分水嶺轉換是一種在影像處理與分析領域中，經常被用作區域性影像切割的方法。分水嶺轉換的概念是基於：模擬大水逐漸淹沒一塊崎嶇不平的地形時，建築水壩防止湖泊合併的過程。本篇首先介紹基於上述概念所設計出來的分水嶺轉換演算法的類型，嚴謹地描述這些演算法的定義與流程，以及說明各種分水嶺轉換演算法可能遭遇的各種問題，並提出或整理解決這些問題的方法。
此外，本篇論文提出了兩個新穎的分水嶺轉換的相關方法。首先，在微小且低對比的目標物的偵測問題上，我們提出了一套有效去除雜訊的方法，並搭配適當的分水嶺演算法，能夠迅速並正確地在動態影像中，偵測到微小且低對比的目標物，並完整地萃取其外型輪廓。另外，我們還提出了一個使用分水嶺轉換來作資料分群和分類的方法，稱作「分水嶺分類法」。絕大多數有關分水嶺轉換的應用都是在影像相關的資料上，分水嶺分類法可對任何型態的資料進行分類的動作，並且不需要資料本身相關知識的介入，資料的分類方式透過決策區域來完成，而不須基於決策理論來進行分類，此點有別於傳統的分類演算法。分水嶺分類法分為非監督式和監督式兩種，監督式的分類法可用來強化非監督式的分類結果。
本篇內容介紹了以上所述的兩個分水嶺轉換的相關方法，並以實驗結果證明其可行性及適用性，最後針對這兩個方法作出總結並提出未來可以改進的方向。

Watershed transform is usually adopted for image segmentation in the area of image processing and image analysis. The concept of watershed transform is based on a processing simulating the immersion of a landscape in a lake that is dams have to be built to prevent the merging of different catchment basins. In this dissertation, the algorithms of watershed transform are firstly introduced. The definitions and procedures of watershed transform will also be thoroughly depicted. Problems that might occur in the watershed transform are addressed and solutions are proposed.
Two novel methods utilizing watershed transform are proposed in this dissertation. First, we proposed an effective noise removal method to resolve the problem of small object detection with low contrast. By integrating with an appropriate watershed algorithm, our proposed method can efficiently and effectively detect small objects with low contrast, and extract their complete contours. Moreover, we propose a method call “watershed classifier” for data clustering and classification using the watershed transform. Most watershed algorithms are utilized for image data, whereas the proposed watershed classifier is capable of classifying arbitrary data without prior knowledge. Unlike traditional data classifiers, the task of data classification of watershed classifier is carried out through the decision regions directly instead of relying on the decision theory. The watershed classifier can be either unsupervised or supervised. The supervised version of the watershed classifier is also devised to enhance the unsupervised classification performance. Experimental results demonstrate that the feasibility and validity of the proposed watershed classifier in data or image classification.

[1] Beucher, S. The watershed transform applied to image segmentation, Proceedings of the Pfefferkorn Conference on Signal and Image Processing in Microscopy and Microanalysis, pp. 299–314, September 1991.
[2] Vincent, L., and Soille, P. Watersheds in digital spaces: An efficient algorithm based on immersion simulations, IEEE Transaction on Pattern Analysis and. Machine Intelligence, vol. 13, no. 6, pp. 583–598, June 1991.
[3] Hernandez, S.E., and Barner, K.E. Joint region merging criteria for watershed-based image segmentation, Proceedings of the IEEE International Conference on Image Processing, vol. 2, pp. 108–111, 2000.
[4] Smet, P.D., Luis, R., and Pires, V.P.M. Implementation and analysis of an optimized rainfalling watershed algorithm, in: Proceedings of the Science and Technology Conference, Image and Video Communications and Processing, January 2000.
[5] Roerdink, J. B. T. M., and Meijsterm, A. The Watershed Transform: Denitions, Algorithms and Parallelization Strategies, Fundamenta Informaticae 41, pp. 187-228, 2001.
[6] Digabel, H., and Lantuejoul, C. Iterative algorithms, Actes du Second Symposium Europeen d''Analyse Quantitative des Microstructures en Sciences des Materiaux, Biologie et Medecine, Caen, 4-7 October 1977, J.-L. Chermant, Ed., Riederer Verlag, Stuttgart, pp. 85-99, 1978.
[7] Lantuejoul, C. La squelettisation et son application aux mesures topologiques des mosaiques polycristallines. PhD thesis, Ecole des Mines, Paris, 1978.
[8] Park, J., and Keller, J.M. Snakes on the watershed, IEEE Trans. on Pattern Recognition and Machine Intelligence, vol. 23, no. 10, pp. 1201-1205, October 2001.
[9] Nguyen, H.T., Worring, M., and Boomgaard, R.V.D. Watersnakes: energy-driven watershed segmentation, IEEE Trans. on Pattern Recognition and Machine Intelligence, vol. 25, no. 3, pp. 330-342, March 2003.
[10] Blaffert, T., Dippel, S., Stahl, M., and Wiemker, R. The Laplace integral for a watershed segmentation, Proceedings of 2000 International Conference on Image Processing, vol. 3, pp. 444-447, 2000.
[11] Moga, A. Parallel watershed algorithms for image segmentation, PHD Thesis, Tampere University of Technology, Tampere, Finland, February 1997.
[12] Moga, A.N., and Gabbouj, M. Parallel maker-based image segmentation with watershed transformation, Journal of Parallel and Distributed Computing 51, pp. 27-45, 1998.
[13] Klein, J.C., Lemonnier, F., Gauthier, M., and Peyrard, R. Hardware implementation of the watershed zone algorithm based on a hierarchical queue structure, Proceedings of IEEE Workshop on Nonlinear Signal and Image processing, Neos Marmaras, Halkidiki, Greece, I. Pitas, Ed., pp. 859-862, June 1995.
[14] Noguet, D., Merle, A., and Lattard, D. A data dependent architecture based on seeded region growing strategy for advanced morphological operators, Mathematical Morphology and its Applications to Image and Signal Processing, P. Maragos, R. W. Shafer, and M. A. Butt, Eds. Kluwer Acad. Publ., Dordrecht, pp. 235-243, 1996.
[15] Kuo, C.J., Odeh, S.F., and Huang, M.C. Image segmentation with improved watershed algorithm and its FPGA implementation, Proceedings of the IEEE International Symposium on Circuits and Systems, pp. 753-756, 2001.
[16] Chien, S.-Y., Huang, Y.-W., and Chen L.-G. Predictive watershed: a fast watershed algorithm for video segmentation, IEEE Transactions on Circuits and Systems for Video Technology, vol. 13, issue 5, pp. 453-461, May 2003.
[17] Beare, R. A locally constrained watershed transform, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 28, issue 7, pp. 1063-1074, July 2006.
[18] Davies, D., Palmer, P., and Mirmehdi, M. Detection and tracking of very small low contrast objects, Proceedings of the British Machine Vision 9th Conference, pp. 599–608, September 1998.
[19] Ffrench, P.A., Zeidler, J.R., and Ku, W.H. Enhanced detectability of small objects in correlated clutter using an improved 2-d adaptive lattice algorithm, IEEE Trans. on Image Process. 3 (6), pp. 383–397, 1997.
[20] Sonka, M., Hlavac, V., and Boyle, R. Image Processing, Analysis, and Machine Vision, 2nd ed., Brooks/Cole Publishing, pp. 77–82, 1999.
[21] Scheaffer, R.L. Introduction to Probability and its Applications, 2nd ed., The Book Company, pp. 285, 1995.
[22] Daubechies, I. Ten Lectures on Wavelets, SIAM, 1992.
[23] Tou, J.T., and Gonzalez, R.C. Pattern Recognition Principles, Addison-Wesley Publishing, 1974.
[24] Dunn, J.C. A fuzzy relative of the ISODATA process and its use in detecting compact well-separated cluster, J. Cybern., vol. 3, no. 3, pp. 32–57, 1973.
[25] Rish, I. An empirical study of the naive Bayes classifier, IJCAI 2001 Workshop on Empirical Methods in Artificial Intelligence, 2001.
[26] Fukushima, K. Cognitron: A Self-Organizing Multilayered Neural Network, Biological Cybernetics 20, pp. 121–136, 1975.
[27] Baum, L.E., and Petrie, T. Statistical inference for probabilistic functions of finite state Markov chains, Ann. Math. Stat., vol. 37, pp. 1554-1563, 1966.
[28] Baum, L.E., and Egon, J. A. An inequality with applications to statistical estimation for probabilistic functions of a Markov process and to a model for ecology, Bull. Amer. Meteorol. Soc., vol. 73, pp. 360-363, 1967.
[29] Baum, L.E., and Sell, G. R. Growth functions for transformations on manifolds, Pac. /. Math., vol. 27, no. 2, pp. 211-227, 1968.
[30] Baum, L.E., Petrie, T., Soules, G., and Weiss, N. A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains, Ann. Math. Stat., vol. 41, no. 1, pp. 164-171, 1970.
[31] Baum, L.E. An inequality and associated maximization technique in statistical estimation for probabilistic functions of Markov processes, Inequalities, vol. 3, pp. 1-8, 1972.
[32] Vapnik, V. Statistical Learning Theory. New York: Wiley, 1998.
[33] Bernhard, S., Christopher, J.C.B., and Alexander, J.S. Advances in Kernel Methods, The MIT Press, 1998.
[34] Hsu, C.-W., and Lin, C.-J. A simple decomposition method for support vector machines, Machine Learning 46, pp. 291-314, 2002.
[35] Hsu, C.-W., and Lin, C.-J. A comparison on methods for multi-class support vector machines, IEEE Transactions on Neural Networks, vol. 13, pp. 415-425, 2002.
[36] Lucas, S.M., and Cho, K.T. Fast convolutional OCR with the scanning N-tuple grid, Proceedings of 8th International Conference on Document Analysis and Recognition, pp. 799-803, August 2005.
[37] Beucher, S., and Lantuejoul, C. Use of watersheds in contour detection, Proceedings of International Workshop on Image Processing, Real-Time Edge and Motion Detection/Estimation, Rennes, September 1979.
[38] Meyer, F., and Beucher, S. Morphological Segmentation, Journal of Visual Communication and Image Representation, vol. 1, Academic Press, pp. 21-46, September 1990.
[39] Beucher, S., and Meyer, F. The morphological approach to segmentation: the watershed transformation, Mathematical Morphology in Image Processing, E. R. Dougherty, Ed. Marcel Dekker, New York, ch. 12, pp. 433-481, 1993.
[40] Beucher, S. Watershed, hierarchical segmentation and waterfall algorithm, Mathematical Morphology and its Applications to Image Processing, J. Serra and P. Soille, Eds. Kluwer Acad. Publ., Dordrecht, pp. 69-76, 1994.
[41] Meyer, F. Topographic distance and watershed lines, Signal Processing 38, pp. 113-125, 1994.
[42] Gao, H., Siu, W.-C., and Hou, C.-H. Improved techniques for automatic image segmentation, IEEE Trans. on Circuits and Systems for Video Technology, vol. 11, no. 12, pp. 1273-1280, December 2001.
[43] Bieniek, A., and Moga, A. A connected component approach to the watershed segmentation, Mathematical Morphology and its Applications to Image and Signal Processing, H. J. A. M. Heijmans and J. B. T. M. Roerdink, Eds. Kluwer Acad. Publ., Dordrecht, pp. 215-222, 1998.
[44] Lezoray, O., and Cardot, H. Cooperation of color pixel classification schemes and color watershed: a study for microscopic images, IEEE Trans. on Image Processing, vol. 11, no. 7, pp. 783-789, July 2002.
[45] Soni, T., Zeidler, J.R., and Ku, W.H. Recursive estimation techniques for detection of small objects in infrared image data, Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing, pp. 581-584, March 1992.