合肥工业大学硕士学位论文基于图论和抠图算法的研究及应用姓名：张婕申请学位级别：硕士专业：信号与信息处理指导教师：蒋建国；詹曙2011-03基于图论和抠图算法的研究及应用基于图论和抠图算法的研究及应用 摘摘 要要 近年来，随着图论方法和抠图算法的引入，在图像分割、图像复原、图像增强等方面都取得了一些进展。本文分别对基于图论的图像分割算法中的图割算法和闭式求解的 alpha matting 算法进行了研究，从减小算法复杂度及提高分割精度的角度，提出了改进型模型，并分别在自然图像及医学图像中验证了改进模型的有效性。具体工作如下： （1）图切分（Graph Cuts，GC）是近年来兴起的基于图论框架的图像分割方法，该理论的新颖之处在于它的全局最优性和结合多种知识的统一性。 但当图像较大，运算将非常耗时。该文提出了一种基于 GC 的层次式图像分割方法。先在低分辨率中用 GC 以较低的分割代价获取粗尺度的初始分割，再将结果轮廓映射回高分辨率图像中并构造出窄带，进而采用 matting 思想，在窄带内获取精确分割。实验结果表明，本文方法在确保分割结果准确性的同时，运算速度大幅度提高。 （2）骨肿瘤 MRI 中病灶组织边缘模糊不清和凹凸多变，传统的图像分割算法提取骨肿瘤区域很困难。本文提出了一个基于数字抠像技术的骨肿瘤 MRI 计算机辅助诊断系统。该系统采用由粗到精的求解策略，利用闭合求解的数字抠像算法来提取病灶区域，只需求解一个稀疏线性方程，即可获得所需的分割结果。实验结果表明，该系统在较低的运算时间开销下，能精确的勾划出病灶区域，为医生下一步的临床诊断提供可靠的依据。 关键词：关键词： 医学图像分割;图割;抠图;骨肿瘤 MRI;计算机辅助诊断 Study and Application Based on Graph Cuts and Image Matting Theory Abstract In recent years, there are a great deal of improvements in image segmentation，restoration and enhancement along with the introduction of graph theory and alpha matting theory. In this paper, we study on the graph cuts method in image segmentation based on graph theory and a closed-form matting algorithm. For sake of minimizing complexity of algorithm and improving the veracity of segmentation, we propose two improved models and validate the efficiency and effectivity of our methods through the natural images and medical images. The main jobs we complete are as follows: (1) Graph Cuts is a novel image segmentation method based on graph theory framework. The innovations of this theory lie in its global optimization and the unity of knowledge. However, if the image is large, computing will be very time-consuming. This paper presents a GC-based Hierarchical image segmentation method. First the initial segmentation is obtained through GC in the low-resolution with a very low computational cost. Then the contour is projected back to the high-resolution image to construct a narrow band. At last use matting arithmetic for accurate segmentation in the narrow-band. Experimental results show that this method can ensure the accuracy of segmentation results with a significant increasing in computing speed. (2) MRIs of bone tumor are vague and irregular. Its very difficult to extract the pathological tissue from the MRIs for the traditional image segmentation methods. This paper presents a new computer-aided diagnosis system of tumor MRI segmentation based on image matting technique. The system uses the solution from coarse to fine strategy, use a closed-form solution to extract the diseased tissue, simply solving a sparse linear equation to obtain the desired segmentation results. Experimental results show that this method can ensure the accuracy of segmentation results with a significant low cost of computing time. The accurate segmentation results can provide a reliable basis for clinical diagnosis for doctors. Key words: medical image segmentation; graph cuts, alpha matting;bone tumor MRI, computer aided diagnoses 图清单 图清单 图 1-1 通过 Graph Cuts 算法在 CT 序列中分割出肝脏 . 5 图 1-2 掩码图像 . 7 图 1-3 待分割区域利用前景和背景信息方式的比较 . 7 图 2-1 网络 G=. 12 图 2-2 图像的 ST 网络 . 13 图 2-3 在生长介绍阶段搜索树 S 和 T 的示例. 15 图 2-4 数字抠像实例. 17 图 2-5 不同的局部邻域几何计算方法. 20 图 2-6 谱分析引导用户交互的抠图方法. 22 图 3-1 图的构造 . 26 图 3-2 层次式分割过程图 . 28 图 3-3 层次式 GC 分割过程实例图. 29 图 3-4 层次式 GC 与传统 GC 分割效果对比图. 30 图 3-5 层次式 GC 与 G 传统 GC 分割时间和内存对比 . 31 图 3-6 自然图像分割实例 . 32 图 3-7 医学图像分割实例 . 32 图 3-8 遥感图像分割实例 . 33 图 4-1 骨肿瘤 MRI 图像. 35 图 4-2 骨肿瘤 MRI 分割过程实例. 40 图 4-3 与水平集分割对比 . 42 图 5-1 骨肿瘤计算机辅助诊断系统流程图.44独 创 性 声 明 独 创 性 声 明 本人声明所呈交的学位论文是本人在导师指导下进行的研究工作及取得的研究成果。据我所知，除了文中特别加以标注和致谢的地方外，论文中不包含其他