Background Updating Technique in Complex Traffic Scene Based on Sensor Fusion

JOURNAL OF TRANSPORTATION SYSTEMS ENGINEERING AND INFORMATION TECHNOLOGY Volume 10, Issue 4, August 2010 Online English edition of the Chinese language journal Cite this article as: J Transpn Sys Eng & IT, 2010, 10(4), 27−32.

RESEARCH PAPER

Background Updating Technique in Complex Traffic Scene Based on Sensor Fusion WANG Guolin, XIAO Deyun* Department of Automation, Tsinghua University, Beijing 100084, China

Abstract: The challenges of constructing complex traffic background discourage the application of video surveillance approaches. In order to solve the problems, a novel background updating method based on sensors fusion is proposed. First of all, A Gaussian mixture model based on Expectation-Maximization (EM) algorithm is proposed to improve the accuracy of background modeling. Secondly, for slowly moving or stationary region of interest, different sample frequencies are set to increase the reliability of modeling data. Meanwhile, data from loop and virtual loop fusion is performed to enhance the accuracy of vehicle speed detected by virtual loop. A local stationary optimal Kalman smoother is introduced in order to improve the self-tuning ability of the data fusion algorithm. Finally, experimental results prove the validness and robustness of the method. Key Words: intelligent transportation; video detection; virtual detection line; sensor fusion; background updating

1

Introduction

With the accelerated pace of China’s urbanization, urban traffic congestion is worsening. To alleviate the traffic pressure and improve traffic operation efficiency, the construction of intelligent transportation system (ITS) is speeding up in many major cities of China. ITS plays an increasingly important role in metropolitan traffic management, which puts forward higher requirements for traffic state detection techniques, such as higher accuracy and wider detection ranges for video sensors. Unfortunately, vehicle detection technique appears to be the weakest link in traffic surveillance and control system, limited by its surveillance range and detection precision. Therefore, the research of comprehensive traffic state detective technology is of great significance to the developing of ITS. The existing traffic state sensors can be classified mainly as buried loop and video. Although buried loops detect vehicles preciously, the most important drawback of the equipment is its limitation in measuring some traffic parameters in the detection points. Compared with loop, video cameras can monitor a wider range. However, the robustness of video-based methods is not effective enough, especially in complex traffic scenes, which always leads to poor detection

accuracy. One of the most important reasons is that the background model in complex traffic scenarios is not accurate. This can be explained by two factors which increase the difficulties of modeling background. One is that the optical flow changes with circumstances. On the other hand, the queue length, queue time, and velocity of vehicles in detection range have a certain randomness and unpredictability. Various methods used to model background have been proposed in the literature, which can be classified into one of the following three categories: frames average method[1,2], selective updating method[3] and mixture of Gaussian method[4,5]. Frames average method is a weighted average of the sampling frames. The advantage of this method is modeling the background accurately for moving objects in video scenes. However, it is very difficult to choose an appropriate sampling frequency with this model, so as to model complex traffic background. If the sample frequency is too low, the constructed background based on this method cannot be adapted to gradual illumination changes. On the contrary, the queued vehicles go into the background model and lead to an incorrect result. Selective updating method is to update the designated area of the background. Nevertheless, it is difficult to choose an appropriate region to update the background because of the uncertainty of vehicle queue length

Received date: Mar 17, 2010; Revised date: May 11, 2010; Accepted date: May 27, 2010 *Corresponding author. E-mail: [email protected] Copyright © 2010, China Association for Science and Technology. Electronic version published by Elsevier Limited. All rights reserved. DOI: 10.1016/S1570-6672(09)60051-9

WANG Guolin et al. / J Transpn Sys Eng & IT, 2010, 10(4), 27−32

and position. While the mixture of the Gaussian method can adapt to the slow light changes, and it will bring out a certain delay when background is constructed. The result of modeling background is not satisfied especially for the scenario where the velocity of vehicles changes frequently. Xu et al.[6] proposed a background pixel differences iterative method to generate and update the background in the case of large traffic flow density, whereas it will take a longer time to generate the background in the condition of darkness. Lei and Li[7] used a random image subtraction method to obtain candidate background pixels. A method integrated with temporal and spatial statistics is used to build the background and the credibility of every pixel. The drawback of this method is that it can only detect part of the stationary target. Different from the aforementioned methods, a novel complex traffic background updating method for complex traffic scenes modeling is presented in this paper. First of all, several virtual detective lines are treated as virtual loops. Second, multisensor fusion between loops and virtual loops are performed, which can be used to increase the detection accuracy of virtual loop and assess the reliability of constructed background when the traffic lights turn green. Finally, different sample frequencies for a given region of interest (ROI) are set based on the velocity of the ROI acquired by data fusion. The main contributions of this paper to model complex background include the following: First, multi-sensors fusion is carried out to improve the detection range and the accuracy of virtual detective lines by evaluating the data obtained by video-based method proposed in this paper. Second, the results of vehicle detection and track are used to establish the background as feedback. The sampling frequency for a given pixel is determined by the detection speed of the ROI if the pixel belongs to the ROI.

2

Mixture of Gaussian method based on EM Algorithm

posterior probability density function at a given data set. The equation is as Eq. (1).

xB , N = arg max xˆB ,N P ( xˆB , N x1 , x2 ," xN )

where xN=I(i, j, N) represents the pixel value in the N-th frame where its coordinate is (i, j), consist of three dimension vector, xB,N denotes the constructed optimal background pixel which satisfies with Eq. (1), xˆ B , N denotes estimation value of xB,N. Therefore, from Eq. (1), it can be observed that the following two fields can be concerned to improve the accuracy of background model. First and foremost, it is helpful to maximize the accuracy of models. Second, it is beneficial to enhance the liability of observational data and can reduce noise caused by queue vehicles. The main work of this paper is to filter the noise caused by stationary vehicles and assuring the adjustability of the proposed algorithm. 2.2 Methodology of proposed algorithm First of all, a background model for complex traffic scene is established based on the expectation maximization (EM) algorithm under the assumption that each sampling pixel from the image sequence is subject to a mixture Gaussian distribution in this paper. Then the ROI in different position can be obtained by subtracting the constructed background from the current sampling image. Furthermore, the position, speed information of different ROI can be acquired by vehicle detecting and tracking algorithm. The accuracy of the background model is enhanced through modified mixture Gaussian algorithm, which is elaborated in Section 2.3. On the other hand, a new method is used to diminish the disturbance brought by sampling data noise as much as possible, which is detailed illustrated in Section 3. Finally, Multi-sensors consisting of loop and virtual detective lines fusion is performed to mend the detection data of virtual loops. The mended data can decide the sampling frequencies of different ROI and assess the constructed background model. The framework of the constructing background proposed in this paper is shown in Fig. 1.

2.1 Problem description The following assumptions are made for modeling background to simplify the problem. (1) Each value of the sampling pixel in the frame is subject to a certain degree of probability distribution. A mixture Gaussian distribution is assumed in the paper. (2) The sampling time interval is fixed and uniform. Each of the video frames can be represented as a data matrix I, and the matrix sequences consist of sampling images from video camera is defined as: {I (i, j, N ), 1 ≤ N ≤ M } where N and M are denoted as the number and the sum number of sampling frames respectively, (i, j) denotes the coordinates of a given pixel in the matrix I. The problem of constructing a background can be described as maximizing the

(1)

Fig. 1 Framework of constructing background based multi-sensor fusion

WANG Guolin et al. / J Transpn Sys Eng & IT, 2010, 10(4), 27−32

2.3

Modified mixture Gaussian method based on EM algorithm Different from traditional background modeling method, the mixture Gaussian method models each pixel as a mixture of Gaussians. The Gaussian distributions of adaptive mixture model are then evaluated to determine those are most likely to result from a background process. One of the advantages of this approach is its robustness to slow-moving objects and light changes. As a result, the method is very flexible for outdoor traffic surveillance. Stauffer and Grimson[4] proposed a mixture Gaussian background modeling method based on k-means algorithm. However, the method suffers from slow learning at the beginning, especially in busy traffic environments. For example, if the first value of a given pixel is a foreground object, there is only one Gaussian where its weight equals unity. With only gray-scale subsequent background values, it will take log(1-α)TB frames until the genuine background can be considered as a background. A modified mixture Gaussian method based on the EM algorithm is proposed to construct an accurate background in the paper. Compared with k-means based approach, the convergence speed of the mean value and covariance matrix obtained by EM-based algorithm is much faster; meanwhile, the adaptation to environments is better. The algorithm is as follows. Suppose that each pixel value is subject to mixture Gaussian distribution, the probability density function that a certain pixel has a value of xN at time N can be written as: K

p ( xN ) = ∑ ωi , Nη ( xN ;θi ) i =1

where K is the number of distributions, ωi,N is the weight parameter of the i-th Gaussian component when the sampling pixel value is xN. η(xN; θi) is the Normal distribution of i-th component represented by 1 − ( x −μ ) Σ ( x −μ ) 1 2 η ( xN ; θ i ) = η ( xN ; μ i , Σ i ) = e D 1 2 (2π) Σi 2 N

i

T

−1 i

N

i

where μi is the mean value and D and Σ i are the dimension and covariance of the i-th Gaussian component respectively. To simple the problem, it can be defined that Σi = σ i I where I denotes an identity matrix. σi represents the variance of the i-th Gaussian component. (i) For a new sampling pixel value xN, the Gaussians are ordered by the value of ωi/σi. The initial value of ωi/σi is predefined. (ii) Check whether xN matches the i-th Gaussian component. The criterion of match is defined as a pixel value subjected to a Gaussian distribution N(μ, σ2) within 2.5 standard deviations, which guarantees the probability of random variances belonging to |μ–2.5σ, μ+2.5σ| is 0.9876. This is beneficial to improve the accuracy of modeling background. The criterion is written as below:

⎧⎪if ( xN − μi , N ≤ 2.5 ⋅ σ i , N match (criterion 1) ⎨ else unmatched ⎪⎩ (iii) If the sampling pixel xN matches the i-th Gaussian component, the mean value and variance are updated as below based on the EM algorithm according to the L-recent samples. 1 ωi , N = ωi , N −1 + (η (ωi , N −1 xN ) − ωi , N −1 ) L 1 η (ωi , N −1 xN ) xN μi , N = μi , N −1 + ( − μi , N −1 ) L ωi , N σ i2, N = σ i2, N −1 + T 1 η (ωi , N −1 xN )( xN − μi , N ) ( xN − μi , N ) − σ i2,N −1 ) ( L ωi , N

If none of the K Gaussian component matches the sampling pixel xN , the least probable component is replaced by a distribution with the current value as its mean, an initially high variance, and a low prior weight parameter. The mean value and covariance of other components remain the same as the N–1 sampling time, and the weights of the prior distribution are adjusted as follows:

ωi , N = (1 − α )ωi , N −1 where α is denoted as learning rate and needed to be set for the system. (iv) The first B distribution is chosen as the background model of the scene where B is estimated as follows: b

B = arg min b (∑ ω K , N > TB ) K =1

where the parameter TB is needed to be preset for the system. Then the weights of the prior B Gaussian component are normalized. The modeled background xB,N can be obtained by calculating the expectation mean value. Finally, whether the current pixel belongs to background or not is decided according to the distribution of the prior B Gaussian component. (v) For new sampling pixel xN+1, loop from Step (i). 2.4 Vehicle detection method based on virtual detective line A vehicle detection algorithm based virtual line used to detect vehicle is proposed in this paper. The position of vehicle is detected according to this method. Furthermore, the velocity of vehicle is obtained by the Kalman filter and a self-tuning Kalman Smoother. The two algorithms being combined, the sampling frequency in different ROI can be decided according to a given sample criterion. The principle of the detective-line-based method is similar to that of buried loop. The value of the ROI, obtained by subtracting constructed background from current frame, is compared with a predefined threshold to decide whether it belongs to vehicle or not. The basic steps are as follows. The foreground pixel value yN(i, j) on the detective lines at the N-th sampling frame is written as follows: y N (i , j ) = x N ( i , j ) − x B , N ( i , j )

WANG Guolin et al. / J Transpn Sys Eng & IT, 2010, 10(4), 27−32

where xB,N(i, j) is denoted as constructed background pixel values obtained by the algorithm discussed in Section 2.3. To eliminate the influence brought by noise, the average foreground value in the detective line is calculated as below: yN =

1 M

M

∑y i =1

N

(i, j )

where M is denoted as the number of pixels in virtual detective line.

3

Vehicle velocity detection technique based on sensor fusion

Compared with video sensors, buried loops detect higher accuracy of vehicle velocity. The vehicle velocity detection accuracy obtained by video cameras can be increased by data-fusion technique. Meanwhile, multi-sensor-based technique can decrease the misdetection rate brought by video-based methods. As a result, it is significant to increase the detection accuracy of video-based method through data-fusion. The precise vehicle velocity acquired by multi-sensors fusion determines the sampling frequencies of different ROI. Furthermore, it benefits the construction of background because of the sampling data with less noise. The proposed method is as follows. When the traffic signal light is in green phase, a self-tuning Kalman smoother is used to detect vehicle velocity based on a multi-sensor fusion. When the signal light is in red phase, vehicle velocity is obtained by the Kalman filter according to data acquired by video-based method. 3.1 Data preprocess After the vehicle is detected by virtual detective lines, a search algorithm is executed along the inverse direction of vehicle traveling. One of the merits is that the search range is finite. Therefore, it is convenient to determine the edge of the ROI and its position coordinate. Then, the vertical and horizontal edge of detected vehicles can be acquired through the least square (LS) algorithm. The mathematical description of horizon edges is written as follows: a1x+b1y=c1 and a1x+b1y=c2 Similarly, the mathematical description of vertical edges is written as follows: a2x+b2y=c3 and a2x+b2y=c4 The parameters a1, b1, c1, c2, a2, b2, c3, c4 are obtained through the LS algorithm. Furthermore, the maximum rectangle framework (MRF) of the ROI is acquired. If the area of the MRF is lower than a given threshold, the MBF will be removed as data noise. Thus, it effectively decreases the disturbance of noise data and increases the robustness to video-based detection. 3.2 Vehicle velocity detection method based on sensors fusion Let d(k), v(k), and α(k) be the position, velocity and acceleration of the blob identified at sampling time k along one of the image directions. Let τ be the fixed sampling time

interval. To simplify the system, the vehicle image dynamics is modeled as a constant acceleration dynamic system accounting for velocity variation and camera perspective effects. The velocity and acceleration of vehicle is a constant in a fixed sampling interval. The perspective effect will be modeled as an acceleration term to α(k) and an external noise source. Denoting the system state vector by S(k) and combining the position, velocity, and acceleration as follows S(k)=[d(k) v(k) α(k)]T. Further assuming the tracker provides noisy (i ) measurements Y( k ) of the vehicle image position detected by the i-th sensor, where i=1, ···, H, and H represents the sum of sensors. Here a detective line is treated as a virtual sensor. The system dynamics and observations can then be described as follows: S( k ) = ΦS( k −1) + Γξ

Y((ki)) = C T S( k ) + η ( i )

with ⎡1 τ τ 2 / 2 ⎤ ⎢ ⎥ Φ = ⎢0 1 τ ⎥ ⎢0 0 1 ⎥⎦ ⎣

C = [1 0 0]

T

Γ = [ 0 0 1]

T

where ξ and η(i) are independent zero-mean Gaussian-distributed random vectors with covariance Q = E{ξ (i )ξ T ( j )} and R(i ) = E{(η (i ) (k ))2 } . (1) Traffic signal light in red phase Vehicle is detected and tracked only based on video-based method. Two steps, consisting of prediction and filtering step, are executed respectively according to the Kalman filter. In the prediction step, the problem consists of determining the estimate of the state vector at time k+1, given only the information available at time k, S( k +1 k ) . Then, the filtering step plays the role of updating the current estimate to reflect the new information contained in the new observation S( k +1 k +1) as follows: Prediction: S( k +1 k ) = ΦS( k k ) Updating or filtering in a recursive algorithm: S((ki )+1 k +1) = S( k +1 k ) + K k( i ) (Y((ki+) 1) − C T S( k +1 k ) ) K k(i ) = Wk(i )C ⎣⎡C T Wk(i )C + R (i ) ⎦⎤ Wk(i ) = ΦPk(−i 1) ΦT + Q Pk( i ) = ⎡⎣ I − K k(i )C T ⎤⎦ Pk(−i 1)

where P0 is preset. (2) Traffic signal light in green phase The observation detected by loop is used to smooth the measurement detected by virtual detective lines. A local stationary optimal the Kalman filter proposed by Deng and Li[8] is introduced in this paper. The smoother is donated as Sˆ((ki )− N k ) , where N represents the time interval when the detected vehicle moves from the virtual line to loop. The self-tuning Kaman prediction:

Sˆ((ki )+1 k ) = Ψ ( i ) Sˆ((ki )k −1) + K ( i )Yk(i )

WANG Guolin et al. / J Transpn Sys Eng & IT, 2010, 10(4), 27−32

with Ψ ( i ) = Φ − K ( i )C T K (i )

⎡ CT ⎤ ⎢ ⎥ = ⎢ CT Φ ⎥ ⎢C T Φ 2 ⎥ ⎣ ⎦

+

⎡ M 1( i ) ⎤ ⎢ (i ) ⎥ ⎢M 2 ⎥ ⎢ M 3( i ) ⎥ ⎣ ⎦

where X+ represents pseudo-inverse of X. M (ji ) = − A1(i ) M (ji−)1 − " − A(j i−)1M 1(i ) + D (j i ) A(j i ) and B (j i ) can be calculated by executing a left-fraction

decomposition of C T ( I − z −1Φ)−1 Γz −1 which can be written as follows:

C T ( I − z −1Φ)−1 Γz −1 = ( A(i ) ( z −1 ))−1 B (i ) ( z −1 ) Meanwhile A(i ) ( z −1 ) and B (i ) ( z −1 ) can be expressed in the format as follows: −1

X (z ) = X (i )

(i ) 0

−1

(i ) − n n

the speed of the ROI where the pixel belongs to. If the detection velocity v is higher than 20 km/h, the sampling data of the pixel is valid. Otherwise, it can be considered as an invalid sampling value. The algorithm is as follows: (i) For a new sampling pixel at time t+kT0, if the new sample is satisfied with the following criterion: v(t + kT0 ) ≥ 20, k ≥ 2, k ∈ N (criterion 2) then, the pixel value in the ROI region is treated as a valid sampling value. Let t=t+kT0, k=0. And then skip to Step 3. If the criterion (2) is not satisfied, then continue. (ii) If the following criterion (3) is satisfied, then it is a valid sample value. Let t=t+kT0, k=1. Then skip to Step (iii). If the criterion (3) is not satisfied, then continue. 1 cT0

+ X z +" + X z (i ) 1

where A0(i ) = I , B0(i ) = 0 . D (i ) ( z −1 ) has similar format as A(i ) ( z −1 ) . D (i ) ( z −1 ) can be obtained by the equation as follows based on the Gevers-Wouters algorithm: A(i ) ( z −1 )Yk( i ) = D (i ) ( z −1 )ε k(i ) where ε k(i ) is independent zero-mean Gaussian distributed white noise with covariance Qεi Self-tuning smoother of the i-th is as follows: N

k

∑ d (t + iT ) ≥ 20 i =1

0

(criterion 3)

where c is a constant and represents the ratio between the real moving distance and the pixel distance in video. (iii) Let k=k+1, loop from step 1 until criterion (2) or (3) is satisfied. Therefore, the sampling frequency of a given ROI is defined as follows: ⎧ f f =⎨ 0 ⎩ f0 / k

v ≥ 20 v < 20

Sˆ((ki )− N k ) = Sˆ((ki )− N k − N −1) + ∑ K (ji )ε (i ) (k − N + j )

4

ε (i ) (k ) = A(i ) ( z −1 )Yk(i ) − D1( i )ε (i ) (k − 1) − "

An experiment based on a section of intersection surveillance video in Beijing is used to verify the validity of the proposed method in this paper. The picture size is 320×240 and the sum of frames is 3200 with fps=10. The traffic video surveillance range includes two overpasses and a crossroad. The experimental results are obtained based on a mixture Gaussian-based method and the method discussed in this paper, respectively, which are shown in Fig. 2. One of the sampling frames is shown in Fig. 2(a), in which the black lines represent the virtual detective lines set in advance. The velocity of vehicles detected by buried loops is provided by Beijing Traffic Management Bureau. By comparing Figs. 2(b) and 2(c), it can be found that the overpass regions in the constructed backgrounds acquired by a mixture of the Gaussian method and the proposed method respectively are quite precise because the speed of vehicles is quite high and there are no existing queue vehicles on the overpass. However, the crossroad region in Fig. 2(b) is not good enough because several queue vehicles are brought into the constructed background. This is caused by uniform sampling. On the contrary, a relatively satisfactory effect is achieved in the crossroad region in Fig. 2(c) because the region is very “clear”. This is resulted from two reasons. First of all, the nonuniform sampling frequencies according to the criterions proposed in Section 3.3 assure the reliability of sampling data. The sampling time interval of queue region is

Experimental results and analysis

j =0

− Dn(di )1 ε ( i ) (k − nd 1 ) K (j i ) = Σ (ji ) (k )(Ψ (i ) )T CQε−i1

Σ (ji ) = Ψ ( i ) Σ (ji−)1 (Ψ (i ) )T + ΓQΓT + K i R ( K i )T 3.3 Setting criterion of ROI sampling frequencies To obtain a more accurate sampling data and avoid bringing the stationary or slow moving vehicles into the background, different sampling frequencies are given for different regions of the ROI. The sampling frequencies are determined by the velocity of vehicles acquired according to the method described in Section 3.2. For vehicle speed lower than 20 km/h is considered traffic congest in traffic management, 20 km/h is selected as a threshold to determine the sampling frequencies of the ROI. According to Section 3.2, the selection of velocity of vehicles depends on the phase of traffic signal lights. When light is in green phase, the velocity is as follows: , d = dˆ v = vˆ k−N k

k −N k

otherwise,

v = vˆk k , d = dˆk k First, assuming that a uniform sampling frequency is f0, and the current sampling time of a pixel in a given ROI region is t. The sampling time interval is T0=1/f0. Whether the data of the pixel at time t+T0 is considered as a valid sample depends on

WANG Guolin et al. / J Transpn Sys Eng & IT, 2010, 10(4), 27−32

Gaussian Mixture Method. The parameters are set as below: a=0.01, Td=0.8. The proposed algorithm proposed in this paper has a faster convergence speed and a better track ability to the change of the background by comparing Fig. 3(b) and Fig. 3(c), which is also accordance with the analysis in Fig. 2. This proves the validity of proposed method.

(a)

(a)

(b)

(b)

(c) Fig. 2 Constructed background based on different methods (a: A sampling frame and the position of detective lines; b: constructed background based on Mixture Gaussian Method; c: constructed background based on proposed method)

extended. Second, the velocity of detected vehicles are quite accurate based on multisensors fusion method. The two reasons together are avoided effectively to bring the queue vehicles into background. To illustrate the convergence speed of proposed algorithm, the convergence speed for construct background pixel in coordinate position [217, 200] is analyzed in Fig. 3. The temporal distribution of 900 sampling points is shown in Fig. 3(a). The convergence track of proposed method is shown in Fig. 3(b). The convergence track in Fig. 3(c) is based on

(c) Fig. 3 Convergence speed analysis of constructed background by different methods (a: temporal distribution of 900 sampling points; b: Convergence track of proposed method a=0.01, Td =0.8; Convergence track of Guassian Mixture Model Method a=0.01, Td =0.8)

WANG Guolin et al. / J Transpn Sys Eng & IT, 2010, 10(4), 27−32

5

Conclusions

This paper presents a novel complex traffic background updating method based on sensors fusion. The accuracy of background modeling is improved based on the expectation-maximization (EM) algorithm. Meanwhile, to increase the liability of sampling data, the idea that the sampling frequencies of the ROI are determined by the speed of the ROI is adopted. The disturbance cased by queue vehicles is decreased a lot according to the proposed method. The detection accuracy of vehicle velocity is increased by multisensors consisting of loop and virtual detective line fusion algorithm. The experimental results have shown the effectiveness of the proposed method. The future work includes how to determine the threshold of the virtual detective line according to the data obtained by the loop and further improve the accuracy and adaptive capacity of the proposed video-based method.

Acknowledgments

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