CN103106666A - Moving object detection method based on sparsity and smoothness - Google Patents

Abstract

The invention discloses a moving target detection method based on sparsity and smoothness in the technical field of video image processing. The method designs a regression model suitable for moving target detection, and then uses the model to estimate the moving target. The constraints of sparsity and smoothness are imposed on the moving target items to obtain the final detection results. The detection result of the moving target in the complex environment of the dynamic background is accurate and reliable.

Description

Moving Object Detection Method Based on Sparsity and Smoothness

technical field

The present invention relates to a method in the technical field of video image processing, in particular to a moving target detection method based on sparsity and smoothness.

Background technique

The research and application of moving object detection methods is an active branch in the field of computer vision and intelligent video analysis, and plays an important role in practical applications such as video surveillance, automatic control, and security inspection. Accurate and reliable moving target detection results are the basis for higher-level information processing, such as target tracking, target recognition, behavior analysis, etc.

The current moving target detection methods have achieved relatively stable and reliable results in common environments, but the performance of these methods in complex scenes is often unsatisfactory. Moving object detection in dynamic background, as one of the difficulties in object detection in several complex scenes, has received extensive attention for many years. It is of great significance to invent a moving object detection method suitable for dynamic background.

The existing moving target detection methods are mainly classified into three categories: optical flow method, frame difference method, and background difference method.

The optical flow method separates moving objects by calculating the motion vectors of pixels. This type of method has a relatively large amount of calculation and high complexity, and is currently mainly used in the mobile camera environment. The inter-frame difference method detects moving objects according to the intensity changes of corresponding pixel points between adjacent frames. Although this type of method is simple, it can only extract the outline of the target, and it is also sensitive to noise, so this type of method is not very practical.

The background subtraction method is currently the most commonly used moving object detection method. Its basic idea is to establish a description of the background by learning the video frame, and then compare and calculate the newly obtained video image with the background model. When the pixel in the new video frame When the point does not conform to the current background description, it is judged as the foreground point, otherwise it belongs to the background point, and the detection of the moving target is completed by point-by-point calculation. The more representative methods in the background difference method include: "Adaptive background mixture models of The Gaussian mixture background model method proposed in the article "real-timetracking" (Adaptive background mixture model for real-time tracking), which considers that the value of the pixel point conforms to the Gaussian distribution, and the value of each pixel point can be determined by multiple adaptive The weighted combination of the Gaussian mixture background model is obtained, thereby establishing the Gaussian mixture background model to realize the detection of moving targets; A.Elgammal, R.Duraiswami, D.Harwood and L.S.Davis et al. Association Journal) published "Background and foreground modeling using non-parametric kernel density estimation for visual surveillance" (for video surveillance based on non-parametric kernel density estimation background foreground modeling) in the article proposed to use the method of kernel density estimation for background Modeling, this method does not make any assumptions about the distribution of pixel values, but calculates the value of pixels through the time domain method to obtain the parameter estimation of the kernel function, and then establishes the background model based on these estimated parameters and kernel function , realized the detection of the target; Mert Dikmen andThomas S.Huang published "Robust Estimation of Foreground in Surveillance Videos by Sparse Error Estimation" in the 19th International Conference on Pattern Recognition (the 19th International Conference on Pattern Recognition) in 2008 (in video surveillance Foreground Detection Based on Sparse Error Estimation) This paper proposes a method based on sparse theory for foreground object detection. This method regards the detection of background and foreground as a kind of signal separation problem: the background signal changes slowly with time; the foreground signal changes differently from the background signal, and the foreground signal has the property of sparseness. Through the conversion of the problem and with the help of the existing sparse theory, the estimation of the sparse signal, that is, the foreground target can be realized.

The above background subtraction methods are often not ideal in dynamic background scenes, and these methods mistakenly detect some background points as foreground points. Therefore, it is necessary to seek a method for detecting moving objects in a dynamic background environment.

The Chinese invention patent with the application number CN201110223892.8 provides a target detection method based on a linear regression model. Although this method can realize the detection of moving targets in a complex environment such as a dynamic background, the effect can be further optimized .

Contents of the invention

The present invention aims at the above-mentioned deficiencies in the prior art, and provides a moving target detection method based on sparsity and smoothness, and the target detection result is accurate and reliable in the complex environment of a dynamic scene.

The present invention is achieved through the following technical solutions. The present invention first designs a regression model suitable for target detection, and then applies sparsity and smoothness to the moving target according to the characteristics of the moving target when using the model to estimate the moving target constraints to get the final detection result.

The regression model suitable for target detection refers to: the regression model can be expressed as the following form:

y=Xw+t+n (1)

Where: y=(y ₁ ,y ₂ ,…,y _m ) ^T represents the dependent variable, X=(x ₁ ,x ₂ ,…,x _m ) ^T represents the independent variable and x ₁ ,x ₂ ,…,x _m Both are p-dimensional vectors, p represents the number of elements contained in each vector, m represents the number of observations and m>p, w=(w ₁ ,w ₂ ,…,w _p ) ^T represents the coefficient of the regression model , t=(t ₁ ,t ₂ ,…,t _m ) ^T represents the part different from the independent variable, n=(n ₁ ,n ₂ ,…,n _m ) ^T represents the random error item, according to the classical linear regression model The assumption of the random error term, n ₁ , n ₂ ,...,n _m all obey the Gaussian distribution with mean value 0 and variance σ ² and the Gaussian distribution is denoted as N(0,σ ² ).

The described use of this model to detect the moving target refers to: corresponding to the formula (1), the current frame is used as the dependent variable y, several historical frames are used as the independent variable X, and the foreground part is used as a part t different from the independent variable, Consider the motion of the background itself as noise n. According to the original intention of the linear regression model, the regression coefficient needs to be estimated according to the data of the historical frame and the current frame. In order to estimate more accurately, a new objective function is defined by using the two characteristics of the foreground part, namely sparsity and smoothness. The coefficient w of the regression model is obtained, and then the part t different from the independent variable is estimated.

The new objective function refers to: assuming that the foreground part is sparse and smooth, then the objective function is expressed as:

$<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}}{\mathrm{<span\; class="notranslate">\; arg</span>}\mathrm{<span\; class="notranslate">\; min</span>}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; wxya</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; t</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

分别表示对模型系数和差异于自变量的部分的估计值，λ₁和λ₂表示调节系数，其中λ₁控制前景信号的稀疏程度，λ₂控制前景信号的平滑程度。由于公式(2)中同时有两个自变量，结合于目标检测实际问题中更关注于差异于自变量的部分

运用一种简化的处理方法进行简化。Where: ||·|| ₀ represents the 0-norm of the vector, t′=(t ₂ -t ₁ ,t ₃ -t ₂ ,…,t _m -t _m-1 ) ^T represents the adjacent element value of the foreground signal A new vector formed by the difference to describe its smoothness,

Represent the estimated value of the model coefficient and the part different from the independent variable, λ ₁ and λ ₂ represent the adjustment coefficient, where λ ₁ controls the sparseness of the foreground signal, and λ ₂ controls the smoothness of the foreground signal. Since there are two independent variables in formula (2) at the same time, it is more concerned about the part that is different from the independent variables in the actual problem of target detection

Simplify using a simplified approach.

Preferably, a simplified treatment of the above method is: first calculate the partial derivative of the formula (2) with respect to the variable w and set the value of the obtained expression to 0, so that the objective function (2) can be obtained after obtaining The value of w corresponding to the minimum value, that is:

$\frac{<span\; class="notranslate">\; \&PartialD;</span><span\; class="notranslate">\; (</span>{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; wxya</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; t</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

By calculating the formula (3), the following formula can be obtained:

$\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; +</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

Where X ⁺ is the pseudo-inverse matrix of X, expressed as X ⁺ =(X ^T X) ^-1 X ^T . Then substitute formula (4) into formula (2), and approximate the 0-norm of the vector with 1-norm, the following simplified objective function can be obtained:

$<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; t</span>}}{\mathrm{<span\; class="notranslate">\; arg</span>}\mathrm{<span\; class="notranslate">\; min</span>}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; t</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Where W=(I _m -XX ⁺ ), I _m is an identity matrix with size m.

即可得到对差异于自变量的部分的估计值，同时考虑到图像矢量化后造成空间信息的丢失，采用以不同方式将图像数据矢量化，然后将估计得到的结果进行融合。According to the existing sparsity theory and solving algorithm, it can be estimated that

The estimated value of the part different from the independent variable can be obtained. At the same time, considering the loss of spatial information after image vectorization, the image data is vectorized in different ways, and then the estimated results are fused.

Said vectorizing the image data in different ways, and then fusing the estimated results refers to: respectively performing horizontal vector straightening and vertical vector straightening on the image, and separately foreground according to the data under these two processing methods The target is estimated, and then the two estimated results are logically or fused to obtain the final result.

Compared with the prior art, the present invention has the following beneficial effects:

The invention provides a moving target detection method in a dynamic background, so that relatively sparse moving targets can be extracted in an environment of background disturbance, and at the same time, for the discrete background noise accompanying the extraction process, the local smoothness of the moving target can be used , the noise is separated and removed, the structure of the moving target in the obtained detection result is clear and complete, accurate and reliable, and the background noise is basically suppressed. Compared with the invention patent CN201110223892.8, the present invention not only utilizes the sparse attribute of the target in the process of estimating the moving target with the linear regression model, but also constrains the local smoothness of the target. The invention provides an effective solution to the technical problem of detecting a moving target under a dynamic background.

Description of drawings

Other characteristics, objects and advantages of the present invention will become more apparent by reading the detailed description of non-limiting embodiments made with reference to the following drawings:

Fig. 1 is a flowchart of an embodiment of the present invention.

Fig. 2 is a schematic diagram of the effect of an embodiment of the present invention.

Detailed ways

The present invention will be described in detail below in conjunction with specific embodiments. The following examples will help those skilled in the art to further understand the present invention, but do not limit the present invention in any form. It should be noted that those skilled in the art can make several modifications and improvements without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

As shown in FIG. 1 , this embodiment provides a method for detecting moving objects based on sparsity and smoothness. The specific implementation details are as follows. For the parts that are not described in detail in the following embodiments, refer to the content of the invention:

(1). Construct the independent variable matrix: extract an image every 10 frames from the first 200 images of the current video frame sequence, and extract a total of 20 images as the training video images of the current frame, and divide each frame image by horizontal (vertical) ) to form a vector in a straightened way, and add the vector to the i-th column of the corresponding independent variable matrix X, where (0<i≤20).

(2). Calculate the pseudo-inverse matrix X ⁺ of the independent variable matrix X.

(3). For non-training frames, convert them into vector y according to the straightening method in step (1).

(4). Estimate the parameters λ ₁ and λ ₂ in the formula (5) according to the existing data X and y. Specific steps are as follows:

(a). Estimate a regression coefficient with a classical linear regression model

(b). Calculate the error vector according to the obtained coefficients

其中med(·)表示取中值操作；(c). Estimate an initial deviation value according to the absolute median deviation method:

Among them, med(·) represents the operation of taking the median value;

(d). Set the parameters of λ ₁ and λ ₂ as ${\mathrm{\&lambda;}}_1=\frac{\widehat{\mathrm{\&sigma;}}}{15}*\sqrt{2\log \left(m\right)},$ ${\mathrm{\&lambda;}}_2=\frac{25*\widehat{\mathrm{\&sigma;}}}{15}*\sqrt{2\log \left(m\right)}.$

(5). Estimate the part t different from the independent variable according to formula (5), and threshold the estimated image. Pixels greater than the threshold are determined as foreground points, otherwise they are background points. Here the threshold is set to 25.

(6). According to the vector formation methods of horizontal straightening and vertical straightening respectively, according to steps (1)-(5) to obtain the corresponding estimation results under these two straightening methods.

(7). The above two estimation results are logically or fused to obtain the final result.

Implementation Effect

According to the above-mentioned steps, experiments are carried out on the public dynamic background test sequences provided on the Internet. The sequence scene is a campus environment, and then motor vehicles and people pass by one after another. During the whole process, the leaves will shake with the wind. This method tests the detection results of moving objects.

As shown in Figure 2, Figure (a) is the sequence input frame, that is, the training image; Figure (b) and Figure (c) are the test image of the 1204th frame of the moving target and its detection results; Figures (d) and Picture (e) is the test image and detection result of the 1385th frame of the moving target; picture (f) and picture (g) are the test image and detection result of the 1668th frame of the moving target respectively. Figure (h) and Figure (i) are the test image and detection results of the 1812th frame of the moving target, respectively. It can be seen from the figure that the method of the present invention can detect moving objects accurately and reliably under a dynamic background, reflecting the effectiveness and value of the present invention.

In order to reflect the advancement of the present invention, the method of the present invention is combined with the traditional Gaussian mixture background model method (proposed by C. Stauffer et al., referred to as GMM), kernel density estimation method (proposed by A. Elgammal et al., referred to as KDE) and the patent number is CN201110223892. 8's invention patent "target detection method based on linear regression model" (referred to as linear regression model method) for quantitative comparison. The present invention adopts F_score to evaluate the detection results of three methods for measuring index:

Among them, the precision rate and recall rate are respectively positioned as:

The higher the F_score indicator, the more effective the method is.

By testing the results of 10 frames arbitrarily selected in the test sequence by the above three methods, and comparing the evaluation results as follows:

The comparison of quantitative evaluation results shows that this method is superior to the above two traditional methods and the linear regression model method in terms of detection performance, which further reflects the value of the method of the present invention.

Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art may make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention.

Claims (2)

1. A moving target detection method based on sparsity and smoothness, characterized in that, by designing a regression model suitable for moving target detection, then when using the model to estimate the moving target, the moving target item is imposed Constraints of sparsity and smoothness to obtain the final detection results; The regression model suitable for moving target detection, the regression model is expressed as the following form: y=Xw+t+n (1) Where: y=(y ₁ ,y ₂ ,…,y _m ) ^T represents the dependent variable, X=(x ₁ ,x ₂ ,…,x _m ) ^T represents the independent variable and x ₁ ,x ₂ ,…,x _m Both are p-dimensional vectors, p represents the number of elements contained in each vector, m represents the number of observations and m>p, w=(w ₁ ,w ₂ ,…,w _p ) ^T represents the coefficient of the regression model , t=(t ₁ ,t ₂ ,…,t _m ) ^T represents the part different from the independent variable, n=(n ₁ ,n ₂ ,…,n _m ) ^T represents the random error item, according to the classical linear regression model The assumption of the random error term, n ₁ , n ₂ ,...,n _m all obey the mean value is 0, the variance is the Gaussian distribution of σ ² and the Gaussian distribution is recorded as N(0, σ ² ); The described use of this model to detect the moving target refers to: corresponding to the formula (1), the current frame is used as the dependent variable y, several historical frames are used as the independent variable X, and the foreground part is used as a part t different from the independent variable, The motion of the background itself is regarded as noise n. According to the original intention of the linear regression model, the regression coefficient needs to be estimated based on the data of the historical frame and the current frame. In order to estimate more accurately, the two characteristics of the foreground part, namely sparsity and smoothness, are used. , define a new objective function to obtain the coefficient w of the regression model, and then estimate the part t different from the independent variable. Considering the loss of spatial information after image vectorization, the image data is vectorized in different ways, and then Combine the estimated results; The new objective function refers to: assuming that the foreground part is sparse and smooth, then the objective function is expressed as: $<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}}{\mathrm{<span\; class="notranslate">\; arg</span>}\mathrm{<span\; class="notranslate">\; min</span>}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; wxya</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; t</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$ Where: ||·|| ₀ represents the 0-norm of the vector, t′=(t ₂ -t ₁ ,t ₃ -t ₂ ,…,t _m -t _m-1 ) ^T represents the adjacent element value of the foreground signal A new vector formed by the difference to describe its smoothness,

Represent the estimated value of the model coefficient and the part different from the independent variable, λ ₁ and λ ₂ represent the adjustment coefficient, where λ ₁ controls the sparseness of the foreground signal, and λ ₂ controls the smoothness of the foreground signal; Said vectorizing the image data in different ways, and then fusing the estimated results refers to: respectively performing horizontal vector straightening and vertical vector straightening on the image, and according to the data under these two processing methods, respectively The foreground object is estimated, and then the two estimated results are logically or fused to obtain the final result. 2. the moving target detection method based on sparsity and smoothness according to claim 1, is characterized in that, a kind of simplified processing of described method is: at first calculate formula (2) to the partial derivative of variable w and put The value of the obtained expression is set to 0, so that the value of w corresponding to the objective function (2) is obtained when the minimum value is obtained, that is: $\frac{<span\; class="notranslate">\; \&PartialD;</span><span\; class="notranslate">\; (</span>{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; wxya</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; t</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$ By calculating the formula (3), the following formula is obtained: $\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; +</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$ Where X ⁺ is the pseudo-inverse matrix of X, expressed as X ⁺ =(X ^T X) ^-1 X ^T , then substitute formula (4) into formula (2), and use the 0-norm of the vector with the 1-norm Approximation, the following simplified objective function is obtained: $<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; t</span>}}{\mathrm{<span\; class="notranslate">\; arg</span>}\mathrm{<span\; class="notranslate">\; min</span>}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; t</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$ Where W=(I _m -XX ⁺ ), I _m is an identity matrix with size m.

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