本論文中，我們提出了一種改良式粒子群演算法，名為單維搜索分工式粒子群演算法(Particle swarm optimization with one dimension multi-modes, ODMPSO)，並應用ODMPSO演算法於影像追蹤系統。標準粒子群演算法中每一個體使用相同的移動方程式，而本文所提的方法，能使粒子根據其位置狀態選擇其移動方程式進行位置的更新。在粒子群最佳化初期，透過特殊的單維搜索機制，讓粒子可以更有效的從局部探索開始，逐漸演化，等到集中收斂至一階段後，再使用分群機制，根據其粒子位置分別置入數個子群中，在子群中的粒子根據其對應的四種模式進行速度更新，以求迅速的把其它個體帶往全域最佳解。本文並利用ODMPSO演算法提升影像追蹤系統上的效能，獲取更好的辨識率與更快的迭代速度。由於我們得知在傳統的高斯混合模型背景相減法(Gaussian mixture model background subtraction)裡，所使用的迭代方式是使用期望值最大化演算法(Expectation Maximization , EM)，而此方法在進行迭代時，緩慢的收斂速度，往往影響了即時的影像辨識系統之實用性，所以本文採取ODMPSO演算法來提升收斂速度，以防止耗費大量的運算，減少系統的運算的複雜度。從實驗結果證實，所提出的ODMPSO可以得到較佳的平均值(Mean)、標準差(Standard deviation)與辨識率，並且能大幅地提升系統的收斂速度，所以證實所提出的演算法的確能有效地增進影像追蹤系統的實用性。

In this thesis, we propose a modified particle swarm optimization algorithm which is called particle swarm optimization with one dimension multi-modes (ODMPSO). The proposed ODMPSO which is different from standard PSO algorithm is moving functions. In ODMPSO method, the particles can be adaptively searched by their environment. There are five modes in ODMPSO method. Each mode has its own specific optimizations. Finally, these modes makes the particles more easily and quickly find the results. Afterwards, we propose a Gaussian mixture model based on ODMPSO (GMM-ODMPSO) method in a visual tracking system. The GMM-ODMPSO method will accelerate the convergence rate of creating the GMM background model and the system also improves the detection of moving targets. The experimental results show that the proposed GMM background model obtains better recognition rate. As seen in the experiments, the GMM-ODMPSO method is a 48% improvement over the computing time, 88% over the convergence rate, and the recognition rate is almost the same as the traditional GMM background model. In the results, we can see our proposed method is more effective.

[1] W. Brand, “Morphable 3D models from video,” in Proc. Of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Vol. 2, pp. 456-463, 2001.
[2] N. Weng, Y. H. Yang, and R. Pierson, “3D surface reconstruction using optical flow for medical imaging,” in Proc. Of the 1996 IEEE Conference on Nuclear Science Symposium, Vol. 3, pp. 1845-1849, 1996.
[3] J. F. Cohn, A. J. Zlochower, J. J. Lien and T. Kanade, “feature-point tracking by optical flow discriminates subtle differences in facial expression,” in Proc. Of the 3^th international Conference on Automatic Face and Gesture Recognition, pp. 396-401, 1998.
[4] A. J. Lipton, “Local application of optic flow to analyze rigid versus non-rigid motion,” Technical Report, CMU-RI-TR-99-13, Robotics Institute, Carnegie Mellon University, 1999.
[5] J. L. Barron, D. J. Fleet, S. S. Beauchemin and T. A. Burkitt, “Performance of Optical Flow Techniques,” in Proc. of the 1992 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp. 236-242, 1992.
[6] W. Hu, T. Tan, L. Wang and S. Maybank, “A survey on visual surveillance of object motion and behaviors,” IEEE Trans on System, Man and Cybernetics, Vol.34,pp. 334-352,2004.
[7] M. Irani, and P. Anandan, “Video Indexing Based on Mosaic Representations,” Proceedings of IEEE, Vol. 86, No. 5, pp. 905-921, May 1998.
[8] Elgammal, R. Duraiswami, D. Harwood, and L. S. Davis, “Background and foreground modeling using nonparametric kernel density estimation for visual surveillance,” Proceedings of IEEE, Vol. 90, No. 7,pp. 1151-1163, July 2002.
[9] J. M. McHugh, J. Konrad, V. Saligrama, P. M. Jodoin, “Foreground-Adaptive Background Subtraction,” IEEE Signal Processing Letters, Vol. 16, No. 5, pp. 390-393, May 2009.
[10] T. M. Chen, R. C. Lou and T. H. Hsiao, “Visual tracking using adaptive color histogram model,” in Proc. of the 25th IEEE Annual Conference on Industrial Electronics Society, Vol. 3,pp. 1336-1341, 1999.
[11] C. Stauffer, W Grimson, “Adaptive Background Mixture Models for Real-time Tracking,” IEEE computer Society conference on computer Vision and Pattern Recognition, Vol. 2, pp. 246-252, 1999.
[12] T. Moeslunda, A. Hiltonb, and V. Krugerc, “A survey of advances in vision-based human motion capture and analysis,” Comput. Vision Image Understanding, Vol. 104, pp. 90–126, Nov. 2006.
[13] A.J. Lipton, C. H. Heartwell, N. Haering, and D. Madden, “Automated video protection, monitoring and detection,” IEEE Aerospace and Electronic Systems Magazine, Vol. 18, pp. 3-18, May 2003.
[14] S. Nadimi and B. Bhanu, “Physical Models for Moving Shadow and Object Detection in Video,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 26, pp. 1079-1087, 2004.
[15] 王俊凱，基於改良式適應性背景相減法與多重影像特徵比對法之多功能即時視覺追蹤系統之設計與實現，成功大學碩士論文，2004。
[16] 賴俊良，移動目標物視覺偵測與追蹤研究，成功大學碩士論文，2006
[17] 鐘承君，統計式背景模型應用於視覺監視之研究，成功大學碩士論文，2008。
[18] J. Kennedy, and R. C. Eberhart. “Particle swarm optimization,”. Proceedings IEEE International Conference on Neural Networks,1995 ，Vol. 4 , pp. 1942 – 1948.
[19] K. Premalatha, A.M. Natarajan. “Hybrid PSO and GA for Global Maximization,”. Int. J. Open Problems Compt. Math., 2009 , Vol. 2 , pp. 597 – 608.
[20] Y. Shi and R.C. Eberhart. “Parameter selection in particle swarm optimization,”. in Proc. 7th Int. Conf. Evol. Program., 1998 , Vol. 1447 , pp. 591 – 600.
[21] F. van den Bergh, A. P.E, “A New Locally Convergent Particle Swarm Optimizer” ngelbrecht Department of Computer Science University of Pretoria Pretoria, South Africa
[22] Riaan Brits, Niching strategies for particle swarm optimization
[23] R. Salomon. “Reevaluating genetic algorithm performance under coordinate rotation of benchmark functions,”. BioSystems, 1996 , pp. 263 – 278.
[24] M. Pant, T. Radha, V.P.Singh. “A new particle swarm optimization with quadratic interpolation,” In Proceedings of IEEE International Conference on Computational Intelligence and Multimedia Applications,2007 , Vol. 1 , pp. 55 – 60.
[25] Y. -L. Zheng, L. -H. Ma, L. -Y. Zhang et al. “Empirical study of particle swarm optimizer with an increasing inertia weight”. in Proc. IEEE Congr. Evol. Comput, 2003 , Vol. 1 , pp. 221 – 226.
[26] K.E. Parsopoulos , M.N. Vrahatis. “UPSO: a unified particle swarm scheme,”. In Lecture series on Computer and Computational Sciences, 2004 , pp. 868 – 873.
[27] R. Mendes, J. Kennedy , J. Neves. “The fully informed particle swarm: simpler, maybe better,” IEEE Transactions on Evolutionary Computation, 2004 , Vol. 8 , pp. 204–210.
[28] J.J. Liang , P.N. Suganthan. “Dynamic multi-swarm particle swarm optimizer,” In Proceedings of IEEE on Swarm Intelligence Symposium, 2005 , pp. 124 – 129.
[29] M. Pant, T. Radha, and V. P. Singh, “A new particle swarm optimization whit quadeatic interpolation,” In Proceedings of IEEE International Conference on Computational Intelligence and Multimedia Applications, 2007, pp. 55 – 60
[30] J. Kennedy, and R.C. Eberhart. “A discrete binary version of the particle swarm algorithm,”. IEEE International Conference on Systems, 1997 , Vol. 5 , pp. 4104 – 4108.
[31] Y. Shi, and R. C. Eberhart. “Fuzzy adaptive particle swarm optimization,”. Proceeding of the 2001 Congress on Evolutionary Computation, 2001 , Vol. 1 , pp. 101 – 106.
[32] 李憲昌，維度經驗重心分享粒子群演算法，中央大學碩士論文，2012。
[33] 李宗勳，改良式粒子群方法之無失真影像預測編碼應用，中央大學碩士論文，2012。
[34] 吳讚展，自調性非線性權重粒子群演算法，中央大學碩士論文，2011。
[35] 陳弘毅，敏捷移動粒子群最佳化方法，中央大學碩士論文，2011。
[36]Y. Shi and R.C. Eberhart, “A modified particle swarm optimizer,”. in Proc. IEEE Int. Conf. Evol. Comput, 1998, pp. 69 – 73.
[37] Y. Shi and R.C. Eberhart . “Empirical study of particle swarm optimization,”. in Proc. IEEE Congr. Evol. Comput, 1999, Vol. 3 , pp. 1945 – 1950.
[38] Y. -L. Zheng, L. -H. Ma, L. -Y. Zhang et al. “On the convergence analysis and parameter selection in particle swarm optimization,”. in Proc. IEEE Int. Conf. Mach. Learning Cybern, 2003 , Vol. 3 , pp. 1802 – 1807.
[39] J.J. Liang , A.K. Qin , P.N Suganthan and S. Baskar. “Comprehensive Learning Particle Swarm Optimizer for Global Optimization of Multimodal Functions,”. IEEE Transactions on Evolutionary Computation, 2006 , Vol. 10 , pp. 281 – 296.
[40] R.Brits, A.P. Engelbrecht, F. van den Bergh, “A niching particle swarm optimizer,” Department of Computer Science, University of Pretoria, Pretoria, South Africa
[41] C. Stauffer and W. E. L. Grimson, “Adaptive background mixture models for real-time tracking” in Proceeding of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp. 246-252, 1999.
[42] Z. Zivkovic and F. van der Heijden, “Recursive unsupervised learning of finite mixture models,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 26, pp. 651-656, 2001.
[43] K. Toyama, J. Krumm, B. Brumitt, and B. Meyers, “Wallflower: principles and practice of background maintenance,” in Proceedings of the IEEE International Conference on Computer Vision. pp. 255 –261, 1999.