear changes, thus providing a basis for target prominence.

[0078] To further improve the stability of background prediction, this invention introduces a joint constraint mechanism of gray-level variance and directional gradient on the basis of directional fitting. Local brightness fluctuations and directional texture intensity are used to weight the fitted model, making the model more inclined to smooth the background in stable regions and suppressing the interference of gradient abrupt changes in high-gradient regions. The results after multi-directional fitting are weighted and fused to form a unified background estimation grayscale image, which is then differiated from the original infrared image to obtain a saliency output image. This saliency output image can significantly weaken the background structure and highlight abnormal bright spots, providing reliable input for subsequent target candidate point selection.

[0079] After obtaining the saliency output map through differencing, this invention employs a local maximum detection strategy to initially select candidate points for the saliency response. Considering that weak targets typically exhibit point-like features, and their local saliency manifests as local peaks in the residual map, local neighborhood maxima analysis can quickly filter out pixel locations in the image where potential targets may exist. This process significantly reduces subsequent computation and ensures that the candidate point set contains most of the true targets, improving the overall algorithm efficiency from an engineering perspective.

[0080] Subsequently, this invention introduces the fourth-order moment as the core discrimination indicator in the target discrimination stage to address the problem that traditional methods relying on low-order statistics such as mean and variance cannot reliably distinguish between "abrupt brightness gradients" and "weak targets." The fourth-order moment essentially characterizes the sharpness of the local grayscale distribution, exhibiting significant sensitivity to local bright spots while maintaining robustness to background layering and brightness gradients. This invention calculates the fourth-order moment within multi-scale local windows, making the discrimination process independent of the exact size of the target and enhancing the target's prominence in local areas through high-order statistical description. Statistically, the sharpness of the local distribution caused by truly weak targets is more pronounced, while noise or background gradients, although potentially causing brightness changes, often lack significant peak characteristics in their local distribution structure. Therefore, the fourth-order moment can serve as a reliable basis for target discrimination.

[0081] However, in engineering practice, cloud edges and regions with abrupt changes in brightness can still lead to abnormally increased local fourth moments, resulting in false targets. Therefore, this invention proposes a local gradient compensation mechanism, introducing background gradient constraints into the fourth moment decision process. Specifically, the local gradient level is estimated within each candidate region. By constructing a dynamic adjustment relationship between the local gradient level and the fourth moment threshold, the fourth moment discrimination focuses more on the "sharpness of bright spots" while suppressing "brightness changes caused by background gradients." The larger the gradient, the more likely the region is to belong to a cloud edge or a region with abrupt background changes, and this invention correspondingly increases the fourth moment threshold; while in regions with stable backgrounds, the gradient is smaller, so a lower threshold is maintained, making truly weak targets more easily stand out. Through this local gradient compensation strategy, this invention can effectively reduce false responses caused by background gradients, significantly improving overall detection accuracy and stability.

[0082] Finally, this invention integrates the fourth-order moment discrimination result with the gradient compensation threshold to form the final detection decision. For each candidate point, if its fourth-order moment feature exceeds the compensated threshold and simultaneously meets the saliency response condition, it is judged as a real target. Through multi-stage and multi-index joint screening, this invention effectively distinguishes real targets from background interference and outputs the final detection result, achieving robust detection of small targets against complex sky backgrounds.

[0083] Example 1

[0084] An infrared image set is obtained by constructing N original infrared images, each of which is 320×256 in size. Weak targets are extracted from each original infrared image using the method proposed in this invention. Any original infrared image is taken as the original infrared image to be calculated and segmented to obtain 320×256 block images, each block image containing one pixel.

[0085] Take the pixel of the f-th image block as the pixel to be detected, and in the neighborhood of the pixel to be detected... Within, extract pixel sequences along four main directions k∈{0°,45°,90°,135°}. And the corresponding grayscale vectors of the pixel sequences. The grayscale prediction model for the pixels to be detected in each direction is obtained through least-squares linear fitting:

[0086] (1);

[0087] In the formula For the residual vector, This represents the rate of change of grayscale with respect to orientation / sequence coordinates. This is the grayscale base value when the orientation position is 0.

[0088] Least squares estimation using equation (1) and direction prediction model :

[0089] (2);

[0090] (3);

[0091] To suppress the influence of noise and abrupt changes in background, local variance is introduced. With directional gradient strength , Let be the directional gradient intensity of the pixel (i,j) to be detected in k directions, which physically represents the magnitude of the gray-level change in those directions. This invention proposes a weighted fusion scheme jointly constrained by gray-level variance and directional gradient, and establishes a weighted background estimation optimization model:

[0092] (4);

[0093] In equation (4), the first term ensures consistency between the background estimation and the direction prediction; the second and third terms are the variance and gradient constraint regularization terms, respectively; and the parameters... Used to control the balance between smoothing and suppression intensity. Here λ 1 = 0.8 λ 2 = 0.2, It is the local variance regularization coefficient, used to constrain / penalize excessively large values ​​of weights in the local variance term, so that weights in high noise and large variance directions are suppressed, thereby improving the robustness of background estimation. This is the directional gradient strength regularization coefficient, used to constrain excessively large values ​​of the weights in the gradient strength term, so that the weights in the edge direction are suppressed, avoiding fitting the target or strong edges as background.

[0094] The weighting factors corresponding to the k-direction, with adjustment parameters α and β, are obtained through Lagrange optimization. And background estimation grayscale image :

[0095] (5);

[0096] (6);

[0097] In equation (5), the weighting factor corresponding to direction k is... Through grayscale variance Local stability is measured by the gradient strength of the direction corresponding to direction k. This allows the absorption of edge extension direction information with small gradients and low variance around the pixel being measured, thus representing the degree of background abrupt changes. This enables effective prediction of the background. Based on this, through residual calculation with the original infrared image, the information of all target points with local characteristics of large gradients and high variance is effectively preserved in the residual map. In this context, the local gradient compensation coefficients are... α =1.5, β =10 -3 .

[0098] Next, we will conduct a preliminary selection of candidate points:

[0099] First, calculate the target threshold. (7);

[0100] Then, candidate points are selected within the binary image based on the target threshold:

[0101] (8);

[0102] (9);

[0103] Next, we introduce a higher-order statistical fourth-moment method. The core of this method lies in using higher-order statistics to characterize the sharpness of the local gray-level distribution in an image, thereby reflecting the presence of pixels with abnormal brightness in local regions. Statistical fourth-moment detection has two major advantages.

[0104] First, it can represent the prominence of a target relative to the background without requiring accurate target size information. Traditional local statistical contrast models rely on background mean and variance estimation, making them extremely sensitive to the division between the target and background windows. In contrast, the statistical fourth moment directly statistically analyzes the morphological characteristics of the local grayscale distribution, highlighting the target through outliers. The definition of the statistical fourth moment is as follows:

[0105] (10);

[0106] (11);

[0107] in, Let be the statistical fourth moment of the local gray-level distribution at pixel (x,y). The fourth central moment of the local gray-level distribution. This is the fourth power of the standard deviation of the local grayscale distribution. For mathematical expectation operators, Let be the grayscale value at pixel (x, y). The average gray value within the local window Ω. This is the square of the gray-level variance within the local window Ω. This is a local neighborhood window centered at pixel (x,y). Let be the grayscale value of pixel (i,j) within the local window Ω.

[0108] In equation (10), and Let Ω be the mean and standard deviation within the local window, respectively. If the pixel grayscale values ​​within the local window Ω follow a stationary Gaussian distribution, then... If there are isolated, bright pixels within a local area, the fourth-order central moment term... The value will increase sharply, the gray-level distribution will deviate from Gaussian properties, and it will exhibit heavy tails. .

[0109] Statistical fourth moments in infrared image models Building upon this foundation, we further centralize each item within a local window:

[0110] (12);

[0111] Where b is the centered background component, s is the centered target component, and v is the centered noise component. For background components, For the target component, For the target component, The mean of the background component. The mean of the target component. This represents the mean of the noise components.

[0112] Under the independence assumption, the fourth central moment of the population can be expanded as follows:

[0113] (13);

[0114] in, The fourth central moment of the overall grayscale signal. The fourth central moment of the background component, Let the fourth central moment of the target component be... The fourth central moment of the noise component. The variance of the background component. Let Variance be the variance of the target component. Let V be the variance of the noise component.

[0115] The overall second moment can be expanded as follows:

[0116] (14);

[0117] in, Let be the second-order central moment of the overall grayscale signal.

[0118] If the background and noise approximately follow a Gaussian distribution, i.e. Therefore, the contributions of pure background and noise to the statistical fourth moment can be approximately canceled out. When there are sparsely highlighted targets in the window, the proportion The brightness is approximately At that time, the target term will introduce a major contribution into the molecule. Therefore, in and Under the given conditions, an approximation can be obtained:

[0119] (15);

[0120] As can be seen from equation (15), when the energy of the target term is small but locally concentrated, the fourth power amplification effect of the molecule in the fourth moment is much greater than that of the second moment, making K very sensitive to the response of weak targets. This shows that the statistical fourth moment can realize a high-order statistical criterion for the existence of a target without the need for precise target size and boundary information.

[0121] Second, statistical fourth-order moment detection can ensure consistent response across the detection space for targets of different scales. When the target brightness difference is... The target area occupies a proportion of the window. When the statistical fourth moment is, it can be approximately expressed as:

[0122] (16);

[0123] in, The average grayscale value of the pixels within the target area. This represents the average grayscale value of the background area within the local window. Let be the area occupied by the target within the local window Ω. This represents the standard deviation of the grayscale values ​​in the local background area.

[0124] As can be seen from equation (16), under the same detection threshold, the larger the target, the stronger the corresponding equivalent target brightness, which meets the actual target detection requirements.

[0125] The statistical fourth-order moment detection method can stably characterize target features in complex, high-frequency backgrounds and provide more reliable target information representation, achieving false alarm suppression. Furthermore, the statistical fourth-order moment method can sensitively capture local anomalies caused by system noise or distortion during optical imaging. Compared to lower-order statistics, it has stronger discriminative power under non-Gaussian noise, enhancing target features, suppressing noise, and evaluating imaging performance at the optical level, thus providing support for system evaluation and image quality analysis.

[0126] The statistical fourth-order moment component of the pixel to be detected is easily affected by background gradient interference, leading to unstable detection results. Therefore, a local gradient compensation algorithm is introduced to achieve adaptive threshold correction, as detailed below.

[0127] When a global gradient is added to an image, its statistical fourth moments will also change. Before adding a local gradient, the statistical fourth moments are: Add gradient perturbation to the N×N local area. row relative to Add gradient to row : Then the changes in the mean and variance of the entire region are:

[0128] (17);

[0129] (18);

[0130] in, The image grayscale value after adding local gradient perturbation, Let be the gray value of the original image at pixel (i,j), and n be the unit gradient magnitude introduced along the row direction. This represents the average gray level of the local window after adding gradient perturbation. To calculate the grayscale variance of the local window after adding gradient perturbation. The mean gray value of the local window before adding gradient perturbation. Let N be the side length of the local window (the window size is N×N). This represents the grayscale variance of the local window before gradient perturbation is applied.

[0131] A Taylor expansion of the fourth-order central moment is performed and approximated as follows:

[0132] (19);

[0133] in, The fourth central moment of the local gray-level distribution after adding gradient perturbation. The fourth central moment of the local gray-level distribution before the gradient perturbation is added.

[0134] In the formula, the first term For the original fourth moment, the second term The third term represents the extreme bias introduced by the gradient perturbation. Contribute to the cross term.

[0135] The statistical fourth moment after gradient perturbation is:

[0136] (20);

[0137] Statistical analysis of the change in the fourth moment:

[0138] (twenty one);

[0139] It can be seen from equations (20) and (21) that when there is a fixed gradient perturbation n in each row of the local region, the statistical fourth moment monotonically increases as the gradient magnitude n increases, and This means that the image grayscale distribution exhibits sharper features and an increase in outlier pixels. This gradient perturbation will cause the statistical fourth moment of the entire local region to be abnormally high.

[0140] To address this, local gradient compensation is introduced to dynamically adjust the threshold. First, the local gradient level is estimated within the detection window. This is used to determine whether there is significant background gradient interference within the detection window. If the local gradient is too large, the threshold is appropriately increased to suppress false alarms caused by background structures; conversely, when there is no significant cloud interference in the area, the threshold is appropriately decreased to enhance sensitivity to real targets. The threshold is defined here as:

[0141] (twenty two);

[0142] In the experiment, the basic threshold of equation (22) The value is 4.5, which is the local gradient compensation coefficient. The value range is [1.5, 2.0]. It is a protective factor to avoid division by zero. and This represents rows and columns. Through this adaptive threshold adjustment, the impact of background gradients on statistical fourth-order moment detection can be effectively reduced, improving the algorithm's detection reliability in complex backgrounds.

[0143] Finally, define candidate points. Statistical fourth-order moment scoring function :

[0144] ;

[0145] like Then the candidate points Add the candidate point to the target point set as the target point; otherwise, remove the candidate point. ;

[0146] Replace the current candidate point with the next candidate point, and repeat steps S31-S35 until all candidate points in the complete candidate point set have been filtered to obtain the target point set. ;

[0147] The weak targets in the q-th original infrared image are output using the following formula. :

[0148] (twenty four).

[0149] To verify the effectiveness of the proposed method, four sets of real infrared aerial target image sequences (totaling over 2000 images) with different levels of complexity were selected for simulation experiments. Sequence 1 and Sequence 2 respectively depicted fragmented cloud scenes and cumulus and striped cloud scenes; Sequence 3 contained images of small sky targets with significant detector noise; and Sequence 4 presented aerial target images against a background of high gradients. The experiments employed the MATLAB algorithm framework, with a computer configuration of 16GB RAM, a 2.2GHz Intel i7 dual-processor, and Windows 11 operating system.

[0150] The performance of seven algorithms, including the method proposed in this invention, is evaluated from both qualitative and quantitative perspectives. Qualitative evaluation involves intuitive analysis of the grayscale saliency maps of the algorithm detection results, while quantitative evaluation focuses on objectively assessing the algorithm's performance metrics. Among the evaluation metrics, Signal-to-Clutter Ratio Gain (SCRG) and Background Suppression Factor (BSF) are used to measure the algorithm's ability to enhance the target and suppress clutter in the saliency output map. Receiver Operating Characteristic Curve (ROC) is used to measure the false alarm rate (FPR) and detection rate (TPR), where the horizontal axis of ROC represents the false alarm rate (FPR) and the vertical axis represents the detection rate (TPR). The Area Under the Curve (AUC) quantifies the overall performance of each algorithm.

[0151] The calculation formulas for each evaluation indicator are as follows:

[0152] (25);

[0153] (26);

[0154] (27);

[0155] In equation (25), and These represent the average gray level in the target area and the average gray level in the background area, respectively. This represents the standard deviation of the background region; and This represents the signal-to-noise ratio (SCR) of the input image and the SCR of the saliency output image after algorithm processing. and The standard deviation of the background region of the original infrared image and the background region of the saliency output image is represented.

[0156] The experiment selected six relatively advanced existing object detection algorithms (State of the Art, SOTA) for comparative testing. The SOTA included two background prediction methods, AAGD (Adaptive Anisotropic Gaussian Difference) and ADMD (Absolute Directional Mean Difference), two local multi-scale contrast enhancement methods, BLCM (Background-Local Contrast Measure) and MLCM (Multi-scale Local Contrast Measure), and two low-rank sparse decomposition methods, ANLPT (Adaptive Nonconvex Low-rank and Sparse Tensor) and PSTNN (Partial Sum of Tensor Nuclear Norm).

[0157] Table 1 presents the average SCGR and BSF of the saliency output maps of SOTA and the proposed method in the four sequences. The average BSF calculation excludes detection frames with missing targets. The maximum values ​​of each indicator are marked in red in Table 1. It can be seen that, in terms of target enhancement, the front-end linear fitting filter algorithm significantly outperforms the SOTA method in sequences 1 and 3, performs slightly worse in sequences 2 and 4, and is second only to PSTNN and AAGD. Regarding background suppression, except for a slightly lower result than ANLPT in sequence 1, the front-end linear fitting filter algorithm based on multi-directional background prediction achieves the best performance in the other three sequences, especially in sequence 4 with a large gradient background, demonstrating strong background suppression capabilities. This indicates that the algorithm proposed in this invention (referred to as "Proposed") still possesses excellent target enhancement and background suppression performance while being implemented quickly.

[0158] Table 1

[0159]

[0160] Figure 3Four image sequences and the detection results of different methods are presented. It can be seen that MLCM has the worst background suppression effect and a high number of false alarms; ADMD, MPCM, and PSTNN can suppress most of the background while also detecting the real target relatively well, but a small number of false alarms still exist; AAGD and ANLPT have low detection success rates, with serious missed detections and false alarms; in contrast, the method proposed in this invention performs best in the visualized detection results of all sequences. It is worth noting that although the saliency output map obtained by front-end linear fitting filtering does not perform optimally on all sequences, when combined with back-end statistical fourth-moment accurate detection, the final target detection result reaches the best level among all methods, greatly improving the ability to suppress interference, enhancing target detection, and reducing the false alarm rate.

[0161] Figure 4 The ROC curves and AUC results of different methods on four image sequences are shown. Figure 4 (a) in the sequence is sequence 1. Figure 4 (b) in the sequence is sequence 2. Figure 4 (c) in the sequence is sequence 3. Figure 4 (d) in the diagram represents sequence 4. In sequences 1 to 3, most state-of-the-art (SOTA) detectors effectively detected the target. However, in sequence 4, due to the presence of large gradient interference, the detection performance of all SOTA detectors significantly decreased. Nevertheless, the ROC curves of the proposed method in all four sequences consistently fell to the upper left of all SOTA curves, and all achieved the highest AUC values, indicating that this method can achieve more stable and superior detection results at lower FPR.

[0162] The infrared weak target detection method proposed in this invention has been verified by field experiments in a real airborne imaging scenario, as detailed below.

[0163] An experimental platform was built using a long-wave infrared camera and turntable manufactured by FLIR Systems. In a high-rise laboratory, images of a commercial airliner taking off from a predetermined location were captured. The long-wave infrared camera's pitch angle was locked at 5°, and its swing angle was set to ±30°. The camera's F-number was 2, and the detector resolution was 640 pixels × 512 pixels, with a pixel size of 15 μm. Images close to clouds and with weaker target radiation intensity were selected as the actual detection samples. Figure 5 Image (a) is the first original image, showing the target with weaker radiation intensity near the clouds. Figure 5 (b) in the image is a second original image where the target's radiation intensity is weaker due to its proximity to the clouds. Figure 5 (a) and Figure 5In (b) of the original images, complex cloud layers and significant brightness gradients exist in the background. Furthermore, the background clutter is significant due to electromagnetic interference from the guiding radar, obscuring small target signals. After front-end processing using the multi-directional background prediction method proposed in this patent, Figure 5 In the image (c), the result of performing multiple background prediction processes on the first original image is shown. Figure 5 In the image, (d) represents the result of performing multiple background prediction processes on the second original image, such as... Figure 5 (c) and Figure 5 As shown in (d), this invention can significantly suppress background interference and obtain several candidate points. Then, statistical fourth-order moment detection is used to precisely screen the candidate points, effectively eliminating false alarm points. The final detection result is as follows: Figure 5 (e) and Figure 5 (f) in: Figure 5 In the figure, (e) represents the result of statistical fourth moments based on the results of multiple background prediction processing on the first original image. Figure 5 In the figure, (f) represents the result of statistical fourth moment of the results of multiple background prediction processing based on the second original image, and all detected targets are marked with boxes.

[0164] The MBFOM algorithm proposed in this invention is compared with the MPCM and PSTNN algorithms, which show superior performance in simulation verification. The results are as follows: Figure 6 As shown. Real targets are marked with rectangles, and false alarm points are circled with dashed lines. Figure 6 Image (a) is the first original image, showing the target with weaker radiation intensity near the clouds. Figure 6 (b) in the image is the second original image, where the target's radiation intensity is weaker due to its proximity to the clouds. Figure 6 (c) and Figure 6 (d) in the figure represents the detection result of the MBFOM algorithm of this invention. Figure 6 (e) and Figure 6 In the diagram, (f) represents the detection result of the MPCM algorithm. Figure 6 (g) and Figure 6 (h) in the table represents the detection result of the PSTNN algorithm.

[0165] To verify the effectiveness of this invention in suppressing gradient background under complex cloud distribution and uneven brightness conditions, in Figure 6 In the results analysis, the normalized overall slope of the image was used to quantize the background gradient, and the overall slope of the original image was set to 1. Simultaneously, the number of target candidate points obtained by each algorithm during processing was statistically analyzed. Under fixed platform detection parameters, 1500 frames of image sequences were continuously processed, and the detection rate and false alarm rate of each algorithm were compared. The experimental results are shown in Table 2.

[0166] Table 2 Results of different detection algorithms

[0167]

[0168] The results above demonstrate that the infrared weak target detection algorithm based on multi-directional background prediction and statistical fourth-order distance discrimination proposed in this invention exhibits stronger stability. In extreme scenarios with complex cloud cover and gradient interference, the gradient suppression effect of this invention can reach over 80%, while the highest suppression rate of the MPCM and PSTNN algorithms is only 52%. The number of false alarms is 1 / 6 and 1 / 8 of that of the MPCM and PSTNN algorithms, respectively. Furthermore, the detection rate of this invention is improved by 8.17% and 11.79% compared to the two comparative algorithms, respectively, while the false alarm rate is reduced by 41.94% and 49.30%, respectively.

[0169] It is important to emphasize that all bold text in this invention is represented by vectors.

[0170] It should be understood that the various forms of processes shown above can be used to reorder, add, or delete steps. For example, the steps described in this invention disclosure can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this invention can be achieved, and this is not limited herein.

[0171] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A method for multi-directional prediction and high-order statistical target detection for airborne airborne imaging, characterized in that: Specifically, the steps include the following: S1: Obtain the original infrared image dataset, perform linear fitting filtering on the q-th original infrared image, and obtain the residual map corresponding to the q-th original infrared image; S2: Set a target threshold corresponding to the q-th original infrared image, and select candidate points in the residual map corresponding to the q-th original infrared image based on the target threshold; S3: Construct a multi-scale window, calculate the statistical fourth moment and local gradient level of each candidate point under the multi-scale window, and filter weak targets in the q-th original infrared image based on the calculation results; S4: Replace the q-th original infrared image with the (q+1)-th original infrared image, and repeat steps S1-S3 to obtain the weak targets in each original infrared image contained in the original infrared image dataset.

2. The multi-directional prediction and high-order statistical target detection method for airborne airborne imaging according to claim 1, characterized in that: Step S1 specifically includes: S11: Obtain the q-th original infrared image, and set the position coordinates in the q-th original infrared image as... Using the pixels to be detected as the pixels, a weighted background estimation optimization model is constructed: ； Where k is the extraction direction, k∈{0°,45°,90°,135°}. Optimize the weighted background estimation model for the pixels to be detected; Let k be the weighting factor corresponding to the pixel to be detected in the k direction. Background estimation for the pixel to be detected. These are the weighting coefficients of the local variance constraint term. These are the weighting coefficients for the directional gradient strength constraint term. Let be the directional gradient intensity of the pixel to be detected in the k-direction. Let K be the local variance of the pixel to be detected in the k-direction. This is the orientation prediction model for the pixel to be detected in the k direction; S12: Calculate the partial derivative of the weighted background estimation optimization model and make the partial derivative result zero to obtain the weighting factor corresponding to the current pixel to be detected. ； in, This is the adjustment coefficient for the directional gradient intensity term. To stabilize the term and prevent the denominator from being zero; S13: Replace the current pixel to be detected with the next pixel to be detected, and repeat steps S11-S12 until the weighting factors corresponding to all pixels of the qth original infrared image are obtained. S14: Calculate the estimated grayscale image of the background corresponding to the q-th original infrared image based on the solution result of step S13. : ； S15: Solve for the residual image corresponding to the qth original infrared image using the following formula. : ； in, This is the qth original infrared image.

3. The multi-directional prediction and high-order statistical target detection method for airborne airborne imaging according to claim 2, characterized in that: The orientation prediction model of the pixel to be detected in the k direction The expression is: ； in, To obtain the position coordinates in the q-th original infrared image The pixels are taken as the pixels to be detected, and the pixel sequence of the pixels to be detected in the 0° direction. This is the direction prediction model parameter vector for the pixel to be detected in the k direction.

4. The multi-directional prediction and high-order statistical target detection method for airborne airborne imaging according to claim 3, characterized in that: The expression for the direction prediction model parameter vector corresponding to the pixel to be detected in direction k is: ； in, Let be the prediction model coefficient matrix composed of the neighborhood samples of the pixel to be detected in the k-direction. To obtain the position coordinates in the q-th original infrared image The pixels are taken as the pixels to be detected, and the gray-level prediction vectors of the pixels to be detected in each direction are given.

5. The multi-directional prediction and high-order statistical target detection method for airborne airborne imaging according to claim 4, characterized in that: The expressions for the grayscale prediction vectors of the pixel to be detected in each direction are: ； in, Let be the prediction model coefficient matrix composed of the neighborhood samples of the pixel to be detected in the k-direction. Let be the direction prediction model parameter vector corresponding to the pixel to be detected in the k direction. This represents the prediction residual of the direction prediction model for the pixel to be detected in the k direction.

6. The multi-directional prediction and high-order statistical target detection method for airborne airborne imaging according to claim 1, characterized in that: In step S2, the target threshold corresponding to the qth original infrared image The expression is: ； in, Let be the mean of the residual image corresponding to the q-th original infrared image. Let be the standard deviation of the residual plot corresponding to the q-th original infrared image.

7. The multi-directional prediction and high-order statistical target detection method for airborne airborne imaging according to claim 3, characterized in that: In step S2, the formula used to select candidate points in the residual map corresponding to the q-th original infrared image based on the target threshold is: ； ； in, For the q-th original infrared image, the th A connected region, Let q be the target threshold corresponding to the q-th original infrared image. Let be the total number of connected regions obtained after target thresholding in the q-th original infrared image. For the candidate point set, For the q-th original infrared image, the th The pixel coordinates corresponding to the pixel maxima of each connected region. The residual map obtained after multi-directional prediction and higher-order statistical processing of the q-th original infrared image is shown in pixel coordinates. The response value at that location.

8. The multi-directional prediction and high-order statistical target detection method for airborne airborne imaging according to claim 1, characterized in that: In step S3, the multi-scale windows include 10×10 windows, 14×14 windows, and 18×18 windows.

9. The multi-directional prediction and high-order statistical target detection method for airborne airborne imaging according to claim 8, characterized in that: Step S3 specifically includes: S31: Calculate candidate points Statistical fourth moment under multi-scale windows: ； in, ( ) is the statistical fourth moment calculation function. For a 10x10 window, For 14x14 windows, For 18x18 windows, For the q-th original infrared image, the th A connected region, The statistical fourth moment value corresponding to the candidate point within a window of scale s(t); S32: Calculate candidate points Local gradient level: ； in, Let be the gradient magnitude distribution of the residual map corresponding to the q-th original infrared image; S33: Based on candidate points The local gradient level is calculated using the following formula for candidate points. Gradient compensation threshold: ； in, Candidate points The corresponding gradient compensation threshold, The basic threshold is obtained based on the global statistical characteristics of the residual map. These are the gradient compensation coefficients. It is the numerical stability constant; S34: Define candidate points Statistical fourth-order moment scoring function : ； S35: If Then the candidate points Add the candidate point to the target point set as the target point; otherwise, remove the candidate point. ; S36: Replace the current candidate point with the next candidate point, and repeat steps S31-S35 until all candidate points in the candidate point set have been filtered to obtain the target point set. ; S37: Output the weak targets in the q-th original infrared image using the following formula. : 。

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