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研究生： 陳奕廷
Chen, Yi-Ting
論文名稱： 基於向量群聚法之創新的影像切割法
A Novel Image Segmentation based on Support Vector Clustering
指導教授： 郭淑美
Guo, Shu-Mei
學位類別： 碩士
Master
系所名稱： 電機資訊學院 - 資訊工程學系
Department of Computer Science and Information Engineering
論文出版年： 2006
畢業學年度： 94
語文別： 英文
論文頁數： 61
中文關鍵詞： 支持向量群聚 、核心函數 、特徵空間 、影像切割 、輪廓
外文關鍵詞： support vector clustering, kernel function, feature space, contours, image segmentation
相關次數： 點閱：110  下載：1 
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    • 摘要
    群聚法(clustering)是一種非監督式學習(unsupervised learning)的分類方法，透過分析資料彼此的關係來達到分群的效果。支持向量群聚(support vector clustering)則是一種最新的群聚方法，它是從支持向量分類器(support vector machine)的理論所改良衍生出來，其基本的原理就是透過一個核心函數(kernel function)將資料投射到一個高維的特徵空間上(feature space)。而我們希望能在這空間中找到一個最小的球體來包含所有的資料，當這個球體投射回原來的空間時，就會形成許多組的輪廓(contours)，而這些輪廓就能夠將資料給區隔開來。
    這篇論文裡，我們應用向量群聚法(SVC)，而提出一個創新的影像切割方法。並且，提出一個改良的分割技巧來加速向量群聚法的程序。藉著向量群聚法的物理特性，我們提出一個創新的概念，這個概念是”利用向量群聚法所找出來的支持向量點(support vector point)，在變數空間中將會是所有輸入變數的最大外圍”。這個概念被利用在我們提出的創新的影像切割上。這個方法的主要目的是簡化向量群聚法的流程，並進一步的減少流程的時間。在這篇論文裡，我們提出一個適合這個簡化的向量群聚法的影像切割流程架構。使用一些人工以及真實的圖片來做實驗，可以發現我們提出來的方法在影像切割的正確性以及抑制過度切割上，有非常好的效能。

    Abstract
    Clustering is an unsupervised learning classification method which has been utilized widely. Recently, a novel clustering method: the support vector clustering which is derived from the support vector machine was first proposed in 2000. Its basic concept is that data points are mapped into a high dimensional feature space by a kernel function. In the feature space, we look for the smallest sphere which encloses the image of the data. This sphere corresponds to a set of contours which enclose all the data points in the original input space.
    Based on the support vector clustering (SVC) approach, a novel image segmentation approach is proposed in this paper. The paper adopts an improved division technique to speed up the SVC process. A novel idea with a physical characteristic of SVC, which denotes support vector points form the maximal outline of all input data, is utilized for the proposed efficient image segmentation. The main idea of this approach is to simplify the process of SVC, and to reduce process time further. The paper presents a framework for image segmentation using simplifying SVC. Using several computer-generated and real images, the high performance of the proposed approach is illustrated in terms of both segmentation accuracy and less over-segmentation.

    Table of Contents Abstract iv Table of Contents vii List of Tables ix List of Figures x Chapter 1 Introduction 1 Chapter 2 Background 6 2.1 Gradient Operator 6 2.1.1 Define 6 2.1.2 Implement 7 2.2 Support Vector Clustering (SVC) 10 2.2.1 Overview of SVC 10 2.2.2 Theory of SVC 11 2.2.2.1 Cluster Boundaries 11 2.2.2.2 Cluster Assignment 19 2.2.3 Parameter Selection of SVC 21 2.2.3.1 Selection of q 21 2.2.3.2 Selection of C 23 Chapter 3 The Novel Image Segmentation Approach 26 3.1 Major Difficulty of Instinctive Image Segmentation using SVC 26 3.1.1 Major Difficulty 26 3.1.2 Spatially Chunking and its defects 27 3.1.3 Improved Division Technique 31 3.2 A Novel Image Segmentation Approach 34 3.3 Post-processing 37 3.3.1 Thinning process 37 3.3.1.1 Basic Set Theory 37 3.3.1.2 Dilation and Erosion 39 3.3.1.3 Thinning 40 3.3.2 Contour Connection 41 3.3.3 Contour Simplification 41 Chapter 4 Experimental Results 44 4.1 Computer-generated Images 44 4.2 Real Images 47 Chapter 5 Conclusion and Future Work 56 5.1 Conclusion 56 5.2 Future Work 57 References 58 List of Tables Table 1. Some general kernel functions and their mathematical forms. 15 Table 2. The three basic logical operations. 39 Table 3. Comparisons of FCM, SGA, EISA, and the proposed approach. 51 List of Figures Fig. 1. A flow chart of image processing. 5 Fig. 2. A 3 3 region of image (these z’s are gray-level values) and various masks used to compute the gradient at point labeled . 8 Fig. 3. Prewitt and Sobel masks for detecting diagonal edges. 10 Fig. 4. Relation of support vector and bounded support vector. 17 Fig. 5. Input Data Distribution. 18 Fig. 6. Support and bounded support vectors. 18 Fig. 7. Cluster assignment result. 19 Fig. 8. Various parameters q and their corresponding clustering results. 22 Fig. 9. Varied cluster boundaries with different parameters q. 23 Fig. 10. Clustering with and without BSV. 24 Fig. 11. Contours of clusters in the data space. 24 Fig. 12. The flowchart of the proposed image segmentation approach. 27 Fig. 13. Four subsets using spatially chunking approach [24] and their corresponding clustering results. 31 Fig. 14. Four subsets using an improved divided method and their corresponding clustering results. 33 Fig. 15. A test image and its result of SVC in 2-D, 3-D and 4-D. 36 Fig. 16. Contour Simplification with morphological approaches. 42 Fig. 17. The smoothing criterion step. 42 Fig. 18. The elimination criterion step. 43 Fig. 19. The test image, this image corrupted with Gaussian noise and their experimental results using the proposed method. 46 Fig. 20. The segmentation result using the snake method. 47 Fig. 21. The proposed experimental results of the test image Lena with the size of 240 240. 49 Fig. 22. Comparisons of four image segmentation approaches for Lena; (a) result of FCM; (b) result of SGA; (c) result of EISA; (d) result of the proposed approach. 50 Fig. 23. The test images “photographer” and its results. 52 Fig. 24. The test images “table tennis” and its results. 53 Fig. 25. The test images “baboon” and its results. 54 Fig. 26. The test images “breast cancer” and its results. 55

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