Research On Algorithms For Image Segmentation Based On Fuzzy Markov Random Fields

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.