Since lane 2 and 3 have more large vehicles relative to lane 1 and 4, thus, only lane 2 and 3 are selected as our targets for the vehicle classification learning. There are totally 43 and 48 vehicles obtained in lane 2 and 3 respectively by using an
71
Figure 7.7: A lane change scenario of a small vehicle and its histogram of peak count.
It indicates that the lane-changing behavior of vehicle is also not proper to describe the lane boundary information.
detection algorithm, if the passed vehicles do not exhibit lane change behavior when passing through the detection area, and the reflected signals of motorcycles are also filtered out. If only small and large vehicles are considered, the accuracies of vehicles appearing in the corresponding lanes can achieve 95% above.
Figure 7.8 shows vehicle feature scatter diagrams in lane 2 and 3. For distin-guishing the different vehicle types’ features, the large vehicles are marked as black squares, and small vehicles are represented by dark gray rhombuses. Each of vehicle sample are described by two features, average energy maximum, and average energy variance shown in x-axis and y-axis of Figure 7.8 respectively. Notably, the scales of axes are different for drawing all of the vehicle samples within a fixed screen size.
Table 7.7 describes the estimated GMM parameters in lane 2 solved by EM algo-rithm and the results can be geometrically plotted in Figure 7.9. The large vehicles
(a)
(b)
Figure 7.8: (a) shows the scatter diagram in lane 2. (b) shows the scatter diagram in lane 3.
73
Table 7.7: GMM parameters for lane 2. The component with the smaller mean represents the small vehicles, and the component with the larger mean represents the large vehicles.
Component 1 Component 2 (Small vehicles) (Large vehicles)
Weight 0.72 0.28
Mean (137.13, 60.11) (277.08, 126.72)
Variance(x) 41.16 56.54
Variance(y) 17.99 28.89
Covariance(x, y) 25.05 33.04
Table 7.8: Compare learned results and real-world date for lane 2. The diagonal counts are vehicles that are classified correctly, and non-diagonal counts are erroneous results.
Small vehicles Large vehicles Learned results
Component 1 31 0 31
Component 2 5 7 12
In real-world 36 7 Accuracy : 88.37%
are marked as dark squares, and small vehicles are of gray squares. Each additional standard deviation, an oval is plotted. The last convergence value of maximum like-lihood is -10.17, and the learned proportion of large vehicles is around 0.28, while the real proportion of large vehicles is 0.16. The accuracy for lane 2 is (31+7) / 43
= 88.37% shown in Table 7.8, where accuracy is equal to that the vehicles classified correctly are divided by total vehicles.
Accuracy = vehicle are chosen correctly
total vehicle × 100%
Table 7.9 is the estimated GMM parameters in lane 3 solved by EM algorithm and such results also can be geometrically shown in Figure 7.10. The last convergence value of maximum likelihood is -8.14, and the learned proportion of large vehicles is around 0.23, whereas the actual proportion is 0.21. The gap between real and statistic
Table 7.9: GMM parameters for lane 3. The component with the smaller mean represents the small vehicles, and the component with the larger mean represents the large vehicles.
Component 1 Component 2 (Small vehicles) (Large vehicles)
Weight 0.77 0.23
Mean (92.3, 30.27) (158.48, 55.26)
Variance(x) 15.97 31.48
Variance(y) 6.56 7.92
Covariance(x, y) 6.45 14.84
Table 7.10: Compare learned results and real-world date for lane 3. The diagonal counts are vehicles that are classified correctly, and non-diagonal counts are erroneous results.
Small vehicles Large vehicles Learned results
Component 1 35 1 36
Component 2 3 9 12
In real-world 38 10 Accuracy : 91.67%
model is very close. The accuracy for lane 3 is (35+9) / 48 = 91.67% according to the results shown in Table 7.10.
75
Figure 7.9: The learned result of a two-dimensional GMM for lane 2.
Figure 7.10: The learned result of a two-dimensional GMM for lane 3.
Chapter 8 Conclusion
The proposed learning procedure for the road-side radar detector is illustrated in detail above, and utilizes span information to form a reliable set describing the ap-propriate lane width. Additionally, the idea of conflict information is derived from the span information without any external interventions, and the proposed variant of EM algorithm achieves the variance of Gaussian components based on the collected data.
Experimental results further indicate that passed vehicles except for motorcycle can be captured with over 95% accuracy, the accuracy can be further improved provided that the passed vehicles do not exhibit lane change behavior when passing through the detection area. This study avoids the ambiguous situation associated with the method mentioned in [11], and shows satisfying results of the proposed on-line traffic lane estimator.
Besides, this study proposes a real-time vehicle classifier applied to multi-lane environments, which introduces a two-dimensional Gaussian Mixed Model to form a learning model. A two-dimensional Gaussian Mixed Model utilizes a pair of features, maximal energy peak and maximal energy variance, extracted from the frequency-domain information of passed vehicles to form its learning samples, and integrates
77
an EM algorithm to enhance the accuracy. Field tests in the suburbs show that an accuracy of vehicle classification can attain above 88%, and present the results are better than all reviewable literatures on this field.
Bibliography
[1] Guillaume Leduc, “Road Traffic Data: Collection Methods and Applications,”
Working Papers on Energy, Transport and Climate Change N.1, 2008.
[2] P. T. Martin, Y. Feng, and X. Wang, “Detector Technology Evaluation,” Tech-nical Report , Utah Transportation Center, 2003.
[3] C. R. Bennett, A. Chamorro, C. Chen, H. de Solminihac, and G. W. Flintsch,
“Detector Technology Evaluation,” Data Collection Technologies for Road Man-agement, Version 1.0, East Asia Pacific Transport Unit, The World Bank, Wash-ington, D.C., April 2005.
[4] M. Schmidt, L. Giorgi, M. Chevreuil, S. Paulin, S. Turvey, and M. Hartmann,
“GALILEO: Impacts on road transport,” JRC-IPTS Technical Report EUR 21865, 2005.
[5] I. Urazghildiiev, R. Ragnarsson, P. Ridderstr¨om, A. Rydberg, E. ¨Ojefors, K. Wallin, P. Enochsson, M. Ericson, and G. L¨ofqvist, “Vehicle Classifica-tion Based on the Radar Measurement of Height Profiles,” IEEE Trans. Intell.
Transp. Syst., vol. 8, no. 2, pp. 245-253, 2007.
[6] M. Cherniakov, R.S.A Raja Abdullah, P. Jancovic, and M. Salous, “Forward Scattering Micro Sensor for Vehicle Classification,” IEEE Digital Object Identi-fier, pp. 184-189, 2005.
79
[7] J. Gajda, R. Sroka, M. Stencel, A. Wajda, and T. Zeglen, “A Vehicle Classifica-tion Based on Inductive Loop Detectors,” IEEE InstrumentaClassifica-tion and Measure-ment Technology Conference, 2001.
[8] S. Gupte, O. Masoud, R. F. K. Martin, and N. P. Papanikolopoulos, “Detec-tion and classifica“Detec-tion of vehicles,” IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, vol. 3, no. 1, pp. 37-47, Mar. 2002.
[9] D. Beymer, P. McLauchlan, B. Coifman, and J. Malik, “A real-time computer vision system for measure traffic parameters ,” In Proc. IEEE Conf. Comput.
Vis. Pattern Recog., pp. 496-501, 1997.
[10] G. L. Foresti, V. Murino, and C. Regazzoni, “Vehicle recognition and tracking from road image sequences,” IEEE Trans. Veh. Technol., vol. 48, no. 1, pp.
301-318, Jan. 1999.
[11] J. L. Waite, T. W. Karlinsey, and D. V. Arnold, Patent No. US 6556916 B2, Apr. 2003.
[12] D. M., Patent No. US2007016359 A1, Jan. 2007.
[13] H. Roe and G. S. Hobson, Improved discrimination of microwave vehicle profiles, In Proc. IEEE MTT-S Int. Microw. Symp. (1992), 717-720.
[14] S. J. Park, T. Y. Kim, S. M. Kang, and K. H. Koo, A Novel Signal Processing Technique for Vehicle Detection Radar, IEEE MTT-S Digest (2003), 607-610.
[15] B. P. Douglass, Real-Time UML, Addison-Wesley, ISBM: 0-201-32579-9, 1998.
[16] K. C. Tzuang, C. H. Chang, H. S. Wu, S. Wang, S. X. Lee, C. C. Chen, C. Y.
Hsu, K. H. Tsai, and J. Chen, “An X-Band CMOS Multifunction-Chip FMCW Radar,” Proc. of the 2006 IEEE MTT-S Int. Microwave Symp. Dig., San Fran-cisco, CA, pp. 2011 2014, Jun. 2006.
81
[17] S. C. Chen, M. L. Shyu, S. Peeta, and C. Zhang, “Learning-Based Spatio-Temporal Vehicle Tracking and Indexing for Transportation Multimedia Database Systems”, IEEE Transations on Intelligent Transportation Systems, vol. 4, no. 3, pp. 154-167, Sep. 2003.
[18] Chengcui Zhang, Xin Chen, and Wei-bang Chen, “A PCA-based Vehicle Classi-fication Framework”, Proceedings of the 22nd International Conference on Data Engineering Workshops, vol. 4, no. 3, pp. 154-167, Sep. 2003.
[19] K. P. Karmann and A. von Brandt, “Moving object recognition using an adap-tive background memory”, in Proc. Time-Varying Image Processing and Moving Object Recognition, vol. 2, V. Capellini, Ed., 1990.
[20] Gian Luca Foresti, Vittor Murino, and Carlo Regazzoni, “Vehicle Recognition and Tracking from Road Image Sequences”, IEEE Transations on Vehicle Techi-nology, vol. 48, no. 1, January 1999.
[21] H. Amirmehrabi and R. Viswanathan, “A New Distributed Constant False Alarm Rate Detector”, Digital Object Identifier, vol. 33, no. 1, January 1997.
[22] A. De Maio, A. Farina, and G. Foglia, “Design and Experimental Validation of Knowledge-Based Constant False Alarm Rate Detectors”, Digital Object Identi-fier, vol. 1, no. 4, pp. 308-316, Aug. 2007.
[23] Mashrur A. Chowdbury and Adel Sadek, Fundamentals of Intelligent Transporta-tion Systems Planning, Artech House Publishers, ISBN: 1-58053-160-1, 2003.
[24] R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classification, 2nd ed., New York: Wiley, pp. 16-17, 2000.
[25] D. H. Fisher Jr, M. J. Pazzani, and P. Langley, Concept Formulation: Knowledge and Experience in Unsupervised Learning, Morgan Kaufmann Publishers, Inc., ISBN: 1-55860-201-1, 1991.
[26] Ethen Alpaydm, Introduction to Machine Learning, The MIT Press, ISBN: 0-262-01211-1, 2004.
[27] N. Shental, A. Bar-Hillel, T. Hertz, and D. Weinshell, “Computing Gaussian Mixture Models with EM using Equivalence Constraints,” Advances in neural information processing systems, MIT Press, pp. 465-472.
[28] K. Wagstaff and C. Cardie, “Clustering with Instance-level Constraints”, Pro-ceedings of the Seventeenth International Conference on Machine Learning, pp.
1103-1110, 2000.
[29] K. Wagstaff, C. Cardie, S. Rogers, and S. Schroedl, “Constrained K-means Clus-tering with Background Knowledge,” Proceedings of the Eighteenth International Conference on Machine Learning, pp. 577-584, 2001.
[30] D. Klein, S. D. Kamvar, and C. D. Manning, “From Instance-level Constraints to Space-level Constraints: Making the Most of Prior Knowledge in Data Cluster-ing,” In The Nineteenth International Conference on Machine Learning, 2002.
[31] J. Ma, T. Wang, and L. Xu, “A gradient BYY harmony learning rule on Gaussian mixture with automated model selection,” Neurocomputing, vol. 56, no. 1, pp.
481-487, 2004.
[32] Z. Lu, “An iterative algorithm for entropy regularized likelihood learning on Gaussian mixture with automatic model selection,” Neurocomputing, vol. 69, pp. 1674-1677, 2006.
[33] L. Li and J. Ma, “A BYY scale-incremental EM algorithm for Gaussian mixture learning,” Applied Mathematics and Computation, vol. 205, no. 2, pp. 832-840, 2008.
83
[34] F. Cardinaux, C. Sanderson, and S. Bengio, “User authentication via adapted statistical models of face images,” IEEE Digital Object Identifier, vol. 54, no. 1, pp. 361-373, 2006.
[35] Z. Zivkovic, “Improved Adaptive Gaussian Mixture Model for Background Sub-traction,” In Proceedings of the 17th International Conference on Pattern Recog-nition, pp. 28-31, 2004.
[36] Y. Wang, J. Yang, and Y. Zhou, “Color-texture segmentation using JSEG based on Gaussian mixture modeling,” Journal of Systems Engineering and Electronics, vol. 17, no. 1, pp. 24-29, 2006.
[37] D. A. Reynolds, T. F. Quatieri, and R. B. Dunn, “Speaker Verification Using Adapted Gaussian Mixture Models,” Digital Signal Processing, pp. 19-41, 2000.
[38] T. H. Dat, K. Takeda, and F. Itakura, “On-line Gaussian mixture modeling in the log-power domain for signal-to-noise ratio estimation and speech enhancement,”
Speech Communication, vol. 48, no. 11, pp. 1515-1527, 2006.
[39] M. H. Zhang and Q. S. Cheng, “Gaussian mixture modelling to detect random walks in capital markets,” Mathematical and Computer Modelling, pp. 503-508, 2003.
[40] J. Ju, E. D. Kolaczyk, and S. Gopal, “Gaussian mixture discriminant analysis and sub-pixel land cover characterization in remote sensing,” Remote Sensing of Environment, vol. 84, no. 4, pp. 550-560, 2003.
[41] I. Buckley, D. Saunders, and L. Seco, “Portfolio optimization when asset re-turns have the Gaussian mixture distribution,” European Journal of Operational Research, vol. 185, no. 3, pp. 1434-1461, 2008.
[42] K. E. Ahmad and A. M. Abd-Elrahman, “Updating a nonlinear discriminant function estimated from a mixture of two Weibull distributions,” Mathematical and Computer Modelling, vol. 19, no. 11, pp. 41-51, 1994.
[43] H.-j. Lee and S. Cho, “Combining Gaussian Mixture Models,” LNCS, pp. 666-671, 2004.
[44] J. D. Banfield and A. E. Raftery,“Model-based Gaussian and non-Gaussian clus-tering,” Biometrics, vol. 49, pp. 803-821, 1993.
[45] A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. R. Statist. Soc., ser. B, no. 39, pp.
1-38, 1977.