CN106815854A - A kind of Online Video prospect background separation method based on normal law error modeling - Google Patents

Abstract

An online video foreground and background separation method based on regular error modeling, 1. Real-time acquisition of video data of the monitoring system; 2. Embedding in the model based on the real-time changes of the video background environment to optimize variables based on the transformation operator of the video background; 3. Construct a regular error modeling model based on the characteristics of real-time changes in video foreground targets; 4. Combine 2 and 3 to build a complete statistical model, and according to the maximum a posteriori estimation method, obtain a complete monitoring video foreground background separation model; 5. For video data Perform down-sampling to accelerate the calculation of the foreground and background separation model of video data in step 4, and realize the real-time solution of the model; 6. According to the foreground and background separation results of the surveillance video data obtained in step 5, output the foreground and background in real time. The invention is a method for separating the foreground and background of online monitoring video with high speed and high precision, and is of great significance in detecting, tracking, identifying and analyzing the monitoring video target in practical applications.

Description

A Foreground and Background Separation Method for Online Video Based on Regularized Error Modeling

technical field

The invention relates to a video processing method for monitoring video, in particular to an online video foreground and background separation method based on regular error modeling.

Background technique

Surveillance video foreground and background separation has important application value in real life, such as object tracking, urban traffic monitoring and so on. But nowadays, surveillance equipment is spread all over the world, and the daily surveillance video data is extremely large and complex in structure. Under the premise of ensuring high precision and high efficiency, it is still a huge challenge to separate the foreground and background of surveillance video in real time.

In the field of image processing, there are quite a few technologies for foreground and background separation of videos. Common techniques include direct separation methods based on statistical assumptions, subspace learning methods, and online separation methods.

The method of direct separation based on statistical assumptions makes a certain statistical distribution assumption on the frame data of the video, and then separates the foreground and background based on some statistics, such as median or mean model, histogram model, etc. In addition, the MoG and MoGG methods consider more delicate statistical distribution wigs for frame data, and use some mixed distributions (such as mixed Gaussian) to fit each frame data, and get better separation effects. However, these methods ignore the structural information of the video, such as the spatial continuity of the foreground, the temporal similarity of the background, etc. In contrast, the subspace learning method encodes the structural information of the video in a more detailed manner. By assuming that the background of the video has a low-rank structure, the spatial continuity of the video foreground and the temporal similarity of the background are integrated into the structural information. In the model, the obtained foreground and background separation effect is ideal.

Although the subspace learning method has achieved remarkable results, there is still a certain distance from the real practical application. In today's society, video data is increasing rapidly all the time, requiring foreground and background separation technology to have high efficiency under the premise of ensuring high precision; on the other hand, in the face of constantly emerging surveillance data, we need to provide A real-time on-line separation technique. Although there are some online separation methods, they often cannot meet the dual requirements of high precision and high efficiency.

In view of the deficiencies of existing technologies, it is necessary to provide a technology that can ensure high precision and high efficiency for real-time online foreground and background separation of continuously emerging surveillance videos, especially for dynamic foreground target types and Dynamic background environment changes should be able to adapt effectively.

Contents of the invention

The purpose of the present invention is to provide an online video foreground and background based on regular error modeling that can more fully and accurately utilize the structural information of the video for statistical modeling, thereby achieving a higher-precision separation effect and ensuring high processing efficiency. Separation method.

In order to achieve the above object, the technical solution adopted in the present invention comprises the following steps:

Step S1: Obtain video data of the monitoring system online;

Step S2: Build a model based on the low-rank structural assumption of the video background, embed adaptive transformation factor variables in the model, encode the dynamic changes of the video background, and realize adaptive modeling of the real video dynamic background;

Step S3: Parametric distribution modeling based on the randomness of video foreground object changes, so that it can adapt to the dynamic changes of video foreground at different times and scenes, and further encode the regularized noise information embedded in the previous video foreground information, Realize adaptive modeling of real video dynamic foreground;

Step S4: Combining steps S2 and S3, construct a complete statistical model for the separation of the foreground and background of the surveillance video;

Step S5: In step S1, down-sampling the video data, and applying the video data foreground and background separation statistical model of step S4 on the basis of the sampled data to accelerate the application of this item;

Step S6: performing TV continuity modeling on the foreground target obtained in step S5;

Step S7: According to the results obtained in steps S5 and S6, output the final detected video foreground object and background scene.

The step S2 builds a model: due to the similarity of the background corresponding to each frame image of the video data, the similarity is encoded by performing the following low-rank expression on the video image:

x ^t =U ^t v ^t +ε ^t (1)

where x ^t ∈ R ^d represents the t-th frame image of the surveillance video, U ^t ∈ R ^d×r is the current expression base of the video background, where r<<d, the subspaces expressed by these bases constitute a low-level subspace of the original image space Rank subspace, v ^t ∈ R ^r is the combination coefficient, U ^t v ^t represents the low-rank mapping representation of x ^t under the subspace U ^t , ε ^t represents the residual;

Embedding adaptive transformation factor variables in the model, that is, improving model (1) to:

Where τ ^t is an affine transformation operator variable for the image x ^t , expressing the video background transformation of rotation, translation, distortion, and scale.

The parametric distribution modeling of the step S3 is to encode the residual variable ε ^t in the model (2) into a mixed Gaussian distribution, so that it is adaptive to the dynamic change of the video foreground, that is, the video background residual at different times and different scenes, The corresponding model is:

in is the ith pixel value of x ^t , is the i-th row of U ^t , represents a hidden variable, The i-th pixel value representing the t-th pixel belongs to the k-th mixed component in the mixed Gaussian distribution, and satisfies Multi means multinomial distribution, is the variance of the tth mixed component;

In order to encode the regularized noise information embedded in the previous video foreground information and realize the adaptive modeling of the real video dynamic foreground, the conjugate prior formal assumptions are made on the noise distribution variables in model (3):

Here Inv-Gamma represents the inverse Gamma distribution, Dir represents the Dirichlet distribution, The expression of is as follows:

in Represents the degree of membership, indicating the degree to which the i-th pixel value of the j-th pixel belongs to the k-th mixed component in the mixed Gaussian distribution, The meaning of is the same as in formula (3).

The step S4 builds a statistical model based on the steps S2 and S3:

Here P(v ^t ) represents a Gaussian distribution with a sufficiently large variance, is the mixing coefficient of the mixed Gaussian distribution to which the t-th residual ε ^t belongs, Represents the variance of each mixture component of the mixture Gaussian distribution, τ ^t represents the adaptive transformation factor, as defined in formula (6);

According to the principle of maximum a posteriori estimation, the video foreground and background separation model converted from the statistical model can be transformed into the following optimization problem, fixed U ^t = U ^t-1 :

Simplifies to:

where D _KL (·||·) represents the KL divergence, and R(π ^t , ∑ ^t ) is the noise regularization term, in the form:

here is the mixing coefficient of the mixed Gaussian distribution to which the t-th residual ε ^t belongs, Represents the variance of each mixture component of the mixed Gaussian distribution, π ^t-1 , ∑ ^t-1 represents the corresponding mixing coefficient and variance vector of the t-1th k, As defined in formula (6), C represents a constant independent of π ^t and Σ ^t .

In the step S5, down-sampling is performed before the t-th frame image modeling solution to speed up the solution, and the subscript set is represented by Ω, then after down-sampling, it is obtained which is

Ω={k ₁ , k ₂ ,..., k _m |1≤k _j ≤d, j=1, 2,..., m}

Correspondingly, downsampling the row vector of U ^t yields

In the step 5, τ ^t in (7) is first-order approximated, and the problem solved for Δτ ^t degenerates into a weighted least squares problem, thereby solving the following model to obtain an updated result:

in is the mixing coefficient of the mixed Gaussian distribution to which the t-th residual ε ^t belongs, Represents the variance of each mixture component of the mixed Gaussian distribution, τ ^t is the adaptive transformation factor variable, J is the Jacobi matrix of x at τ, and u _i is the ith row of the basis matrix U.

The step S5 uses the EM algorithm to update the parameters π ^t in the online foreground and background separation model, ∑ ^t , v ^t , and the superscript s in the following formula represents the sth iteration, and the specific process includes:

S7.1: Give the E-step membership degree in the EM algorithm The update formula for is:

S7.2: Give the iteration format and termination condition of the M step in the EM algorithm:

The iteration format is:

in:

The iteration termination condition is:

S7.3: Set the iteration initial value:

Use the PCA method for the initial l-frame data to obtain the initial subspace decomposition, and then use the MoG method to initialize the parameters π ^{t, 0} , ∑ ^{t, 0} , v ^{t, 0} ;

S7.4: Carry out the iterative operation of (8)-(13) until the termination condition (14) is satisfied.

In the step S5, for the tth frame data, on the basis of updating parameters π ^t , Σ ^t , v ^t , τ ^t , the following model is used to fine-tune the background base U ^t-1 to obtain an updated U ^t :

in

Model (15) has the following solution:

in denote the ith row of U ^t , with The expression of is as follows:

Update U ^t according to formula (16)-(18), and output the foreground

In described step S6, utilize monitoring video background continuity feature to set up TV norm model as follows:

Here ||·|| _TV represents the TV norm, is the output result of formula (19), and λ is set as ( is the maximum variance), the above optimization problem is transformed into:

stF=Z _i , i=1,2 (21) where Z ₁ , Z ₂ ∈R ^m×n , S _i (·) are defined as follows:

The TV norm model of equation (21) is solved by using the ADMM of alternating direction multipliers:

S9.1: Give the augmented Lagrangian function of problem (18):

where P ₁ , P ₂ ∈ R ^m×n ,

S9.2: Establish the iteration format and termination condition of the alternating direction multiplier method:

The iteration format is:

Where ρ is a positive number greater than 1, take 1.5;

The iteration termination condition is:

S9.3: Solve (22)(23), and give the specific calculation formula of iteration;

S9.4: Set the initial value of iteration:

S9.5: Perform the iterative operation of (22)-(24) until the termination condition (25) is satisfied.

In the step S7, foreground FG ^t and background BG ^t =x ^t −FG ^t are finally output, where FG ^t and BG ^t respectively represent the foreground and background of the tth detection data.

The present invention establishes the foreground and background based on the monitoring video data and carries out targeted analysis and encoding respectively, so as to realize a fast and high-precision online monitoring video foreground and background separation model and method, which is useful for monitoring video targets in practical applications. It has important application significance for detection, tracking, identification, analysis, etc.

Description of drawings

Fig. 1 is a flowchart of the present invention.

Figure 2 shows the frame data of some videos in the LiDatasets dataset.

Figure 3 is the downsampling effect diagram in step S5, the first row is the original image in the Li Datasets dataset, and the second row is the result obtained after 1% downsampling.

Fig. 4 is the video separation effect diagram of the present invention, and the first column represents the original image in the Li Datasets data set, the second column is the real label of the pre-marked foreground, the third column is the foreground image separated in step S5, the fourth column Listed as the foreground image separated in step S7.

detailed description

The present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments.

Embodiment 1: The data set Li Datasets (https://fling.seas.upenn.edu/~xiaowz/dynamic/wordpress/decolor/) is used as the computer simulation experiment object of the present invention (see the first column in FIG. 4 ). See the following table (the foreground background separation speed of each video application of the present invention in the Li Datasets data set, wherein FPS represents the number of data frames processed per second):

The dataset contains 9 surveillance video datasets, including static background videos, background videos that change with lighting conditions, and dynamic background videos, and some of the data have real annotations of pre-marked foregrounds (see the second column of Figure 4 ), the frame data of part of the video is shown in Figure 2. The present invention extracts 200 frames of data from various videos for experiments. The process is shown in Figure 1:

Step S1: Obtain Li Datasets video data;

Step S2: Construct a low-rank decomposition model for the t-th frame data through the basic principle of foreground and background separation. Here, the present invention uses a mixed Gaussian with three mixed components to fit the noise. The specific expression is as follows:

x ^t =U ^t v ^t +ε ^t (26)

where x ^t ∈ R ^d represents the t-th frame image of the surveillance video, U ^t ∈ R ^d×r is the current expression base of the video background, where r<<d, the subspaces expressed by these bases constitute a low-level subspace of the original image space Rank subspace, v ^t ∈ R ^r is the combination coefficient, U ^t v ^t represents the low-rank mapping representation of x ^t under the subspace U ^t , ε ^t represents the residual;

Embedding adaptive transformation factor variables in the model, that is, improving the model (26) to:

Where τ ^t is an affine transformation operator variable for the image x ^t , expressing the video background transformation of rotation, translation, distortion, and scale.

Step S3: According to the assumption of the mixed Gaussian distribution of noise, there is

in is the ith pixel value of x ^t , is the i-th row of U ^t , represents a hidden variable, The i-th pixel value representing the t-th pixel belongs to the k-th mixed component in the mixed Gaussian distribution, and satisfies Multi means multinomial distribution, is the variance of the kth mixed component;

According to the similarity between the data backgrounds of each frame of video surveillance video, the following prior distribution can be assumed:

Here Inv-Gamma represents the inverse Gamma distribution, Dir represents the Dirichlet distribution, The expression of is as follows:

in Represents the degree of membership, indicating the degree to which the i-th pixel value of the j-th pixel belongs to the k-th mixed component in the mixed Gaussian distribution, has the same meaning as in (28).

Step S4: Combining steps S2 and S3 and the maximum a posteriori estimation method, the following surveillance video foreground and background separation optimization problem can be obtained:

Simplifies to:

here is the mixing coefficient of the mixed Gaussian distribution to which the t-th residual ε ^t belongs, Represents the variance of each mixture component of the mixed Gaussian distribution, π ^t-1 , ∑ ^t-1 represents the corresponding mixing coefficient and variance vector of the t-1th k, As defined in (29), C represents a constant independent of π ^t and Σ ^t .

Step S5: Referring to Figure 3, based on the video data input in step S1, apply the maximum a posteriori model in step S4 to construct a video foreground and background separation algorithm

A. Use the PCA algorithm for the first 50 frames of data to obtain the initial subspace U and v, and then use the following MoG algorithm 1 to initialize each parameter:

B. Down-sampling process, down-sampling the t-th frame data x ^t according to the ratio of 1%, to get Here Ω represents the set of subscripts, namely

Ω={k ₁ , k ₂ ,..., km|1≤k _j ≤d, j=1, 2,..., m}

Downsampling U ^t similarly gives

C. Fix U=U ^t-1 , use EM algorithm to update π ^t , ∑ ^t , v ^t , iteration (the superscript s indicates the number of iterations) format is as follows:

E-step:

M-step:

D. Iteration termination condition:

E. After updating π ^t , ∑ ^t , and v ^t according to the above process, to update U ^t , only some of the elements For fine-tuning, the specific optimization model is as follows:

in

The above model (30) has the following explicit solution:

here express the ith row of with The expression of is as follows:

F. Output Prospect (See third column in Figure 4)

Step S6: On the foreground object obtained in step S5, use the monitoring video background continuity feature to establish a TV norm model as follows:

Here ||·|| _TV represents the TV norm, For the foreground output in step S5, λ is set to ( is the maximum variance). The above optimization problem can be transformed into:

stF=Z _i , i=1, 2

Where Z ₁ , Z ₂ ∈R ^m×n , S _i (·) are defined as follows:

The solution process uses the following iterative format:

Where ρ is a positive number greater than 1, here 1.5 is taken.

A. (32) formula promptly solves the following problem:

Problem (35) has the following optimal solution:

B. The formula is to solve the following problem:

Problem (36) can be decomposed into the following two sub-problems (i=1, 2) to be solved respectively:

Equivalently there are

here

Let v ₁ , v ₂ ,..., v _n represent the column vectors of Z _i , t ₁ , t ₂ ,..., t _n represent the column vectors of T _i , then problem (37) can be decomposed into the following n sub-problems Solve individually:

And problem (38) can be solved using the following 1D TV denoising algorithm:

Step S7: Final output FG ^t (solution of formula (31) in step S6), background BG ^t =x ^t −FG ^t (see the fourth column in FIG. 4 ).

Claims (10)

1. it is a kind of based on normal law error modeling Online Video prospect background separation method, it is characterised in that comprise the following steps：

Step S1：The online video data for obtaining monitoring system；

Step S2：Model is built on the basis of the low-rank structure of video background is assumed, the adaptive transformation factor is embedded in a model Variable, the dynamic change of encoded video background realizes the adaptive modeling for real video dynamic background；

Step S3：Randomness based on video foreground object variations carries out parametrization distribution modeling, can be adaptive to not With the dynamic change of video foreground under time different scenes, the regularization noise of video foreground information before being further embedded in it Information is encoded, and realizes the adaptive modeling for real video dynamic prospect；

Step S4：With reference to step S2 and step S3, the statistical model that complete monitor video prospect background is separate is built；

Step S5：On step S1, carry out down-sampling to video data, and applying step S4 is regarded on the basis of this sampled data Frequency separates statistical model to this application acceleration according to prospect background；

Step S6：On the foreground target that step S5 is obtained, TV continuity modelings are carried out to it；

Step S7：According to step S5, the result that S6 is obtained, the video foreground target and background scene of the final detection of output.

2. the Online Video prospect background separation method based on normal law error modeling according to claim 1, its feature exists In：The step S2 builds model：Due to the similitude of the background corresponding to each two field picture of video data, the similitude is by right Video image carries out following low-rank expression and is encoded：

x^t=U^tv^t+ε^t (1)

Wherein x^t∈R^dRepresent the t two field pictures of monitor video, U^t∈R^d×rIt is the current expression base of the video background, wherein r ＜ ＜ d, the subspace of these substrates expression constitutes a low-rank subspace of artwork image space, v^t∈R^rIt is combination coefficient, U^tv^tTable Show x^tIn subspace U^tUnder low-rank mapping represent, ε^tRepresent residual error；

Be embedded in adaptive transformation factor variable in a model, will model (1) be improved to：

Wherein τ^tIt is to picture x^tAffine transformation operator variable, expression rotation, translation, distortion, yardstick video background conversion.

3. the Online Video prospect background separation method based on normal law error modeling according to claim 2, its feature exists In：The parametrization distribution modeling of the step S3 is by the residual error variable ε in model (2)^tGaussian mixtures are encoded to, make it The video foreground i.e. dynamic change of video background residual error under different time different scenes is adaptive to, correspondence model is：

$x_i^t~\underset{k=1}{\overset{K}{\&Pi;}}N{\left(x_i^t\right|{\left(u_i^t\right)}^T{v}^t,{\mathrm{\&sigma;}}_k^{t^2})}^{z_{ik}^t},Z_i^t~Multi\left(Z_i^t\right|{\mathrm{\&pi;}}^t)---\left(3\right)$

WhereinIt is x^tIth pixel value,It is U^tThe i-th row,Represent hidden variable, K-th blending constituent that the ith pixel value that t detects belongs in Gaussian mixtures is represented, and MeetMulti representative polynomials are distributed,It is t-th variance of blending constituent；

It is the regularization noise information coding of video foreground information before being embedded in it, realizes for real video dynamic prospect Adaptive modeling, carries out conjugate prior form hypothesis to noise distribution variable in model (3) respectively：

${\mathrm{\&sigma;}}_k^{t^2}~Inv-Gamma\left({\mathrm{\&sigma;}}_k^{t^2}\right|\frac{N_k^{t-1}}{2}-1,\frac{N_k^{t-1}{\mathrm{\&sigma;}}_k^{t-1^2}}{2})---\left(4\right)$

${\mathrm{\&pi;}}^t~Dir\left({\mathrm{\&pi;}}^t\right|\mathrm{\&alpha;}),\mathrm{\&alpha;}=(N^{t-1}{\mathrm{\&pi;}}_1^{t-1}+1,...,N^{t-1}{\mathrm{\&pi;}}_K^{t-1})---\left(5\right)$

Here Inv-Gamma represents Inv-Gamma distribution, and Dir represents that Dirichlet is distributed, Expression formula it is as follows：

${\mathrm{\&gamma;}}_{ik}^j=P(z_{ik}^j=1|x_i^j)=\frac{P\left(x_i^j\right|z_{ik}^j=1)P(z_{ik}^j=1)}{{\&Sigma;}_{k=1}^{K}P\left(x_i^j\right|z_{ik}^j=1)P(z_{ik}^j=1)}=\frac{{\mathrm{\&pi;}}_k^{j-1}N\left(x_i^j\right|{\left(u_i^j\right)}^T{v}^j,{\mathrm{\&sigma;}}_k^{j^2})}{{\&Sigma;}_{k=1}^K{\mathrm{\&pi;}}_k^{j-1}N\left(x_i^j\right|{\left(u_i^j\right)}^T{v}^j,{\mathrm{\&sigma;}}_k^{j^2})}---\left(6\right)$

WhereinDegree of membership is represented, k-th blending constituent that the ith pixel value that jth is detectd belongs in Gaussian mixtures is represented Degree,Meaning it is identical with formula (3).

4. the Online Video prospect background separation method based on normal law error modeling according to claim 1, its feature exists In：The step S4 is based on step S2, S3 and builds statistical model：

Here P (v^t) the sufficiently large Gaussian Profile of variance is represented,It is residual epsilon that t is detectd^tIt is affiliated Gaussian mixtures mixed coefficint,Represent Gaussian mixtures each blending constituents Variance, t^tThe adaptive transformation factor is represented,As (6) formula is defined；

According to MAP estimation principle, the video foreground background separation model converted by statistical model can be converted into following excellent Change problem, fixed U^t=U^t-1：

Abbreviation is：

Wherein D_KL(| |) represent KL divergences, R (π^t,∑^t) it is noise regular terms, form is：

$\begin{array}{c}R({\&Pi;}^t,{\&Sigma;}^t)=\underset{k=1}{\overset{K}{\&Sigma;}}{N}_k^{t-1}{D}_{KL}\left(N\right(0,{\mathrm{\&sigma;}}_k^{t-1^2}\left)\right|\left|N\right(0,){\mathrm{\&sigma;}}_k^{t^2})\\ +N^{t-1}{D}_{KL}\left(Multi\right({\mathrm{\&pi;}}^{t-1})\left|\right|Multi\left({\mathrm{\&pi;}}^t\right))+C.\end{array}$

HereIt is residual epsilon that t is detectd^tThe mixed coefficint of affiliated Gaussian mixtures,Represent the variance of each blending constituent of Gaussian mixtures, 4^t-1, ∑^t-1Represent corresponding Mixed coefficint and variance vectors that t-1 is detectd, As (6) formula is defined, C is represented and π^t, ∑^tUnrelated constant.

5. the Online Video prospect background separation method based on normal law error modeling according to claim 1, its feature exists In：In the step S5, to carrying out down-sampling to accelerate solving speed before t two field picture model solutions, subscript is represented with Ω Collection, then obtained after down-samplingI.e.

Ω={ k₁,k₂,…,k_m|1≤k_j≤ d, j=1,2 ..., m }

$x_{\mathrm{\&Omega;}}^t={\&lsqb;x_{k_1}^t,x_{k_2}^t,...,x_{k_m}^t\&rsqb;}^T$

Correspondingly, to U^tRow vector carry out down-sampling and can obtain

6. the Online Video prospect background separation method based on normal law error modeling according to claim 4, its feature exists In：To τ in (7) in the step 5^tCarry out single order to approach, to Δ τ^tThe problem of solution deteriorates to weighted least-squares problem, from And solve and update result as drag is obtained：

WhereinIt is residual epsilon that t is detectd^tThe mixed coefficint of affiliated Gaussian mixtures,Represent the variance of each blending constituent of Gaussian mixtures, τ^tFor the adaptive transformation factor becomes Amount, J is Jacobi matrixes of the x at τ, u_iIt is i-th row of basis matrix U.

7. the Online Video prospect background separation method based on normal law error modeling according to claim 1, its feature exists In：The step S5 updates the parameter π in online prospect background disjunctive model using EM algorithms^t,∑^t,v^t, in below equation on Mark s represents the s times iteration, and detailed process includes：

S7.1：Provide E step degrees of membership in EM algorithmsMore new formula：

${\mathrm{\&gamma;}}_{ik}^{t,s+1}=\frac{{\mathrm{\&pi;}}_k^{t,s}N\left(x_{\mathrm{\&Omega;}i}^t\right|{\left(u_{\mathrm{\&Omega;}i}^t\right)}^T{v}^{t,s},{\mathrm{\&sigma;}}_k^{t,s^2})}{{\&Sigma;}_{k=1}^K{\mathrm{\&pi;}}_k^{t,s}N\left(x_{\mathrm{\&Omega;}i}^t\right|{\left(u_{\mathrm{\&Omega;}i}^t\right)}^T{v}^{t,s},{\mathrm{\&sigma;}}_k^{t,s^2})}---\left(8\right)$

S7.2：Provide the Iteration and end condition of M steps in EM algorithms：

Iteration is：

${\mathrm{\&pi;}}_k^{t,s+1}={\mathrm{\&pi;}}_k^{t-1}-\frac{{\stackrel{\&OverBar;}{N}}^{t,s}}{N^{t,s}}({\mathrm{\&pi;}}_k^{t-1}-{\stackrel{\&OverBar;}{\mathrm{\&pi;}}}_k^{t,s})---\left(9\right)$

${\mathrm{\&sigma;}}_k^{t,s+1^2}={\mathrm{\&sigma;}}_k^{t-1^2}-\frac{{\stackrel{\&OverBar;}{N}}_k^{t,s}}{{\stackrel{\&OverBar;}{N}}_k^{t,s}}({\mathrm{\&sigma;}}_k^{t-1^2}-{\stackrel{\&OverBar;}{\mathrm{\&sigma;}}}_k^{t,s^2})---\left(10\right)$

$w_i^{s+1}=\sqrt{{\mathrm{\&Sigma;}}_{k=1}^K\frac{{\mathrm{\&gamma;}}_{i,k}^{t,s+1}}{2{\mathrm{\&sigma;}}_k^{t,s+1^2}}},i=1,2...,m---\left(11\right)$

$w^{s+1}={\&lsqb;w_1^{s+1},w_2^{s+1},\mathrm{...},w_d^{s+1}\&rsqb;}^T---\left(12\right)$

$v^{t,s+1}={\left(U_{\mathrm{\&Omega;}}^{T}di\mathrm{\&alpha;}g{\left(w^{s+1}\right)}^2{U}_{\mathrm{\&Omega;}}\right)}^{-1}{U}_{\mathrm{\&Omega;}}^{T}diag{\left(w^{s+1}\right)}^2{x}_{\mathrm{\&Omega;}}^t---\left(13\right)$

Wherein：

${\stackrel{\&OverBar;}{N}}_k^{t,s}=\underset{i=1}{\overset{d}{\&Sigma;}}{\mathrm{\&gamma;}}_{ik}^{t,s},{\stackrel{\&OverBar;}{N}}^{t,s}=\underset{k=1}{\overset{K}{\&Sigma;}}{\stackrel{\&OverBar;}{N}}_k^{t,s},{\stackrel{\&OverBar;}{\mathrm{\&pi;}}}_k^{t,s}=\frac{{\stackrel{\&OverBar;}{N}}_k^{t,s}}{{\stackrel{\&OverBar;}{N}}^{t,s}}$

$N_k^{t,s}={\stackrel{\&OverBar;}{N}}_k^{t,s}+N_k^{t-1},N^{t,s}={\stackrel{\&OverBar;}{N}}^{t,s}+N^{t-1},{\stackrel{\&OverBar;}{\mathrm{\&sigma;}}}_k^{t,s^2}=\frac{1}{{\stackrel{\&OverBar;}{N}}_k^{t,s}}\underset{i=1}{\overset{m}{\&Sigma;}}{\mathrm{\&gamma;}}_{ik}^{t,s}{(x_{\mathrm{\&Omega;}i}^t-{\left(u_i^t\right)}^T{v}^{t,s})}^2$

Stopping criterion for iteration is：

$\frac{|L({\&Pi;}^{t,s+1},{\&Sigma;}^{t,s+1},v^{t,s+1}l)-L({\&Pi;}^{t,s},{\&Sigma;}^{t,s},v^{t,s})|}{\left|L({\&Pi;}^{t,s+1},{\&Sigma;}^{t,s+1},v^{t,s+1})\right|}<{10}^{-4}---\left(14\right)$

S7.3：Iteration initial value is set：

Initial sub-spaces are obtained using PCA methods to decompose, then use MoG method initiation parameters π to initial l frame data^t,0, ∑^t,0,v^t,0；

S7.4：The interative computation of (8)-(13) formula is carried out, until meeting end condition (14) formula.

8. the Online Video prospect background separation method based on normal law error modeling according to claim 6, its feature exists In：In the step S5, to t frame data, in undated parameter π^t,∑^t,v^t, τ^tOn the basis of, by such as drag to background Base U^t-1It is finely adjusted the U for being updated^t：

Wherein

Model (15) is with following solution：

$u_i^t=A_i^t{b}_i^t---\left(16\right)$

WhereinRepresent U^tThe i-th row,WithExpression formula it is as follows：

$\begin{array}{c}{A}_i^t={\left({\&Sigma;}_{j=1}^t{w}_i^{j^2}{v}^j{v}^{j^T}\right)}^{-1}\\ ={({\left(A_i^{t-1}\right)}^{-1}+w_i^{t^2}{v}^t{v}^{t^T})}^{-1}\\ =A_i^{t-1}-\frac{w_i^{t^2}{A}_i^{t-1}{v}^t{v}^{t^T}{A}_i^{t-1}}{1+w_i^{t^2}{v}^{t^T}{A}_i^{t-1}{v}^t}\end{array}---\left(17\right)$

$\begin{array}{c}{b}_i^t=\underset{j=1}{\overset{t}{\&Sigma;}}{w}_i^{j^2}{x}_{\mathrm{\&Omega;}i}^j{v}^j\\ =b_i^{t-1}+w_i^{t^2}{x}_{\mathrm{\&Omega;}i}^t{v}^t\end{array}---\left(18\right)$

U is updated by (16)-(18) formula^t, and export prospect

${\mathrm{FG}}_0^t=x^t-U^t{v}^t---\left(19\right)$

9. the Online Video prospect background separation method based on normal law error modeling according to claim 8, its feature exists In：In the step S6, TV Norm Models are set up using monitor video background continuity Characteristics as follows：

${\mathrm{FG}}^t=\arg \underset{F}{\min }\frac{1}{2}\left|\right|F-{\mathrm{FG}}_0^t|{|}^2+\mathrm{\&lambda;}|\left|F\right|{|}_{TV}---\left(20\right)$

Here ‖ ‖_TVTV norms are represented,It is the output result of formula (19), λ is set to(For most Big variance), above optimization problem is converted into：

$\underset{F,Z_1,Z_2}{\min }\frac{1}{2}\left|\right|F-{\mathrm{FG}}_0^t|{|}_2^2+\mathrm{\&lambda;}\underset{i=1}{\overset{2}{\&Sigma;}}{S}_i\left(Z_i\right)$

S.t. F=Z_i, i=1,2 (21) wherein Z₁,Z₂∈R^m×n,S_i() is defined as follows：

$S_1\left(Z_k\right)=\underset{j=1}{\overset{n}{\&Sigma;}}\underset{i=1}{\overset{m-1}{\&Sigma;}}|{\left(Z_k\right)}_{ij}-{\left(Z_k\right)}_{i+1,j}|$

$S_1\left(Z_k\right)=\underset{i=1}{\overset{m}{\&Sigma;}}\underset{j=1}{\overset{n-1}{\&Sigma;}}|{\left(Z_k\right)}_{ij}-{\left(Z_k\right)}_{i,j+1}|$

The TV Norm Models of (21) formula are solved using alternating direction multiplier method ADMM：

S9.1：To the Augmented Lagrangian Functions of (18) of ging wrong：

$L(F,Z_i,P_i)=\frac{1}{2}\left|\right|F-{\mathrm{FG}}_0^t|{|}_2^2+\mathrm{\&lambda;}\underset{i=1}{\overset{1}{\&Sigma;}}<P_i,Z_i-F>+\frac{\mathrm{\&rho;}}{2}\underset{i=1}{\overset{2}{\&Sigma;}}||Z_i-F|{|}_2^2$

Wherein P₁,P₂∈R^m×n,

S9.2：Set up the Iteration and end condition of alternating direction multiplier method：

Iteration is：

$F^{s+1}=\arg \underset{F}{\min }L(F,Z_i^s,P_i^s)---\left(22\right)$

$\{Z_1^{s+1},Z_2^{s+1}\}=\arg \underset{Z_1,Z_2}{\min }L(F^{s+1},Z_i,P_i^s)---\left(23\right)$

$P_i^{s+1}=P_i^s+\mathrm{\&rho;}(Z_k^{s+1}-F^{s+1})---\left(24\right)$

Wherein ρ is a positive number more than 1, takes 1.5；

Stopping criterion for iteration is：

$\max \left\{\frac{\left|\right|Z_i^{s+1}-F^{s+1}|{|}_2^1}{\left|\right|Z_i^{s+1}|{|}_2^2}\right\}\&le;{10}^{-4}---\left(25\right)$

S9.3：(22) (23) are solved, the specific formula of iteration is given；

S9.4：The initial value of iteration is set：

S9.5：The interative computation of (22)-(24) is carried out, until meeting end condition (25) formula.

10. the Online Video prospect background separation method based on normal law error modeling according to claim 1, its feature exists In：In the step S7, final output prospect FG^t, background BG^t=x^t-FG^t, FG here^t,BG^tRepresent that t detects data respectively Foreground and background.