An infrared small target detection method and device based on clustering and Bayesian oriented tracking

Abstract

The application discloses an infrared small target detection method and device based on clustering and Bayesian oriented tracking. The method comprises the following steps: (1) constructing a three-dimensional space-time tensor from a thermal infrared image sequence; (2) establishing a low-rank sparse tensor decomposition model based on the properties of background, target and noise; (3) clustering the background tube fibers by improving the K-means clustering algorithm, and proposing a low-rank estimation norm based on the improved K-means clustering; (4) establishing a tracking regularization term based on Bayesian derivation from an observation model and a state transition model; (5) establishing a small target detection model based on clustering and Bayesian oriented tracking; and (6) solving the model in the step (5) to obtain a detection result of the infrared image sequence to be detected, so that the infrared small target detection based on clustering and Bayesian oriented tracking is realized. The infrared small target detection model and solving algorithm based on clustering and Bayesian oriented tracking can effectively improve the detection performance of the infrared small target.

Description

Technical Field

[0001] This invention relates to the field of image processing, and in particular to an infrared small target detection method and apparatus based on clustering and Bayesian guided tracking. Background Technology

[0002] In recent years, infrared detection and tracking systems have become increasingly popular in military and civilian fields, such as long-range maritime surveillance, air defense, and forest fire monitoring. However, infrared small target detection technology faces the following challenges: First, complex backgrounds and long distances between the imaging sensor and the target result in low signal-to-noise ratios in infrared images; second, infrared small targets are typically in the 2×2 to 9×9 scale range, lacking specific shape and texture information; third, random noise in the environment and inherent noise in the sensor affect the quality of infrared images, and noise can lead to false alarms during small target detection; furthermore, practical applications require real-time performance in target detection technology. In light of these issues, many scholars have proposed numerous methods; however, current infrared small target detection technology still lacks satisfactory target detection and background suppression capabilities. Therefore, improving target detection and background suppression capabilities in complex scenarios while maintaining fast detection speeds is essential.

[0003] In general, based on the technical approach of infrared small target detection and tracking algorithms, existing methods can be mainly divided into two categories: model-based methods and deep learning-based methods.

[0004] In fact, deep learning-based methods, also known as data-driven methods, include AGPCNet, STDMANet, LW-IRSTNet, IR-TransDet, and DPS-LC. These network models heavily rely on data and computational resources to learn complex sample features. Deep learning-based network models lack generalization performance to some extent, and their performance may be affected when detecting small infrared targets in contexts with significantly different data distributions. Furthermore, the computational complexity of the network may limit its real-time performance.

[0005] Model-based methods mainly include Track Before Detection (TBD) and Detect Before Tracking (DBT) techniques. TBD assumes that the target's trajectory in the infrared image sequence is continuous and uses the target's motion characteristics to predict the current motion state of all potential targets. TDB not only depends on the current frame but also needs to accumulate the target's energy from the entire image sequence to mitigate the impact of noise in each frame. However, it requires a large amount of computational resources, which limits the algorithm's real-time performance to some extent. Deep Target Detection (DBT) can be further divided into three categories: The first is background filtering-based methods, which design filters based on the location and brightness distribution characteristics of the background to suppress background signals; however, these methods are prone to false alarms in complex scenes. The second category is methods based on the human visual system, which utilize local contrast metrics to extract target components; however, in complex scenes with pixel size and high-contrast noise, these methods may confuse them with real targets. The third category is component analysis-based methods, which treat infrared images as a combination of low-rank background signals, sparse target signals, and random noise signals, and extract target components through algorithms based on low-rank sparse decomposition. With the development of tensor analysis theory, researchers have extended component analysis-based methods from the matrix domain to the tensor domain, further decomposing the original tensor into different components, including background tensors, target tensors, and noise tensors. Thanks to the fusion of spatial-temporal information, tensor-based component analysis methods perform well in target detection. However, three key problems remain: the first involves accurately estimating background and target components; the second involves how to build a more comprehensive infrared small target detection model; and the third involves achieving excellent real-time performance.

[0006] Therefore, existing research needs to explore the above issues in depth and propose a superior component analysis method to further improve target detection capability, background suppression capability, and real-time performance. Summary of the Invention

[0007] To address the shortcomings of existing technologies, the present invention aims to provide an infrared small target detection method and apparatus based on clustering and Bayesian guided tracking. This method fully utilizes the spatiotemporal information carried in infrared image sequences to construct a three-dimensional spatiotemporal tensor. From a component analysis perspective, a small target detection model based on low-rank sparse tensor decomposition is established. Furthermore, by improving the traditional K-means clustering algorithm, cluster analysis is performed on the background tensor tube fibers. The low-rank characteristics of the background components are analyzed using the clustered background tube fiber clusters. An improved low-rank estimation norm based on K-means clustering is proposed to improve the accuracy of background estimation. In addition, for the observed target tensor, Bayesian theory is used... This paper proposes an observation model and a state transition model to model and predict the spatiotemporal trajectory changes of infrared small targets, and then establishes a tracking regularization term based on Bayesian derivation. Combining the three-dimensional spatiotemporal tensor, based on the low-rank estimation norm of improved K-means clustering and the tracking regularization term based on Bayesian derivation, an infrared small target detection model based on clustering and Bayesian guided tracking is established. Through an effective iterative solution framework based on the ADMM algorithm, the effectiveness of small target detection results in the infrared image sequence to be detected is improved, and infrared small target detection is achieved. Furthermore, the target detection capability and background suppression capability of the infrared small target detection method proposed in this invention have been effectively verified.

[0008] To achieve the above objectives, the present invention provides the following technical solution:

[0009] This invention discloses an infrared small target detection method based on clustering and Bayesian guided tracking, characterized by the following steps:

[0010] Step 1): Take the thermal infrared image sequence D containing the weak target to be detected, stack the image frames sequentially according to the time order of the frames, and construct a three-dimensional space-time tensor.

[0011] Step 2): Based on the low-rank nature of the background, the sparsity of the target, and the properties of the noise, establish a model based on low-rank sparse tensor decomposition.

[0012] Step 3): Combining local and global features, improve the K-means clustering algorithm and perform improved K-means clustering on the background tube fibers. Design a low-rank estimation norm based on the improved K-means clustering algorithm from the background tube fiber clusters. Here, the background tube fiber represents the vector extracted from the background tensor with the first and second dimensions fixed and the third dimension extracted.

[0013] Step 4): Using Bayesian theory, the spatiotemporal trajectory changes of small infrared targets are modeled and predicted through observation and state transition models, and a tracking regularization term based on Bayesian derivation is established.

[0014] Step 5): The three-dimensional spacetime tensor based on Step 1). Combining steps 2) to 4), a small target detection model based on clustering and Bayesian guided tracking is established;

[0015] Step 6): Use the ADMM algorithm to solve the low-rank sparse tensor decomposition model based on clustering and Bayesian guided tracking to obtain the target tensor. Then, extract each front slice from the target tensor in turn as the infrared small target detection result corresponding to the infrared image sequence to be detected, thereby realizing the small target detection of the infrared image sequence.

[0016] Preferably, the thermal infrared image sequence D of the present invention can be a thermal infrared image sequence containing a small target to be detected and against a complex sky, ground and forest scene. The present invention can realize the detection of small infrared targets against such complex backgrounds.

[0017] The present invention also discloses an infrared small target detection device based on clustering and Bayesian guided tracking for implementing the method, comprising:

[0018] The 3D spatiotemporal tensor construction module constructs a 3D spatiotemporal tensor from the infrared image sequence D to be detected. This lays the data foundation for the subsequent establishment of tensor decomposition models;

[0019] The model building module based on low-rank sparse tensor decomposition establishes a model based on low-rank sparse tensor decomposition by utilizing the characteristics of low-rank background components, sparse target components, and noise components.

[0020] The low-rank background estimation norm design module combines local and global features to improve the K-means clustering algorithm, performs improved K-means clustering on background tube fibers, and designs a low-rank estimation norm based on the improved K-means clustering algorithm.

[0021] The tracking regularization term design module, based on Bayesian theory, models and predicts the spatiotemporal trajectory changes of small infrared targets through observation and state transition models, and establishes a tracking regularization term based on Bayesian derivation.

[0022] A module for establishing a small target detection model based on clustering and Bayesian guided tracking is constructed by combining a three-dimensional space-time tensor, improving the K-means clustering algorithm and a tracking regularization term based on Bayesian derivation.

[0023] The model optimization and solution module uses the ADMM algorithm to solve the small target detection model based on clustering and Bayesian guided tracking, obtains the target tensor, and extracts the front slice of the target tensor as the infrared small target detection result of the infrared image sequence to be detected;

[0024] The target detection result output module is used to output the infrared small target detection result sequence corresponding to the infrared image sequence.

[0025] Compared with the prior art, the beneficial effects of the present invention include:

[0026] 1) This invention fully utilizes the temporal-spatial information carried by infrared image sequences to establish a three-dimensional spatiotemporal tensor; considering the local and global features of background components, the traditional K-means clustering algorithm is improved, thereby performing improved K-means clustering on the background tube fibers in the three-dimensional spatiotemporal tensor to obtain low-rank background fiber clusters; thus, a low-rank estimation norm based on the improved K-means clustering algorithm is proposed to achieve more accurate low-rank background estimation and improve the thoroughness of target and background separation based on low-rank sparse tensor decomposition;

[0027] 2) This invention utilizes the Gaussian curvature surface corresponding to the infrared image to introduce a target sparsity weighted tensor. Based on the observed target tensor And target sparsity weighted tensor By utilizing Bayesian theory, an observation model and a state transition model are constructed to model and predict the spatiotemporal trajectory changes of small infrared targets, thereby establishing a tracking regularization term based on Bayesian derivation. Based on this, an infrared small target detection model based on clustering and Bayesian guided tracking is established. The ADMM algorithm is used to solve the infrared small target detection model based on clustering and Bayesian guided tracking, which significantly improves the effectiveness of target detection results. Attached Figure Description

[0028] Figure 1 This is a schematic diagram of the three-dimensional spacetime tensor construction process in this invention;

[0029] Figure 2 This is a schematic diagram of the infrared small target detection device based on clustering and Bayesian guided tracking according to the present invention.

[0030] Figure 3 Example frame images of a thermal infrared image sequence used for experimental testing;

[0031] Figure 4 The thermal infrared small target detection results are obtained by using the method proposed in this invention on example frames of thermal infrared image sequences used for experimental testing.

[0032] Figure 5 Example frames of a thermal infrared image sequence, and infrared small target detection results obtained by applying the proposed methods rcDoGF, GCM, IPCE, 4D-TR, RCTVW, STT-TRNR, DGRL, and AGPCNet to these example frames. Detailed Implementation

[0033] To make the objectives, technical solutions, and advantages of this invention clearer, the invention is described in detail below with reference to specific embodiments. Specific embodiments are described below to simplify the invention. However, it should be understood that the invention is not limited to the described embodiments, and various modifications are possible without departing from the basic principles; these equivalent forms also fall within the scope defined by the appended claims.

[0034] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0035] The basic steps of the iterative single-frame infrared image small target detection method of the present invention in this embodiment mainly include:

[0036] Step 1: Take the thermal infrared image sequence D containing the weak target to be detected, stack the image frames sequentially according to the time order of the frames, and construct a three-dimensional space-time tensor.

[0037] Specifically, such as Figure 1 As shown, the thermal infrared image sequence D containing the weak target to be detected is arranged in frame order, with the third dimension, i.e., the time dimension, as consecutive frames of image D. t Construct a three-dimensional spacetime tensor for t = 1, 2, ..., f. express The size is n1×n2×n3, where n1 represents The width of the front slice, n2 represents The height of the front slice, n3 represents The thickness, n3, has the same value as f;

[0038] In the specific implementation example, n3 is set to 7, and the constructed three-dimensional spacetime tensor The dimensions are 256×256×7.

[0039] Step 2: Based on the low-rank nature of the background, the sparsity of the target, and the properties of the noise, establish a model based on low-rank sparse tensor decomposition.

[0040] Specifically, based on the low-rank characteristics of the background, the sparsity of the target, and the properties of the noise, a single-frame infrared image D is modeled as a linear combination of a low-rank background matrix B, a sparse target matrix B, and a noise component matrix N. The model based on low-rank sparse matrix decomposition is shown in Equation (1):

[0041]

[0042] Where rank(·) represents the operator for the background rank, and ||·|0 represents the l0 norm for estimating the sparsity of the target. α1 and α2 represent the square of the Frobenius norm that measures random noise, and the weighting coefficients are α1 and α2.

[0043] Based on the three-dimensional spacetime tensor constructed in step 1), The three-dimensional spacetime tensor is derived from the low-rank sparse matrix decomposition model in step 2). Modeled as a low-rank background tensor Sparse target tensor and noise tensor A linear combination of these factors is used to establish a model based on low-rank sparse tensor decomposition:

[0044]

[0045] Where, ||·||1 represents the l1 norm used for the optimal approximation of the l0 norm.

[0046] Step 3: Combining local and global features, improve the K-means clustering algorithm to perform improved K-means clustering on the background tube fibers, and design a low-rank estimation norm based on the improved K-means clustering algorithm from the background tube fiber clusters;

[0047] Specifically, improve the K-means clustering algorithm: for three-dimensional space-time tensors All background tube fibers It is also expressed as Represents a three-dimensional spacetime tensor The background tube fibers in the i-th row and j-th column; randomly select K background tube fibers as initial cluster centers, where K is determined by singular value decomposition, and then convert the background tensor... Expand the matrix B according to pattern-3 as the background. (3) , represented as unfold3(·) represents the pattern-3 unfold operator, resulting in the background unfolded matrix B. (3) The height is n3, the width is n1n2, and B (3) The height is numerically related to the three-dimensional spacetime tensor. The thickness n3 is the same, (·) T The transpose operator for a matrix is... and Representing the background tensor respectively The 1st, 2nd, and nth side slices; to determine the initial number of cluster centers K, the background expansion matrix B is... (3) Perform singular value decomposition to obtain [U,S,V] T ] = svd(B(3) ), svd(·) denotes the singular value decomposition operator, S denotes the singular value matrix, and U and V denote unitary matrices; the singular value matrix S has N elements on its diagonal, where N is min(n1, n2, n3), and the vectors corresponding to the N elements are... And there are When σ is satisfied u+1 >ησ u When η is a positive coefficient, K is taken as u; the cluster center set C is defined as c k (i k ,j k ) represents the k-th cluster center c k The coordinates are c k (i k ,j k ), in the three-dimensional spacetime tensor In the middle, the position is the i-th k row, j k The background tube fiber of the column is used as the kth cluster center c k ;The k-th cluster center c k (i k ,j k The corresponding background tube fiber cluster is defined as Therefore, the k-th cluster center is updated as follows:

[0048]

[0049] Where r represents the number of iterations, and m{·} represents the mean operator for the background tube fiber cluster. This represents the calculation of the mean tube fiber of the k-th background tube fiber cluster as a local feature. This represents the calculation of the mean value of all background tubular fibers as a global feature, where ω1 and ω2 represent the weighting coefficients assigned to the local and global features, respectively, and k = 1, 2, ..., K; when the convergence condition is met... δ represents the convergence error, and C is the cluster center obtained in the (r+1)th iteration. (r+1) These are the final determined cluster centers;

[0050] In the specific embodiment, η is set to 1;

[0051] Low-rank estimation norm based on improved K-means clustering algorithm: K background tube fiber clusters obtained based on improved K-means clustering algorithm K background tube fiber clusters The objective functions are to minimize the sum of intra-class distances and maximize the inter-class distances of the K background tube fiber clusters.

[0052]

[0053] Among them, β represents a positive constant, and d(·) represents calculating the Frobenius norm of all background tube fibers in the background tube fiber cluster as the within-class distance of the background tube fiber. d k d x d y respectively represent the within-class distances of the background tube fiber clusters , where 1 ≤ k ≤ K, 1 ≤ x < y ≤ K; thus, based on the improved K-means clustering, the low-rank estimated norm ‖·‖ IKCR is defined as:

[0054]

[0055] Among them, #{·} represents calculating the number of background tube fibers in the background tube fiber cluster, and var(d1,…,d K ) represents calculating the variance of the within-class distances of K background tube fiber clusters as the between-class distance, and var(·) represents the variance calculation operator.

[0056] Step 4: According to Bayesian theory, through the observation model and the state transition model, model and predict the spatio-temporal trajectory change of the infrared small target, and establish a tracking regularization term based on Bayesian derivation;

[0057] Specifically, for each pixel point (x, y) in the infrared image D, the Hessian matrix is defined as where D xx (x,y), D yy (x,y) respectively represent the second-order derivatives of the pixel point (x, y) in the infrared image D along the x direction and the y direction, represents the second-order partial differential result calculated successively along the x direction and the y direction for the pixel point (x, y) in the infrared image D; based on the Hessian matrix of each pixel point (x, y), define the Gaussian curvature surface G corresponding to the infrared image D, and the Gaussian curvature value G(x,y) corresponding to the pixel point (x, y) on this Gaussian curvature surface is:

[0058]

[0059] where represents the gradient calculation operator of the matrix, det(·) represents the determinant calculation operator of the matrix H(x,y), represents the square of the gradient of the Hessian matrix H(x,y); for the three-dimensional spatio-temporal tensor Each of the n3 frontal slices yields a corresponding n3 Gaussian curvature surface G. These n3 Gaussian curvature surfaces are stacked sequentially according to the temporal order of their corresponding frames, ultimately resulting in a single Gaussian curvature surface tensor.

[0060] For the Gaussian curvature surface tensor Determining the target sparsity weighted tensor using an adaptive threshold

[0061]

[0062] in, express The element with index (i,j,k) in the middle. Represents the Gaussian curvature surface tensor The maximum value in the range, where θ represents a positive constant;

[0063] Using target sparsity to weight the tensor and target tensor The tracking regularization term based on Bayesian derivation is designed as follows:

[0064] Assume O τ ={o1,o2,…,o τ} is based on the target tensor Gaussian curvature surface tensor The entire target observation set, s t It is the t-th variable in the state set, representing the target tensor. The state of the t-th frontal slice or at time t, 1≤t≤τ=n³; based on Bayesian theory, the posterior probability p(s) t |O t ) is defined as:

[0065] p(s t |O t )∝p1(o t |s t )∫p2(s t |s t-1 )p(s t-1 |O t-1 )ds t-1 (8)

[0066] Where ∝ represents proportional to, O t Let ∫p2(s) represent the observation set corresponding to the first t time steps, and let ∫p2(s) be the integral term. t |s t-1 )p(s t-1 |O t-1 )ds t-1Essentially, p2(s) represents a weighted summation over all possible previous states (during the time interval from time 1 to time t-1). t |s t-1 ) represents the weighted weight; p1(o t |s t p2(s) represents the observation probability model that measures the similarity between the observation set and the actual situation. t |s t-1 ) indicates a description of state s t-1 Transition to state s t State transition probability model; p1(o t |s t ) and p2(s t |s t-1 Modeling using a Gaussian distribution, specifically, N(;) represents the Gaussian distribution function, A t-1 Let ∑ represent the state transition matrix. 1t Let ∑ denote the covariance matrix of the observation probability model. 2t Represents the covariance matrix of the state transition probability model;

[0067] Therefore, combining the target sparsity weighted tensor By maximizing the joint probability P(s) of the observation probability model and the state transition probability model t This allows us to obtain the optimal state at time t, enabling the modeling and prediction of the spatiotemporal trajectory changes of small infrared targets.

[0068]

[0069] In step 2), in model (2) based on low-rank sparse tensor decomposition, the o observed at time t... t State s at time t-1 t-1 and the state s at time t t They are respectively represented as ⊙ represents the Hadamarda accumulation;

[0070] By minimizing the joint probability P(s) t The logarithm of the reciprocal of ) is given by equation (9), which is then transformed into equation (10) as follows:

[0071]

[0072] Where log(·) represents the log operator;

[0073] Therefore, for the target tensor Tracking regularization term derived from Bayesian inference as follows:

[0074]

[0075] in, Represents the state transition tensor. Represent tensors respectively The t-th frontal slice, Represent tensors respectively The t-1th frontal slice, and Let represent the inverse matrices of the t-th front slice of tensors ε1 and ε2, respectively;

[0076] Specifically, in the embodiment, the state transition tensor Each frontal slice is taken as the identity matrix, and the covariance matrix of the observation probability model is ∑. 1t Let ∑ be the identity matrix, and let ∑ be the covariance matrix of the state transition probability model. 2t Take it as the identity matrix;

[0077] Step 5: Based on the three-dimensional spacetime tensor of Step 1) Combining steps 2) to 4), a small target detection model based on clustering and Bayesian guided tracking is established;

[0078] Specifically, based on the three-dimensional spacetime tensor of step 1). Combining the low-rank estimation norm based on the improved K-means clustering algorithm in step 3) and the tracking regularization term based on Bayesian derivation in step 4), and the model based on low-rank sparse matrix decomposition in step 2), a small target detection model based on clustering and Bayesian guided tracking is established as follows (12):

[0079]

[0080] Where λ1, λ3, and λ3 represent positive constants;

[0081] To accelerate the solution speed of model (12), a sparsity reweighting strategy is introduced into model (12) based on clustering and Bayesian guided tracing low-rank sparse tensor decomposition. Calculate the sparsity reweight of the target As shown in formula (13):

[0082]

[0083] Where ε represents a positive constant, (·) -1 The symbol represents the inverse operation, and |·| represents the absolute value operation.

[0084] Combining formulas (12) and (13), the final small target detection model based on clustering and Bayesian guided tracking is obtained, as shown in formula (14):

[0085]

[0086] In the specific embodiment, ε is set to 0.0001.

[0087] Step 6: Use the ADMM algorithm to solve the low-rank sparse tensor decomposition model based on clustering and Bayesian guided tracking to obtain the target tensor. Then, extract each front slice from the target tensor in turn as the infrared small target detection result corresponding to the infrared image sequence to be detected, thereby realizing the small target detection of the infrared image sequence.

[0088] Specifically, the ADMM algorithm is used to solve the small target detection model based on clustering and Bayesian guided tracking (14), and auxiliary variables are introduced respectively. We obtain the equivalent formula (15) of (14):

[0089]

[0090] The augmented Lagrangian function corresponding to formula (15) is:

[0091]

[0092] in, Let μ be a Lagrange multiplier and μ be a penalty term; the solution is obtained by iteratively solving for each variable, and the iterative update of each variable is as follows:

[0093] 1) The iterative formula is

[0094]

[0095] Where argmin represents the parameter value corresponding to obtaining the minimum value of the function, and i represents the number of iterations;

[0096] Based on formulas (3) to (5) in step 3), the improved K-means clustering algorithm is used to... Clustering of tubular fibers yields As shown in formula (18):

[0097]

[0098] in, and then, Updated to

[0099]

[0100] 2) The iterative formula is

[0101]

[0102] From formula (20) on variables Taking the derivative and setting the equation to 0, we get... The iterative update formula is:

[0103]

[0104] Here, fold3(·) represents the operator that converts a matrix into a three-dimensional tensor according to mode -3;

[0105] 3) The iterative formula is

[0106]

[0107] Among them, Th (·) (·) is the soft threshold shrinkage operator, and Th (τ) (x) = sign(x)·max(|x|-τ,0), where sign(·) is the sign function and τ is the soft threshold;

[0108] 4) The iterative formula is

[0109]

[0110] 5) The iterative formula is

[0111]

[0112] First, the target sparse weighted tensor in step 4). The iterative formula is

[0113]

[0114] Among them, through Determine the Gaussian curvature surface tensor express The element at index (i,j,k);

[0115] based on The iterative formula is

[0116]

[0117] in, Represents unit tensor The t-th frontal slice, ι=max(t-1,1),1≤t≤n3;

[0118] 6) The iterative formula is

[0119]

[0120] 7) Lagrange multipliers The iterative formula is

[0121]

[0122]

[0123]

[0124] 8) The iterative formula for the penalty term μ is:

[0125] μ (i+1) =min(γμ) (i) ,μ max (30)

[0126] Where γ represents the update coefficient, μ max This represents the maximum value of μ;

[0127] The iteration stopping condition is as follows:

[0128] 1) When relative error The iteration terminates when the error is less than ε1, where ε1 represents the overall iteration error.

[0129] 2) When adjacent iterations When ε2 represents the background iteration error, iteration stops;

[0130] 3) Stop iterating when the number of non-zero elements in the target tensor obtained from adjacent iterations no longer changes;

[0131] Furthermore, the final target tensor is extracted sequentially. The front slice is used as the infrared small target detection result image sequence T corresponding to the infrared frame image sequence D to be detected, realizing infrared small target detection based on clustering and Bayesian guided tracking.

[0132] In the specific embodiment, λ2 = 80λ1, λ2 = 10λ1, λ L =13.3, μ max =100, γ=0.5, μ (0) =0.001, α = 0.0001;

[0133] Corresponding to the aforementioned embodiment of an infrared small target detection method based on clustering and Bayesian guided tracking, the present invention also provides an embodiment of an infrared small target detection device based on clustering and Bayesian guided tracking.

[0134] Figure 2 This is a block diagram illustrating an infrared small target detection device based on clustering and Bayesian guided tracking according to an exemplary embodiment, such as... Figure 2 As shown, the device includes:

[0135] The 3D spatiotemporal tensor construction module constructs a 3D spatiotemporal tensor from the infrared image sequence D to be detected. This lays the data foundation for the subsequent establishment of tensor decomposition models;

[0136] The model building module based on low-rank sparse tensor decomposition establishes a model based on low-rank sparse tensor decomposition by utilizing the characteristics of low-rank background components, sparse target components, and noise components.

[0137] The low-rank background estimation norm design module combines local and global features to improve the K-means clustering algorithm, performs improved K-means clustering on background tube fibers, and designs a low-rank estimation norm based on the improved K-means clustering algorithm.

[0138] The tracking regularization term design module, based on Bayesian theory, models and predicts the spatiotemporal trajectory changes of small infrared targets through observation and state transition models, and establishes a tracking regularization term based on Bayesian derivation.

[0139] A module for establishing a small target detection model based on clustering and Bayesian guided tracking is constructed by combining a three-dimensional space-time tensor, improving the K-means clustering algorithm and a tracking regularization term based on Bayesian derivation.

[0140] The model optimization and solution module uses the ADMM algorithm to solve the small target detection model based on clustering and Bayesian guided tracking, obtains the target tensor, and extracts the front slice of the target tensor as the infrared small target detection result of the infrared image sequence to be detected;

[0141] The target detection result output module is used to output the infrared small target detection result sequence corresponding to the infrared image sequence.

[0142] Regarding the apparatus in the above embodiments, the specific manner in which each module performs its operation has been described in detail in the embodiments related to the method, and will not be elaborated upon here.

[0143] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to the description of the method embodiments. The device embodiments described above are merely illustrative; the various modules in the device represent a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules may be combined or integrated into another unit. Furthermore, the connections between the displayed or discussed modules may be communication connections through some interfaces, which may be electrical or other forms. Some or all of the modules can be selected to achieve the purpose of this application according to actual needs. Those skilled in the art can understand and implement this without creative effort. The following uses a publicly available real thermal infrared image sequence as an example to illustrate specific implementation methods to demonstrate the technical effects of the present invention; specific steps in the embodiments will not be repeated.

[0144] Example

[0145] The accompanying drawings illustrating the embodiments of the present invention will make the objectives, technical solutions, and advantages of the present invention clearer. It should be noted that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of the invention. All equivalent substitutions and improvements made within the framework of the methods and principles provided by the present invention should be included within the protection scope of the present invention.

[0146] In this embodiment, the effectiveness of the thermal infrared small target detection algorithm will be verified using a publicly available infrared image sequence. The publicly available infrared image sequence is described as follows: the number of frames is 100, the frame image size is 256×256, the background is mainly a pastoral scene, containing a large number of tree structures and bright linear structures, and the small target is a slowly flying drone. Figure 3 This is a test instance frame of the infrared image sequence. Figure 4 The image shows the target detection results obtained by the method of this invention using example frames from an infrared image sequence test. The results show that the salience of small targets is enhanced, while background and noise components are completely suppressed. To further evaluate the effectiveness of the small target detection model based on clustering and Bayesian guided tracking proposed in this invention, the small target detection results of example frames from this infrared image sequence are used for qualitative evaluation; from a quantitative perspective, the detection performance of the proposed method is evaluated using the 3D-ROC evaluation index system. The 3D-ROC evaluation index system includes three categories of indicators: target detection capability (TD), background suppression capability (BS), and the overall effectiveness evaluation index of the detector. The specific descriptions of the indicators are as follows:

[0147] 1) The target detection capability indicators include AUC. (D,τ) , representing (P D The AUC value of the (τ) curve can measure the target detection capability of the detector; AUCTD Defined as 0≤AUC TD =AUC (D,F) +AUC (D,τ) If )≤2, it indicates the combined detection capability of the detectors;

[0148] 2) Background detection capability metrics include AUC (F,τ) Representative (P) D The AUC value of the curve (τ) characterizes the background suppression capability of the detector, where 0 ≤ AUC. (F,τ) ≤1; AUC BS Defined as -1≤AUC BS =AUC (D,F) -AUC (F,τ) AUC ≤ 1, characterizing the joint background suppression capability of the detector; SNPR Defined as Characterize the signal-to-noise ratio of the detector;

[0149] 3) The overall effectiveness metrics of the detector include AUC. TDBS Defined as -1≤AUC TDBS =AUC (D,τ) -AUC (F,τ) AUC ≤ 1, representing the detector's combined ability to detect targets and suppress backgrounds; (D,F) Defined as 0≤AUC (D,F) ≤1, representing (P) D ,P F The AUC value of the curve characterizes the effectiveness of the detector; AUC ODP The total detection probability of the characterizing detector is defined as -1 ≤ AUC. ODP =AUC (D,F) +AUC (D,τ) -AUC (F,τ) ≤2.

[0150] Table 1 presents the 3D-ROC evaluation results of small target detection using rcDoGF, GCM, IPCE, 4D-TR, RCTVW, STT-TRNR, DGRL, AGPCNet, and the method of this invention for the thermal infrared image sequences used in the experimental tests. The bold and underlined values ​​represent the corresponding optimal and second-best AUC values, respectively. Specifically, rcDoGF and GCM are infrared small target detection algorithms based on local contrast measurement; DGRL is a small target detection algorithm based on single-frame low-rank sparse matrix factorization; IPCE is a small target detection algorithm based on single-frame low-rank sparse tensor factorization; 4D-TR, RCTVW, and STT-TRNR are small target detection algorithms based on multi-frame low-rank sparse tensor factorization; and AGPCNet is an infrared small target detection algorithm based on deep learning.

[0151] rcDoGF is from Li, Yongsong, et al. "Infrared Small Target Detection Based on 1-D Difference of Guided Filtering." IEEE Geoscience and Remote Sensing Letters 20(2023): 1-5.

[0152] GCM is from Tang, Ye, Kun Xiong, and Chunxi Wang. "Fast Infrared Small Target Detection Based on Global Contrast Measure Using Dilate Operation." IEEE Geoscience and Remote Sensing Letters 20(2023): 1-5.

[0153] IPCE is from Zhang, Chunmin, et al. "Infrared small target detection via interpatch correlation enhancement and joint local visual saliency prior." IEEE Transactions on Geoscience and Remote Sensing 60(2021): 1-14.

[0154] 4D-TR is from Wu, Fengyi, et al. "Infrared Small Target Detection Using Spatio-Temporal 4D Tensor Train and Ring Unfolding." IEEE Transactions on Geoscience and Remote Sensing(2023).

[0155] RCTVW is from Liu, Ting, et al. "Representative Coefficient Total Variation for Efficient Infrared Small Target Detection." IEEE Transactions on Geoscience and Remote Sensing(2023).

[0156] STT-TRNR comes from Yi, Haiyang, et al. "Spatial-Temporal Tensor Ring NormRegularization for Infrared Small Target Detection." IEEE Geoscience andRemote Sensing Letters 20(2023):1-5.

[0157] DGRL comes from Zhou, Fei, et al. "Robust infrared small target detection via jointly sparse constraint of l 1 / 2-metric and dual-graph regularization." Remote Sensing 12.12(2020):1963.

[0158] AGPCNet comes from Zhang, Tianfang, et al. "AGPCNet: Attention-guided pyramidcontext networks for infrared small target detection." arXiv preprint arXiv:2111.03580(2021).

[0159] Table 1. Quantitative indicators of the detection results of thermal infrared image example sequences using rcDoGF, GCM, IPCE, 4D-TR, RCTVW, STT-TRNR, DGRL, AGPCNet, and the proposed method.

[0160] This invention 1.000 0.999 2.412e-7 1.999 1.000 4.142e6 0.999 1.999 rcDoGF 1.000 <![CDATA[ 0.996 ]]> 1.362e-5 <![CDATA[ 1.996 ]]> 1.000 7.312e4 <![CDATA[ 0.996 ]]> <![CDATA[ 1.996 ]]> GCM 1.000 <![CDATA[ 0.996 ]]> 1.362e-5 <![CDATA[ 1.996 ]]> 1.000 7.312e4 <![CDATA[ 0.996 ]]> <![CDATA[ 1.996 ]]> IPCE 1.000 0.994 9.869e-4 1.994 <![CDATA[ 0.999 ]]> 1.007e3 0.993 1.993 4D-TR 0.580 0.539 4.209e-5 1.119 0.580 1.281e4 0.539 1.119 RCTVW 1.000 <![CDATA[ 0.996 ]]> 4.653e-2 <![CDATA[ 1.996 ]]> 0.953 2.140e1 0.949 1.949 STT-TRNR 0.950 0.950 <![CDATA[ 6.847e-6 ]]> 1.900 0.950 <![CDATA[ 1.387e5 ]]> 0.950 1.900 DGRL 0.770 0.769 9.621e-2 1.539 0.674 7.988 0.672 1.442 AGPCNet 1.000 0.975 9.612e-5 1.975 1.000 1.014e4 0.974 1.974

[0161] Figure 5 The example frame image used for experimental testing is a thermal infrared image showing the detection results of small thermal infrared targets obtained through rcDoGF, GCM, IPCE, 4D-TR, RCTVW, STT-TRNR, DGRL, AGPCNet, and the method of this invention. From... Figure 5The qualitative results show that IPCE, STT-TRNR, and AGPCNet resulted in target misses, while GCM, IPCE, 4D-TR, and DGRL exhibited significant background and noise residue. In contrast, the method proposed in this invention effectively enhances the saliency of small targets and significantly suppresses background and noise components. Statistical results in Table 1 show that the infrared small target detection method proposed in this invention achieves optimal values ​​across all eight 3D-ROC evaluation metrics, with 4D-TR exhibiting the weakest overall detection capability (AUC). ODP =1.119, followed by DGRL and STT-TRNR; combining the above qualitative and quantitative analyses, thanks to the improved K-means clustering algorithm and the tracking regularization term based on Bayesian derivation, the infrared small target detection method based on clustering and Bayesian guided tracking proposed in this invention has excellent target detection capability, background suppression capability and comprehensive effectiveness.

[0162] The accompanying drawings illustrating the embodiments of the present invention will make the objectives, technical solutions, and advantages of the present invention clearer. It should be noted that the specific embodiments described herein are merely illustrative and not intended to limit the scope of the invention. All equivalent substitutions and improvements made within the framework of the methods and principles provided by the present invention should be included within the protection scope of the present invention.

Claims

1. A method for detecting small infrared targets based on clustering and Bayesian guided tracking, characterized in that, Includes the following steps: Step 1): Take the thermal infrared image sequence D containing the weak target to be detected, stack the image frames sequentially according to the time order of the frames, and construct a three-dimensional space-time tensor. ; Step 2): Based on the low-rank nature of the background, the sparsity of the target, and the properties of the noise, establish a model based on low-rank sparse tensor decomposition. Step 3): Combining local and global features, improve the K-means clustering algorithm to perform improved K-means clustering on the background tube fibers, and design a low-rank estimation norm based on the improved K-means clustering algorithm from the background tube fiber clusters; The improved K-means clustering algorithm described in step 3) is as follows: 3D spacetime tensor The Middle line, number The background tube fiber of the column is denoted as , It is also expressed as ; K background tube fibers are randomly selected as initial cluster centers, and K is determined by singular value decomposition. To determine the initial number of cluster centers K, the background tensor is... Expand the matrix according to pattern-3 as the background. , represented as , The pattern-3 expansion operator produces the background expansion matrix. The height is Width is , The height is numerically related to the three-dimensional spacetime tensor. thickness same, The transpose operator for a matrix is... , and Representing the background tensor respectively The 1st, 2nd and Zhang's side section; Background expansion matrix Perform singular value decomposition to obtain , This represents the singular value decomposition operator. Represents a singular value matrix. and Unitary matrix; singular value matrix There are on the diagonal One element, The value is , The vector corresponding to each element is Each singular value satisfies From 1 to When the first satisfaction hour, K is taken as The preset positive coefficient; Cluster center set Defined as , Indicates the first Cluster centers The coordinates are In the three-dimensional spacetime tensor In the middle, the position is the line, number The background tube fiber of the column as the first Cluster centers ; will the first Cluster centers The corresponding background tube fiber cluster is defined as Therefore, the first The cluster centers have been updated to: （3） in, Indicates the number of iterations. The operator representing the mean of the background tube fiber clusters. Indicates the calculation of the first The mean value of the tube fibers in a background tube fiber cluster is used as a local feature. This means calculating the mean value of all background tube fibers as a global feature. and represent the weighting coefficients assigned to local and global features, respectively. When the convergence condition is met , Represents the convergence error, the first... Cluster centers obtained from rounds of iteration These are the final determined cluster centers; The low-rank estimation norm based on the improved K-means clustering algorithm mentioned in step 3) is specifically as follows: K background tube fiber clusters were obtained based on the improved K-means clustering algorithm. , K background tube fiber clusters The objective functions are to minimize the sum of intra-class distances and maximize the inter-class distances of the K background tube fiber clusters. （4） in, Represents positive numbers. This means that the intra-class distance of a background fiber is obtained by calculating the Frobenius norm of all background fibers in the background fiber cluster. , , , , , These represent background tube fiber clusters. , , Intra-class distance, , Therefore, the low-rank estimation norm based on improved K-means clustering is... Defined as: （5） in, This indicates the number of background tube fibers in the calculated background tube fiber cluster. The variance of the intra-class distances of K background tube fiber clusters is used as the inter-class distance. Operator for calculating variance; Step 4): Using Bayesian theory, the spatiotemporal trajectory changes of small infrared targets are modeled and predicted through observation and state transition models, and a tracking regularization term based on Bayesian derivation is established. Step 5): Three-dimensional spacetime tensor based on Step 1). Combining steps 2) to 4), a small target detection model based on clustering and Bayesian guided tracking is established; Step 6): Use the ADMM algorithm to solve the low-rank sparse tensor decomposition model based on clustering and Bayesian guided tracking to obtain the target tensor. Then, extract each front slice from the target tensor in sequence as the infrared small target detection result corresponding to the infrared image sequence to be detected, thereby realizing the small target detection of the infrared image sequence.

2. The infrared small target detection method based on clustering and Bayesian guided tracking according to claim 1, characterized in that, Step 1) specifically refers to: The thermal infrared image sequence D containing the weak target to be detected is stacked sequentially in the third dimension, i.e., the time dimension, according to the frame order. Constructing a three-dimensional spacetime tensor , The size is , express The width of the front slice, express The height of the front slice, express thickness, The value and same.

3. The infrared small target detection method based on clustering and Bayesian guided tracking according to claim 1, characterized in that, Step 2) specifically refers to: Based on the low-rank characteristics of the background, the sparsity of the target, and the properties of the noise, a single frame infrared image is... Modeled as a low-rank background matrix sparse target matrix T and noise component matrix A linear combination of these elements is used to establish a model based on low-rank sparse matrix decomposition, as shown in equation (1): （1） in, Operators representing background rank, This represents the estimated sparsity of the target. Norm, This represents the square of the Frobenius norm, which measures random noise. and Indicates the weighting coefficient; Based on the three-dimensional spacetime tensor constructed in step 1), The three-dimensional spacetime tensor is derived from the low-rank sparse matrix decomposition model in step 2). Modeled as a low-rank background tensor sparse target tensor and noise tensor A linear combination of these factors is used to establish a model based on low-rank sparse tensor decomposition: （2） in, Indicates the use of optimal approximation norm Norm.

4. The infrared small target detection method based on clustering and Bayesian guided tracking according to claim 1, characterized in that, Step 4) specifically refers to: For infrared images Each pixel The Hessian matrix is ​​defined as ,in, , Representing infrared images medium pixel The second derivatives along the x and y directions, Infrared image medium pixel The second-order partial derivative results are calculated sequentially along the x and y directions; based on each pixel. The Hessian matrix defines the infrared image. The corresponding Gaussian curvature surface Pixels on the Gaussian curvature surface The corresponding Gaussian curvature value for: （6） in, The gradient operator of a matrix is ​​used to calculate the gradient. Representation matrix Determinant calculation operator, Represents the Hessian matrix The square of the gradient; for a three-dimensional spacetime tensor of Each frontal slice can yield the corresponding... Zhang Gaussian Curvature Surface ,Will The Gaussian curvature surfaces are stacked sequentially according to the temporal order of the corresponding frames, ultimately resulting in a Gaussian curvature surface tensor. ; For the Gaussian curvature surface tensor The target sparsity weighted tensor is determined by an adaptive threshold. : （7） in, express The index is elements, Represents the Gaussian curvature surface tensor The maximum value in, Represent a positive integer; Using target sparsity to weight the tensor and target tensor The tracking regularization term based on Bayesian inference is designed as follows: Assumption For target tensor Gaussian curvature surface tensor The entire target observation set, It is the first state in the state set There are 1 variable, representing the target tensor. The Middle The frontal slice or the first The state at any given moment, Based on Bayesian theory, posterior probability Defined as: （8） in, Indicates proportional to, Indicates the preceding The observation set corresponding to each time point, the integral term Essentially, this represents a weighted summation of all possible previous states. Indicates the weighted weight; This represents an observation probability model that measures the similarity between the observation set and the actual situation. This indicates a description of the state. Transition to state State transition probability model; Therefore, combining the target sparsity weighted tensor By maximizing the joint probability of the observation probability model and the state transition probability model To obtain The optimal state at any given time enables modeling and prediction of the spatiotemporal trajectory changes of small infrared targets: （9） In model (2) based on low-rank sparse tensor decomposition in step 2), Time-observed , Moment State and state of time They are respectively represented as , , , It represents the Hadamardi (or Hadama) stack; By minimizing the joint probability The logarithm of the reciprocal of , equation (9) is transformed into equation (10) as follows: （10） in, This represents the logarithmic operator; Therefore, for the target tensor Tracking regularization term derived from Bayesian inference as follows: （11） in, Represents the state transition tensor. , Represent tensors respectively , The A frontal slice, , , Represent tensors respectively , , The A frontal slice, and Represent tensors respectively and The The inverse matrix of a frontal slice.

5. The infrared small target detection method based on clustering and Bayesian guided tracking according to claim 4, characterized in that, The and Modeling using a Gaussian distribution, specifically, , , Represents the Gaussian distribution function. Represents the state transition matrix. The covariance matrix represents the probability model of observations. This represents the covariance matrix of the state transition probability model.

6. The infrared small target detection method based on clustering and Bayesian guided tracking according to claim 1, characterized in that, Step 5) specifically refers to: Based on the three-dimensional spacetime tensor of step 1). Combining the low-rank estimation norm based on the improved K-means clustering algorithm in step 3) and the tracking regularization term based on Bayesian derivation in step 4), and the model based on low-rank sparse matrix decomposition in step 2), a small target detection model based on clustering and Bayesian guided tracking is established as follows (12): （12） in, , , Represents positive numbers; To accelerate the solution speed of model (12), a sparsity reweighting strategy is introduced into model (12) based on clustering and Bayesian guided tracing low-rank sparse tensor decomposition. Calculate the sparsity reweight of the target As shown in formula (13): （13） in, Represents positive numbers. This indicates the element-wise inversion operation. This represents the absolute value operation; Combining formulas (12) and (13), the final small target detection model based on clustering and Bayesian guided tracking is obtained, as shown in formula (14): （14）。 7. The infrared small target detection method based on clustering and Bayesian guided tracking according to claim 1, characterized in that, Step 6) specifically refers to: The ADMM algorithm is used to solve the small target detection model based on clustering and Bayesian guided tracking (14), and auxiliary variables are introduced respectively. Thus, we obtain the equivalent formula (15) of (14): （15） The augmented Lagrangian function corresponding to formula (15) is: （16） in, For Lagrange multipliers, This is a penalty term; the solution is performed for each variable through alternating iterations, and the iterative update of each variable is as follows: 1) The iterative formula is （17） in, This indicates obtaining the parameter value corresponding to the minimum value of the function. Indicates the number of iterations; Based on formulas (3) to (5) in step 3), the improved K-means clustering algorithm is used to... Clustering of tubular fibers yields As shown in formula (18): （18） in, ;and then, Updated to （19） 2) The iterative formula is （20） From formula (20) on variables Taking the derivative and setting the equation to 0, we get... The iterative update formula is: （20） in, This is an operator that converts a matrix into a three-dimensional tensor according to mode -3; 3) The iterative formula is （21） in, It is a soft-threshold shrinkage operator, and has , For symbolic functions, Soft threshold; 4) The iterative formula is （22） 5) The iterative formula is （23） First, the target sparse weighted tensor in step 4). The iterative formula is （24） Among them, through Determine the Gaussian curvature surface tensor , express The index position is Element; based on , The iterative formula is （25） in, Represents unit tensor The A frontal slice, ; 6) The iterative formula is （26） 7) Lagrange multipliers The iterative formula is （27） （28） （29） 8) Penalty Items The iterative formula is （30） in, Indicates the update coefficients. express The maximum value; The iteration stopping condition is as follows: 1) When relative error Less than the error When the iteration terminates, Indicates the overall iteration error; 2) When adjacent iterations hour, Indicates background iteration error; stop iteration. 3) Stop iterating when the number of non-zero elements in the target tensor obtained from adjacent iterations no longer changes; Furthermore, the final target tensor is extracted sequentially. The front slice is used as the infrared small target detection result image sequence T corresponding to the infrared frame image sequence D to be detected, realizing infrared small target detection based on clustering and Bayesian guided tracking.

8. An infrared small target detection device based on clustering and Bayesian guided tracking, implementing the method of claim 1, characterized in that, include: The 3D spatiotemporal tensor construction module constructs a 3D spatiotemporal tensor from the infrared image sequence D to be detected. This lays the data foundation for the subsequent establishment of the tensor decomposition model; The model building module based on low-rank sparse tensor decomposition establishes a model based on low-rank sparse tensor decomposition by utilizing the characteristics of low-rank background components, sparse target components, and noise components. The low-rank background estimation norm design module combines local and global features to improve the K-means clustering algorithm, performs improved K-means clustering on background tube fibers, and designs a low-rank estimation norm based on the improved K-means clustering algorithm. The tracking regularization term design module, based on Bayesian theory, models and predicts the spatiotemporal trajectory changes of small infrared targets through observation and state transition models, and establishes a tracking regularization term based on Bayesian derivation. A module for establishing a small target detection model based on clustering and Bayesian guided tracking is constructed by combining a three-dimensional space-time tensor, improving the K-means clustering algorithm and a tracking regularization term based on Bayesian derivation. The model optimization and solution module uses the ADMM algorithm to solve the small target detection model based on clustering and Bayesian guided tracking, obtains the target tensor, and extracts the front slice of the target tensor as the infrared small target detection result of the infrared image sequence to be detected; The target detection result output module is used to output the infrared small target detection result sequence corresponding to the infrared image sequence.

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