1. Ehsan Nateghinia Hadi Moradi (University of Tehran, Tehran, Iran) Video-Based Multiple Vehicle Tracking at Intersections

2. Introduction Proposed Method Foreground Detection Vehicle Tracking Experiments Conclusions 2

3. Introduction Proposed Method Foreground Detection Vehicle Tracking Experiments Conclusions 3

4. Propose a method to track multiple vehicles in a video stream of an intersection. Two issues: Detection to track assignment problem Occlusion handling Two methods: Global nearest neighbor(Munkres algorithm) Partitioning template matching 4

5. Introduction Proposed Method Foreground Detection Vehicle Tracking Experiments Conclusions 5

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9. Gaussian average background subtraction method + local binary pattern technique 1) Running Gaussian Average - Background Modeling [10] fist we estimate the background model using the mean of initial M frames. For next video frames a foreground detection is made by By using running Gaussian average, many environmental dynamic textures such as leaves movement, camera jitter and noisy pixel may reduce the accuracy of object detection. 9 [10] C. R. Wren, A. Azarbayejani, T. Darrell, and A. P. Pentland, “Pfinder: real-time tracking of the human body,” IEEE Trans. Pattern Anal. Mach.Intell., vol. 19, no. 7, pp. 780–785, Jul. 1997.

10. Hence, we need a dynamical texture modeling method to remove these effects 2) Modified Local Binary Pattern (MLBP) 10

11. Combination of Running Gaussian Average and Local Binary Pattern 11

12. For any object in scene, a distance function between camera point and central position of object is calculated as following: Those objects that satisfy the following condition will keep remain in the scene; otherwise they will be removed. 12

13. In this study, we have implemented point prediction and template matching simultaneously. 1) Data Association The main phase of usual data association is to find a correct relationship between two point sets: Observation set (Z), and prediction set (X). Measurement gate is defined as follow [13]: 13 [13] Y. Bar-Shalom, F. Daum, and J. Huang, “The probabilistic data association filter,” IEEE Control Syst., vol. 29, no. 6, pp. 82–100, Dec.2009.

14. In order to obtain multiple object tracking, we used GNN. This algorithm has two steps. First, the assignment matrix A, is calculated as: The purpose of GNN is to solve the linear assignment problem. In this paper, we use the Munkres algorithm, which is proposed in [15], 14 [15] J. Munkres, “Algorithms for the Assignment and Transportation Problems,” J. Soc. Ind. Appl. Math., vol. 5, no. 1, pp. 32–38, Mar. 1957.

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20. 20 [17] K. Briechle and U. D. Hanebeck, “Template matching using fast normalized cross correlation,” 2001, vol. 4387, pp. 95–102.

21. 21 [16] R. Brunelli, Template Matching Techniques in Computer Vision: Theory and Practice. Wiley Publishing, 2009. [17] K. Briechle and U. D. Hanebeck, “Template matching using fast normalized cross correlation,” 2001, vol. 4387, pp. 95–102. [18] A. J. H. Hii, C. E. Hann, J. G. Chase, and E. E. W. Van Houten, “Fast normalized cross correlation for motion tracking using basis functions,” Comput. Methods Programs Biomed., vol. 82, no. 2, pp. 144–156, May 2006.

22. When the most part of interest pattern in a new frame is hidden by other object, FNCC can fail. To solve the occlusion, we partitioned template into 8 new templates, and then 9 FNCC step is calculated for this templates. 22

23. 3) Recursive Point Prediction The main idea of point tracking is to identify the trajectory of moving vehicle in the scene. The goal of the prediction models is to estimate next X-Y position according to current frame. Weighted Recursive Least Square (WRLS) is used as the point prediction tool.[19] The formulation of the X-coordinate predictor can be formulated as follows: 23 [19] M. C. Campi, “Exponentially weighted least squares identification of time-varying systems with white disturbances, ” IEEE Trans. Signal Process., vol. 42, no. 11, pp. 2906–2914, Nov. 1994.

24. At the next step, covariance matrix estimation is done using: Then position covariance at frame t + 1 is calculated as follow: Now the posterior estimation of x is calculated as: 24

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26. Introduction Proposed Method Foreground Detection Vehicle Tracking Experiments Conclusions 26

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29. 29 (a), (b) are template images of vehicles without occlusion. (c) is search space image. Templates are correctly found in (d).

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31. Introduction Proposed Method Foreground Detection Vehicle Tracking Experiments Conclusions 31

32. We developed and implemented a multiple vehicle tracking system. Foreground mask is obtained from a combination rule of statistical background model and dynamic texture model. Afterward, a detection to tracks assignment is solved by Munkres algorithm. At the next step a point tracking algorithm is used to build a model for a vehicle’s trajectory. 32