结合马尔可夫高斯模型的双邻域模糊聚类分割算法

摘要

Traditional fuzzy C-means (FCM) algorithm is sensitive to noises and outliers since it uses the Euclid-ean distance to describe the dissimilarity between the pixel and its cluster. In this paper, we establish a double neighborhood system on the feature field and label field by the Markov-Gaussian model and propose a fuzzy clustering image segmentation algorithm on this basis. First, the characteristic of Markov model is used to construct an energy function of neighbor pixels on the label field to ensure that pixels in the same neighbor-hood system could have a higher probability to be in the same cluster than pixels do not belongs to the same neighborhood system. Thus the neighborhood system on the label field is defined. Second, the dissimilarities between pixels and their clusters are described by a Gaussian model. Neighborhood system on the feature field is defined by taking the influence of neighbor pixels on the depiction of dissimilarities. In other word, the zero mean Gaussian noise between the observed data and its cluster is replaced by that between both the observed pixel and pixels in its neighborhood system and their clusters. Finally, the neighborhood system of both the la-bel and feature fields are used to model a fuzzy clustering algorithm to realize the high segmentation accuracy. The efficiency of the proposed algorithm is demonstrated through experiments on simulated and real color images and the comparison of the segmentation results with other FCM based algorithms.%针对传统模糊 C 均值(FCM)算法采用欧几里得测度描述像素与聚类间的非相似性对噪声和异常值敏感的问题，提出基于马尔可夫-高斯模型、且包含特征场和标号场双邻域的模糊聚类分割算法。首先根据马尔可夫模型能够结合邻域像素作用的特点在标号场上建立与邻域像素相关联的能量函数，确保相同邻域系统内的像素属于相同类别的概率较之不在相同邻域系统内的像素更大，最终实现标号场邻域系统的建立；而后在特征场上利用 Gaussian 模型描述像素与聚类间的非相似性测度，并结合相邻像素对非相似性的影响构建特征场邻域模型，即利用中心像素和邻域像素特征与聚类均值矢量的差异代替传统像素特征与均值矢量的差异构建 Gaussian 模型；最后结合标号场和特征场邻域构建包含双邻域的模糊聚类分割模型，实现高精度模糊聚类分割。通过与现有多种典型FCM算法对模拟影像和真实彩色影像的实验以及分割结果的对比分析，证明了文中算法的有效性。