Nowadays traffic surveillance systems are widely used on highways and city roads. And the traditional manual surveillance watching cannot meet the needs of analyzing the huge amount of video data. Using the “intelligent” computer to discover the abnormal behavior in surveillance video becomes more important and gets more attention [1]-[3].

Recently, many scholars have done their own research works in this field. Zhao, Y.T., Li, X.Y. and Luo, D.H. [4] used the vehicle's tracking trajectory to separate the vehicles behavior into four elements: forward, backward, stop, left or right and then a vehicle behavior model is built based on them. Wang, W.G. and Ma, R. G. [5] proposed a weighed support vector machine (SVM) method based on the importance of the samples to solve the low detection problem caused by imbalanced samples. Liu, Q.C., Lu, J. and Chen, S.Y. [6] proposed a traffic incident detection method based on the random forest. Amin, M.S., Reaz, M. B. I. and Nasir, S. S. [7] proposed an incident detection and location method by fusing vehicle acceleration and GPS data.

To analysis abnormal vehicles behavior effectively, the whole process is divided into three steps in this paper: Firstly, a three-frame-differencing method and the improved tracking algorithm based on Kalman predictor are proposed to track vehicle. Then, an adaptive segmented linear fitting algorithm based on the least square method is proposed to achieve vehicle trajectory fitting which can reduce the amount of computation. Finally, two parameters including the rate of velocity variation and the rate of direction variation are used to establish vehicle abnormal behavior detection model. So the three highly dangerous vehicle behavior including sharp brake, sharp turn and sharp turn brake in surveillance video can be detected effectively.

Vehicle motion parameters will affect the detection of the abnormal vehicle behavior directly. The Kalman and the Camshift algorithm [8] can improve the tracking result, but it needs to initialize the search window manually and the computation is complex. Aiming at this shortage, we make a further improvement as below.

After target detection and tracking, analysis of tracking trajectory is necessary. The traditional fitting trajectory is curve-fitting, but it requires a large number of complex operations and the following process is more complex. Here, an adaptive segmented linear fitting method based on least square is adopted. According to the principle of overall minimum fitting error, the best segmentation fitting points are automatically determined, so the speed and accuracy can be improved. When the trajectory appears curvilinear, the linear fitting method can not be closely matched the trajectory. Therefore, the tracking points are grouped and fitted in each group, that is the idea of the segmented linear fitting.

The function of a line is, is the slope of the line, is ordinate at the origin.

Define error:

The ordered track point is divided into k group:

The overall fitting error is related to the number of groups and the value of segmentation point. Therefore, according to the principle of overall minimum fitting error, the value of and are automatically determined and the adaptive segmentation of the trajectory is realized.

Define overall fitting error:

when, are the best segmentation points for track points divided into groups.

Define difference of errors:

is the difference between the overall minimum fitting error of groups linear fitting and the overall minimum fitting error of groups linear fitting, if the difference is less than the setting error-threshold, This shows that the overall fitting error is relatively small when the track points divided into groups, and is the number of groups.

Usually, sharp brake, sharp turn, and sharp turn brake are dangerous events in driving [11]. The detection of abnormal vehicle behavior can control the transportation system effectively. Here, we pay more attention to the variation of velocity and direction in a short time, so these two parameters are used to establish abnormal vehicle behavior detection model.

Define the intersection point of two adjacent fitting lines as the inflection point of trajectory:

and are the parameters of linear fitting equation.

Define the rate of direction variation:

Define the rate of velocity variation:

is the inflection point of trajectory, is the Pixel distance of two inflection points, is the

time interval of two inflection points, D is the rate of direction variation at the inflection point, A is the rate of velocity variation at the inflection point.

When a vehicle brakes, the rate of velocity variation increases rapidly. When a vehicle takes a sharp turn, the rate of direction variation increases rapidly. when a vehicle takes a sharp turn brake, the rate of velocity variation and direction variation increase rapidly. Specifically as follows Table 1.

Test results are shown in Figures 3-5, the result of target tracking is (a), the result of linear fitting is (b), Figure 3 is two scenes of sharp brake, n is the number of inflection points that satisfy and which is bigger than the half of inflection points’ total number N, Figure 4 is two scenes of sharp turn, n is the number of inflection points that satisfy and which is bigger than the half of inflection points’ total number N, the Figure 5 is two scenes of sharp turn brake, n is the number of inflection points that satisfy

and which is bigger than the half of inflection points’ total number N. Based on many experiments, we set,.

Experiment result shows that the three high dangerous vehicle behaviors in the road surveillance videos can be detected effectively: sharp brake, sharp turn, and sharp turn brake.

In this paper, an abnormal vehicle behavior detection method based on trajectory fitting is proposed. Firstly, a three-frame-differencing method and the improved tracking algorithm based on Kalman predictor are proposed. Then, an adaptive segmented linear fitting algorithm based on the least square is proposed. Finally, two parameters including the rate of velocity variation and the rate of direction variation are adopted to establish abnormal

vehicle behavior detection model. Experiment result shows that the three high dangerous vehicle behaviors can be detected effectively: sharp brake, sharp turn, and sharp turn brake.

Enyuan Jiang,Xuejun Wang, (2015) Analysis of Abnormal Vehicle Behavior Based on Trajectory Fitting. Journal of Computer and Communications,03,13-18. doi: 10.4236/jcc.2015.311003