本論文探討粒子群聚最佳化演算法在碎形影像壓縮及主動輪廓模型上的應用。此論文共分為兩部份：第一部分的研究是有關碎形影像壓縮，而第二部分的研究是有關主動輪廓模型。碎形影像壓縮不論在理論上或實務上都是一個具有前瞻性的影像壓縮方法。但因為傳統徹底搜尋法之碎形影像壓縮的編碼速率太慢，使得它無法運用於即時的工作上。本論文提出多個基於粒子群聚最佳化演算法來加速編碼流程的方法。這些方法結合了影像區塊的邊緣特性，並能維持不錯的重建影像品質。此方法大量降低了傳統徹底搜尋法之龐大運算量，且會根據影像區塊的邊緣性質建立一個導引粒子的走向地圖，使得在群聚中的粒子能被導引至更合適的影像區塊，而這些區塊在做完線性轉換後將更有機會具有較高的相似度。因此除了避掉多數無效的搜尋以達到加速的效果外，同時因整個策略是根據影像邊緣的性質來完成，此演算法將能保留更好的視覺效果。以 Lena 影像為例，本方法的壓縮速度比傳統徹底搜尋法快了 125 倍，且在影像品質的表現上只減少了 0.89 分貝。
在論文的第二部分中，我們探討主動輪廓模型在物件邊界自動鑑別的運用。在傳統的主動輪廓模型方法上，每個控制點只能在一個小小的鄰近區域中尋找它的下一個新位置，因此無法精準地朝向影像物件邊界上的凹面收斂。在過去，許多文獻提出方法來改善這個問題，但多數還是耗時的。為了解決這個缺陷，本論文提出一個新穎的多群體粒子群聚最佳化演算法來加強主動輪廓模型搜尋邊界凹面的能力，使得主動輪廓模型能搜尋較大的區域，並只花費少許的時間。在這樣的方法架構中，主動輪廓模型內的每一個控制點都各有一個粒子群來最佳化它的下一個新位置，因此控制點的位置會隨著最佳群體粒子的位置而演化，直到所有控制點組成的主動輪廓模型不再變動且收斂在影像物件的邊緣上。這樣的一個最佳化合作機制不只可以在群體與群體之中交換資訊，並且繼承了原本粒子群聚最佳化既有的精神。實驗結果顯示，此研究所提出的方法可以順利地找到影像物件的凹面且不花費額外的時間。

In this dissertation, particle swarm optimization (PSO) is utilized for fractal image compression (FIC) and active contour model (ACM). The dissertation is divided into two parts. The first part is concerned with the FIC and the second part with ACM. FIC is promising both theoretically and practically for image compression. However, since the encoding speed of the traditional full search method is very time-consuming, FIC with full search is unsuitable for real-time applications. In this dissertation, several novel PSO-based approaches incorporating the edge property of the image blocks are proposed to speedup the encoder and preserve the image quality. Instead of the full search, a direction map is built according to the edge type of the image blocks, which directs the particles in the swarm to regions consisting of candidates of higher similarity. Therefore, the searching space is reduced and the speedup can be achieved. Also, since the strategy is performed according to the edge property, better visual effect can be preserved. Experimental results show that the visual-based particle swarm optimization speeds up the encoder 125 times faster with only 0.89 dB decay of image quality in comparison to the full search method.
The second part of the dissertation is concerned with the active contour model for automatic object boundary identification. In the traditional methods for ACM, each control point searches its new position in a small nearby window. Consequently, the boundary concavities cannot be searched accurately. Some improvements have been made in the past to enlarge the searching space, yet they are still time-consuming. To overcome these drawbacks, a novel multi-population PSO technique is adopted in this dissertation to enhance the concavity searching capability and reduce the search time but in a larger searching window. In the proposed scheme, to each control point in the contour there is a corresponding swarm of particles with the best swarm particle as the new control point. The proposed optimizer not only inherits the spirit of the original PSO in each swarm but also shares information of the surrounding swarms. Experimental results demonstrate that the proposed method can improve the search of object concavities without extra computation time.

致謝 i
摘要 ii
ABSTRACT iii
LIST OF FIGURES v
LIST OF TABLES vii
GLOSSARY OF SYMBOLS viii
LIST OF ABBREVIATIONS ix
CHAPTER 1 INTRODUCTION.. 1
1.1 Motivation... 1
1.2 Brief Sketch of the Contents... 4
CHAPTER 2 PARTICLE SWARM OPTIMIZATION 6
2.1 Overview 6
2.2 Basic Concepts... 8
CHAPTER 3 FRACTAL IMAGE COMPRESSION. 11
3.1 Preliminaries 11
3.2 Implementation. 13
3.3 Existing Methods.. 17
CHAPTER 4 PARTICLE SWARM OPTIMIZATION FOR FRACTAL IMAGE
COMPRESSION.... 18
4.1 PSO for FIC.. 18
4.2 Experimental Results 20
CHAPTER 5 VISUAL-BASED PARTICLE SWARM OPTIMIZATION FOR
FRACTAL IMAGE COMPRESSION.... 24
5.1 Edge-type Classifier.. 24
5.2 Visual-based PSO for FIC. 27
5.3 Experimental Results 34
CHAPTER 6 ACTIVE CONTOUR MODEL... 41
6.1 Primal Method.. 42
6.2 Drawbacks and Remedies. 45
CHAPTER 7 MULTI-POPULATION PARTICLE SWARM OPTIMIZATION
FOR ACTIVE CONTOUR MODEL.. 46
7.1 Multi-population PSO for ACM... 46
7.2 Experimental Results 49
CHAPTER 8 CONCLUSIONS AND DISCUSSIONS. 54
REFERENCES.. 58

[Bar.1] Barnsley, M. F., Fractal everywhere. Academic Press, California, 1988.
[Bar.2] Barnsley, M. F. and Demko, S., Iterated function systems and the global construction of fractals. Royal Society of London, A399, pp. 243-275, 1985.
[Bar.3] Barnsley, M. F., Elton, J. H., and Hard, D. P., Recurrent iterated function systems. Constructive Approximation, pp. 3-31, 1989.
[Chen.1] Chen, D. R., Chang, R. F., Chen, C. J., Ho, M. F., Kuo, S. J., Chen, S. T., Hung, S. J., and Woo, K. M., Classification of breast ultrasound images using fractal feature. Clinical Imaging, 29 (4), pp. 235-245, 2005.
[Coh.1] Cohen, L. D., On active contour models and balloons. in CVGIP: Image Understanding, 53 (2), pp. 211-218, 1991.
[Cri.1] Crilly, J., Earnshaw, R. A., and Jones, H., Fractals and chaos. Springer-Verlag, New York, 1991.
[Dis.1] Distasi, R., Nappi, M., and Riccio, D., A range/domain approximation error-based approach for fractal image compression. IEEE Transactions on Image Processing, 15 (1), pp. 89-97, 2006.
[Ebe.1] Eberhart, R. C. and Kennedy, J., A new optimizer using particle swarm theory. Proceedings IEEE International Symposium on Micro Machine and Human Science, Nagoya, Japan, pp. 39-43, 1995.
[Ebe.2] Eberhart, R. C. and Shi, Y. H., Particle swarm optimization: developments, applications and resources. Proceedings IEEE International Congress on Evolutionary Computation, Seoul, Korea, 1, pp. 81-86, 2001.
[Ebe.3] Eberhart, R. C. and Shi, Y., Evolving artificial neural networks. Proceedings 1998 International Conference on Neural Networks and Brain, Beijing, P.R.C., Pl5-PL13, 1998.
[Ebe.4] Eberhart, R. C. and Hu, X., Human tremor analysis using particle swarm optimization. Proceedings Congress on Evolutionary Computation 1999, Washington, DC, pp 1927-1930, 1999.
[Ebe.5] Eberhart, R. C., Simpson, P. K., and Dobbins, R. W., Computational intelligence PC tools. Academic Press Professional, Boston, 1996.
[Fis.1] Fisher, Y., Fractal image compression: theory and application. Springer-Verlag, Berlin, 1995.
[Fu.1] Fu, Y., Erdem, A. T., and Trkalp, A. M., Tracking visible boundary of objects using occlusion adaptive motion snake. IEEE Transactions on Image Processing, 9 (12), pp. 2051-2060, 2000.
[Gol.1] Goldberg, D. E., Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, Massachusetts, 1989.
[Hau.1] Haupt, R. L. and Haupt, S. E., Practical genetic algorithms. Wiley-Interscience, New York, 1998.
[Hol.1] Holland, J. H., Adaptation in natural and artificial systems. The University of Michigan Press, Michigan, 1975.
[Irr.1] Irrgang, R. and Irrgang, H., An intelligent snake growing algorithm for fuzzy shape detection. Expert Systems with Applications, 11 (4), pp. 531-536, 1996.
[Jac.1] Jacquin, A. E., Image coding based on a fractal theory of iterated contractive image transformations. IEEE Transactions on Image Processing, 1 (1), pp. 18-30, 1992.
[Jang.1] Jang, D. S. and Choi, H. I., Active models for tracking moving objects. Pattern Recognition, 33, pp. 1135-1146, 2000.
[Kass.1] Kass, M., Witkin, A., and Terzopoulos, D., Snake: active contour models. International Journal of Computer Vision, 1, pp. 321-332, 1988.
[Ken.1] Kennedy, J. and Eberhart, R. C., Particle swarm optimization. Proceedings IEEE International Conference on Neural Networks, Perth, Australia, 4, pp. 1942-1948, 1995.
[Kim.1] Kim, D. H., GA–PSO based vector control of indirect three phase induction motor. Applied Soft Computing, 7 (2), pp. 601-611, 2007.
[Lee.1] Lee, Z. J., A novel hybrid algorithm for function approximation. Expert Systems with Applications, 34(1), pp. 384-390, 2008.
[Li.1] Li, C. H. and Wang, S. S., Digital watermarking using fractal image coding. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, E83-A (6), pp. 1286-1288, 2000.
[Lin.1] Linnell, T. A. and Derari, F., Mapping vector accumulator: fractal domain feature for character recognition. Electronics Letters, 40 (22), pp. 1406-1407, 2004.
[Mai.1] Maitra, M. and Chatterjee, A., A hybrid cooperative-comprehensive learning based PSO algorithm for image segmentation using multilevel thresholding. Expert Systems with Applications, 34 (2), pp. 1341-1350, 2008.
[Mci.1] McInerney, T. and Terzopoulos, D., Deformable models in medical image analysis: a survey. Medical Image Analysis, 1, pp. 91-108, 1996.
[Mci.2] McInerney, T. and Terzopoulos, D., Topologically adaptable snake. International Conference on Computer Vision (ICCV’95), pp. 840-845, 1995.
[Mci.3] McInerney, T. and Terzopoulos, D., Topologically adaptable deformable surfaces for medical image volume segmentation. IEEE Transactions on Medical Imaging, 18 (10), pp. 840-845, 1999.
[Mit.1] Mitra, S. K., Murthy, C.A., and Kundu, M.K., Technique for fractal image compression using genetic algorithm. IEEE Transactions on Image Processing, 4 (7), pp. 586-593, 1998.
[Park.1] Park, H., Schoepflin, T., and Kim, Y., Active contour model with gradient directional information: directional snake. IEEE Transactions on Circuits and Systems for Video Technology, 11 (2), pp. 252-256, 2001.
[Park.2] Park, J. and Keller, J. M., Snake on the watershed. IEEE Transactions on Pattern Analysis and Machine Intelligence, 23 (10), pp. 1201-1205, 2001.
[Pei.1] Peitgen, H. O., Henriques, J. M., and Penedo, L. F., Fractals in the fundamental and applied sciences. Elsevier Science Publishing Company Inc., New York, 1991.
[Seo.1] Seo, K. H., Kim, W., On, C., and Lee, J. J., Face detection and facial extraction using color snake. IEEE Transactions Symposium on Industrial Electronics, L’A quila, Italy, 2, pp. 457-462, 2002.
[Ter.1] Terzopoulos, D. and Fleischer, K., Deformable models. The Visual Computer, 4 (6), pp. 306-331, 1988.
[Tru.1] Truong, T. K., Jeng, J. H., Reed, I. S., Lee, P. C., and Li, A. Q., A fast encoding algorithm for fractal image compression using the DCT inner product. IEEE Transactions on Image Processing, 9 (4), pp. 529-535, 2000.
[Tse.1] Tseng, C. C., Hsieh, J. G., and Jeng, J. H., Fractal image compression using visual-based particle swarm optimization. Image and Vision Computing, 26, pp. 1154-1162, 2008.
[Tse.2] Tseng, C. C., Hsieh, J. G., and Jeng, J. H., Active contour model via multi-population particle swarm optimization. Expert Systems with Applications, 42 (4), 2008, in press.
[Ven.1] Vences, L. and Rudomin, I., Genetic algorithms for fractal image and image sequence compression. Proceedings Computacion Visual, Universidad Nacional Autonoma de Mexico, pp. 35-44, 1997.
[Wang.1] Wang, C. T., Chen, T. S., and He, S. H., Detecting and restoring the tampered images based on iteration-free fractal compression. Journal of Systems and Software, 67 (2), pp. 131-140, 2003.
[Wang.2] Wang. Z., Zhang. D., and Yu, Y. L., Hybrid image coding based on partial fractal mapping. Signal Processing: Image Communication, 15, pp. 767-779, 2000.
[Wong.1] Wong, Y. Y., Yuen, P. C., and Tong, C. S., Segmented snake for contour detection. Pattern Recognition, 31, pp. 1669-1679, 1998.
[Wu.1] Wu, M. S., Jeng, J. H., and Hsieh, J. G., Schema genetic algorithm for fractal image compression. Engineering Applications of Artificial Intelligence, 20, pp. 531-538, 2007.
[Wu.2] Wu, M. S., Teng, W. C., Jeng, J. H., and Hsieh, J. G., Spatial correlation genetic algorithm for fractal image compression. Chaos, Solitons & Fractals, 28 (2), pp. 497-510, 2006.
[Xu.1] Xu, C. and Prince, J. L., Snake, shapes, and gradient vector flow. IEEE Transactions on Image Processing, 7 (3), pp. 359-369, 1998.
[Yao.1] Yao, Z., Fixed point in fractal image compression as watermarking. International Conference on Image Processing (ICIP 2003), 2, pp. 475-478, 2003.
[Yos.1] Yoshida, H., Kawata, K., Fukuyama, Y., and Nakanishi, Y., A particle swarm optimization for reactive power and voltage control considering voltage stability. Proceedings International Conference on Intelligent System Application to Power Systems, Rio de Janeiro, Brazil, pp. 117-121, 1999.
[Zha.1] Zhang, C.K., Shao, H., and Li, Y., Particle swarm optimization for evolving artificial neural network. Proceedings IEEE International Conference on Systems, Man, and Cybernetics, Nashville, Tennessee, 4, pp. 2487-2490, 2000.