圖像分割是圖像處理中的一個非常重要的課題，其目的是辨認給定圖像中所包含物體的邊界。目前已經有很多非常有效的圖像分割方法，例如：基於模型的方法、模式識別技術、基於搜索的方法、基於人工智能的方法等等。在本論文中，我們主要討論兩類圖像分割問題，一類是醫學圖像中的血管分割問題，另一類是一般性圖像的分割問題，即對於例如醫學、噪聲和模糊等圖像，如何對其實現有效的雙級和多級分割。 / 在本論中的第一部分，我們討論第一個問題，即醫學圖像中的血管分割問題，我們將提出我們的基於tight-frame的血管分割方法。Tight-frame作為正交小波的一般情形，已經被成功的應用於圖像處理中的許多問題，包括：圖像修復、去除脈衝噪聲、高分辨率圖像恢復等等。在這部分，我們將應用tight-frame方法來自動識別醫學圖像中的管狀結構。我們的方法是反覆的改進血管的潛在邊界的區間。在迭代的每一步，我們用tight-frame方法來使血管的潛在邊界去噪和光滑，並同時壓縮血管的潛在邊界的區間。毎一步迭代的計算量跟所處理圖像的元素個數是成比例的。可以證明，我們的方法在有限步迭代後將自動收斂到一個二值圖像。在得到的二值图像中，血管部分可以直接分割出來。从构造的和真实的2D/3D圖像的數值例子中可以得出，我們的方法比現有的很多有代表性的分割方法來的更加精確，並且在很少步的迭代後收斂。 / 在本論中的第二部分，我們討論一般性的圖像分割問題。Mumford-Shah模型是一個非常重要的圖像分割模型，對其的深入研究已經經歷了20多年。在這部分，基於Mumford-Shah模型，我們將提出一種圖像分割的凸模型。它可以被看作是尋找一個光滑解g來估計Mumford-Shah模型的分段光滑解。當g得到後，把合適的閥值作用於g 即可實現圖像的雙級和多級分割。使用者可以自己選擇合適的閥值來揭示圖像的特殊特徵，也可以用K-means的方法來自動的選取閥值。由於我們所提模型的凸性，g可以用諸如split-Bregman或者Chambolle-Pock的方法來快速有效的求出。可以證明，我們所提出的模型有且只有一個解g。對於我們所提出的分割方法，在求出g之前不需要預先指定分割的級數K(K>=2)。當g求出後，選取(K-1)個合適的閥值即可實現圖像的K級分解，在閥值更換的情形下並不需要重新求解g。實驗結果表明，對於一般的圖像，例如：抗結塊，噪聲和模糊等圖像，我們的方法優於很多現有的有效的雙級和多級分割方法。 / Image segmentation is a very important topic in image processing. It is the process of identifying object outlines within images. There are quite a few efficient algorithms for segmentation such as the model based approaches, pattern recognition techniques, tracking-based approaches, artificial intelligence-based approaches, etc. In this thesis, we mainly study two kinds of image segmentation problems. More precisely, one kind problem is the vessel segmentation problem in medical imaging, the other is the generic image segmentation problem, i.e., two-phase and multiphase image segmentation for very general images, for example medical, noisy, and blurry images, etc. / In Part I of this thesis, we focus on the vessel segmentation problem in medical Images, and our tight-frame based vessel segmentation algorithm will be proposed. Tight-frame, a generalization of orthogonal wavelets, has been used successfully in various problems in image processing, including inpainting, impulse noise removal, super-resolution image restoration, etc. In this part, we propose to apply the tight-frame approach to automatically identify tube-like structures in medical imaging, with the primary application of segmenting blood vessels in magnetic resonance angiography images. Our method iteratively refines a region that encloses the potential boundary of the vessels. At each iteration, we apply the tight-frame algorithm to denoise and smooth the potential boundary and sharpen the region. The cost per iteration is proportional to the number of pixels in the image. We prove that the iteration converges in a finite number of steps to a binary image whereby the segmentation of the vessels can be done straightforwardly. Numerical experiments on synthetic and real 2D/3D images demonstrate that our method is more accuracy when compared with some representative segmentation methods, and it usually converges within a few iterations. / Part II of this thesis focuses on generic image segmentation problem. The Mumford-Shah model is one of the most important image segmentation models, and has been studied extensively in the last twenty years. In this part, based on the Mumford-Shah model, our convex image segmentation model will be proposed. It can be seen as finding a smooth approximation go to the piecewise smooth solution of the Mumford-Shah model. Once g is obtained, the two-phase or multiphase segmentation is done by thresholding g. The thresholds can be given by the users to reveal specific features in the image or they can be obtained automatically using a K-means method. Because of the convexity of our model, g can be solved efficiently by techniques like the split-Bregman algorithm or the Chambolle-Pock method. We prove that our model is convergent and the solution g is always unique. In our method, there is no need to specify the number of segments K (K ≥ 2) before finding g. We can obtain any K-phase segmentations by choosing (K-1) thresholds after g is found; and there is no need to recompute g if the thresholds are changed. Experimental results show that our method performs better than many standard 2-phase or multi-phase segmentation methods for very general images, including anti-mass, noisy, and blurry images. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Cai, Xiaohao. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 70-80). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Introduction to Chapter 2 (part I) on Vessel Segmentation in Medical Imaging Using a Tight-frame Based Algorithm --- p.2 / Chapter 1.2 --- Introduction to Chapter 3 (part II) on Image Segmentation by Convex Approximation of the Mumford-Shah Model --- p.5 / Chapter 2 --- Vessel Segmentation inMedical Imaging Using a Tightframe Based Algorithm --- p.9 / Chapter 2.1 --- Introduction --- p.9 / Chapter 2.2 --- Tight-Frame Algorithm --- p.11 / Chapter 2.3 --- Tight-Frame Based Algorithm for Segmentation --- p.14 / Chapter 2.4 --- Numerical Examples --- p.20 / Chapter 2.4.1 --- Synthetic vessel segmentation --- p.21 / Chapter 2.4.2 --- 2D vessel segmentation --- p.23 / Chapter 2.4.3 --- 3D vessel segmentation --- p.29 / Chapter 2.5 --- Conclusion and Future Work --- p.32 / Chapter 3 --- Image Segmentation by Convex Approximation of the Mumford-Shah Model --- p.39 / Chapter 3.1 --- Introduction --- p.39 / Chapter 3.2 --- Our model --- p.42 / Chapter 3.2.1 --- Derivation of our model --- p.43 / Chapter 3.2.2 --- Relationship with image restoration --- p.46 / Chapter 3.3 --- Numerical aspects --- p.47 / Chapter 3.3.1 --- Solution of our segmentation model --- p.47 / Chapter 3.3.2 --- Determining the thresholds --- p.50 / Chapter 3.4 --- Experimental results --- p.51 / Chapter 3.4.1 --- Two-phase segmentation --- p.52 / Chapter 3.4.2 --- Multiphase segmentation --- p.58 / Chapter 3.5 --- Conclusions --- p.62 / Chapter 4 --- Conclusions --- p.65 / Chapter 5 --- Appendix --- p.67 / Bibliography --- p.70
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_328290 |
| Date | January 2012 |
| Contributors | Cai, Xiaohao., Chinese University of Hong Kong Graduate School. Division of Mathematics. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | electronic resource, electronic resource, remote, 1 online resource (viii, 80 leaves) : ill. (some col.) |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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