【作者】 颜刚；

【导师】 陈武凡；

【作者基本信息】 第一军医大学 ， 生物医学工程， 2005， 博士

【摘要】 医学图像的分割,就是将感兴趣区从背景中分割开来,或将不同的感兴趣区互不交迭地区分开来。图像分割是其他医学图像处理与模式识别问题,如特征量化、特征配准、三维重建等的前处理技术,并可以为临床诊断和辅助治疗提供有力的支持。尤其是,对心肺脏器的序列图像来说,分割是其运动估计的主要技术之一,因此对感兴趣区的分割研究具重要价值,也是国内外学者的研究热点问题。 本文深入讨论了基于模糊集和基于马尔可夫场的分割算法,这是分割中的两大主流算法。对于基于模糊集的算法,主要讨论模糊集在图像处理应用中的有关问题,如隶属度的选择、去模糊化方法以及模糊贝叶斯决策等。而对于模糊集的三大框架定理只涉及到分解定理,因为模糊集依赖分解定理与普通集联系起来。模糊集的核心是打破常规思维中的非此即彼的逻辑,即排中律,引入模糊逻辑。当做决策时,一旦做出错误的决策,算法很难从相反的方向走到正确的方向上,这就是经典的二值逻辑。所以,初始决策时,不必作出确定的回答,而是以不同程度作出多种决策,在算法迭代中逐步修正,最终作出正确的决策,这是个渐变的过程,是一个从量变到质变的过程。作者认为,这是模糊集方法的核心指导思想。 基于马尔可夫场的图像分割算法一直以来备受人们的青睐,马尔可夫场因其能有效的刻划图像的空间相关性,又因为理论与性质完善,所以在图像处理中广泛应用,特别是图像分割。图像具有空间上高度相关的性质,很多的分割算法都试图将图像的空间信息引入到图像分割算法中,也取得了很好的效果。但是,马尔可夫随机场的联合分布,即Gibbs分布本身就是利用空间信息建立起来的,它描述图像的空间信息更直接、有效。从1984年Geman S开创性的利用马尔可夫场到图像分割以来,每年都有一些基于马尔可夫场的分割算法涌现出更多还原

【Abstract】 The main purpose of the medical image segmentation is to extracting the region of interesting (ROI) from the background, or partitioning the different ROIs into nonoverlapping regions. Image segmentation is very important to image preprocessing and patter recognition, such as feature quantification, image registration 3D reconstruction and etc. Particularly, it is one of the key techniques for motion estimate in cardiac sequential images.In this paper, two main kinds of the algorithms, fuzzy set-based and Markov model-based algorithms, are discussed. In the fuzzy set-based methods, we focus on the fuzzy set in the image processing, including selection of membership function, methods of defuzzification and fuzzy bayes rule. Only decomposition theorem in the three basic thorems is concerned. The relationship between conventional set and fuzzy set is developed depending on the decomposition thorem. The essence of the fuzzy set-based methods is the fuzzy logic, while it is the binary logic in the conventional set. Many problems can be regarded as the decision making problem. In many crasp methods, once you select the wrong decision, it is very difficult to correct this wrong selection obviously. However, it is not the case in the fuzzy logic. In every step of fuzzy logic, you will not need to make a definite decision, but you can make many decisions with different grade. The correct decision will be yielded finally when the iterarion terminated. It is the process from the quantitative change to qualitative change. This is, I think, the guidline of the fuzzy set-based method.The Markov model-based methods are very popular to image segmentation all along. The Markov random field (MRF) is widely used in the image process, because it can describe the spatial information effectively, moreover, it has a complete theory. Many researchers tried to introduce the spatial information and obtained better results. The joint distribution of the MRF obeys Gibbs form, which is established using spatial construction of images. So MRF can represent the spatial information more diretedly and more efficiently. The parameter estimate plays an import role in Gibbs distribution. Smaller parameter cannot correctly reflect the spatial correlationship, but larger parameter can lead to a case of over-smoothing. Duo to the high computational complexitation in the Gibbs distribution, many optimization algorithms are used to ensure that the computation can be implement successfully. The optimization algorithms are dicussed in the chapter n. But the optimization algorithms have been developed very slowly. We discuss optimization algorithms in the chapter n.The fuzzy set-based and the Markov model-based algorithms have their respective advantages. So we combine the fuzziness and randomness, and developed the Fuzzy Markov random field (FMRF) based on the fuzzy random variable, which can describe the fuzziness and randomness simultaneously. The FMRF fuse the fuzzy set-based and the Markov model-based methods. The fuzzy random variable takes a fuzzy set as its values for any sample point. When the event is no fuzziness, the fuzzy random variable will degenerate into a conventional random variable; and when no randomness, it takes the same value with different sample point, i.e., it degenerates into a fuzzy set.We creativly applied the fuzzy random variable to image segmentation in chapter IV, and obtained better results. A new unsupervised segmentation algorithm based on FMRF is proposed. This algorithm, named as FGS and constrained by the prior FMRF, can deal with fuzziness and randomness simultaneously during segmentation. A Classical MRF (CMRF) serves as bridge between prior FMRF and original image. The FMRF is equivalent to CMRF when no fuzziness is considered in FMRF; therefore, the FGRF is obviously a generalization of the CMRF. The prior FMRF is described in the Potts model, whose parameter is estimated by the maximum pesudolikelihood (MPL) method. The segmentation results are obtained by ftizzifying the image, updating the membership of FMRF based on maximum a posteriori (MAP)criteria, and defuzzifying the image according to maximum membership principle (MMP). Specially, this algorithm can filter the noise effectively when processing the degraded image. The experiments show that this algorithm is obviously better than CMRF-based methods and conventional fuzzy c-means (FCM) clustering methods as well.Generalized fuzzy set (GFS) is proposed by Professor Chen in 1995, and successfully applied to edge detection and other image processing fields. GFS, which is an extention of fuzzy set, is characterized by its generalized memebership function (GMF). The GMF includes two parts: the negative and positive part. The negative part characterizes the elements belonging to the GFS with a relative smaller extent, and conversely, the positive part characterizes the elements belonging to the GFS with a relative larger extent. The zero point of GMF is called fuzzy critical point. The GMF takes values in the symmetric closed interval from -1 to 1, and this property can bring us convenient handling in many aspects.In chapter V, a novel soft segmentation algorithm is proposed based on the GFS. As a predetermination, generalized fuzzy Markov random (GFMR) model is to be established to describe the randomness and fuzziness of every pixel, which must be assigned a class and a membership value to the class. Each class is considered as a subset of GFS on gray level. The outliers in the image data are attached with negative part of GMF to improve the treatment more effectively. In MAP scheme, prior distribution can be obtained by GFMR model, and it must be decided that each pixel ought to belong to which class with what membership degree. The center of every class is updated with fuzzy centroid during the iterative process. In this algorithm, the parameters, which depict the interaction between a candidate pixel and its neighbors, can be determined by the values of GMF. Hence, it is a complete unsupervised segmentation algorithm. The experiments show that our algorithm can significantly filter the noise and eliminate the partial volume effect, and is more robust.The number of class in an image should be detected as part of the parameter estimation procedure prior to image segmentation for a segmentation algorithm. It is very important in theory and application for estimating the class number correctly. In chapter HI, an adaptive joint energy criterion (AJEC) to cluster validation is proposed based on the MRF in the image segmentation. The criterion is composed of two parts:one part is inner-energy, which can describe the difference in the same class, and measured by data likelihood; another is inter-class energy, which can describe the edge information, and measured by Markov local probability. The correct class number of different images can be obtained by minimizing the AJEC. The parameters in the criterion are estimated by expectation maximum (EM) algorithm and MPL algorithm. The high complexity in computation is optimized by the mixture of simulated algorithm (SA) and iterated conditional mode (ICM). The experiments show that the class number can be automatically detected by automatically adjusting the hyper-parameter in MRF.In this dissertation, we investigate the fuzzy set-based and stochastic Markov model-based methods, and put emphasis on the fusion of randomness and fuzziness. We develope the FMRF and propose the corresponding segmentation algorithms. The study covers the modeling, parameter estimate and opimization methods. We aim to improve the accuracy and robustness of segmentation.更多还原