FCM聚类的软划分:以遥感图像城镇下垫面聚类为例

Soft partition of FCM clustering results:A case study on the clustering of urban underlying surface from remotely sensed imagery

FCM是应用最广泛的模糊聚类方法之一.与分明聚类不同,模糊聚类以隶属度描述实体类属的确定程度,对于聚类过程中的质心调整和聚类结果分析等,具有重要参考价值.常规FCM应用中,一般以最大隶属度确定聚类结果中像素的类别归属,这种硬性划分,常常会将一些像素划分给了不恰当的类.本文采用的是一种软划分方法,它利用FCM聚类隶属度,对聚类结果做自适应解模糊处理.处理主要依据隶属度的背离特性(以类间隶属度标准差表征)和像素的空间依存关系(以邻域像素归属比例等表征).主要流程包括:①以FCM聚类获取聚类隶属度矩阵;②计算一个像素属于各类别隶属度的标准差,并以标准差取反的商作为该像素最大隶属度的权;③按类别统计像素邻域元素的隶属度加权元素密度(中心像元赋予3倍权重);④同时以2和3的结果作为中心像素划分的依据.为了免除人工干预,一些重要可调参数(如邻域窗口尺寸等)由自适应计算确定.实验表明以聚类图斑平均面积作为窗口尺寸能获得理想的结果.MATLAB仿真测试表明,以解模糊方法获得的聚类精度比最大隶属度方法的平均高出9%.

FCM is one of the most widely used fuzzy clustering methods. Being different from the distinct clustering, the fuzzy clustering provides variations of membership of entity. The var iations serve as useful references for adjusting centroids and allocating clusters during and after the clustering respectively. It is a commonly used way in FCM applications to allocate a pixel ac- cording to the maximum of memberships of this pixel owns. Such ＂hard partition＂ will likely al- locate the pixel to an inappropriate class. Therefore, a soft partition approach, called as SP FCM, has been investigated in this paper. The soft partition depends on both the dispersion degree of the memberships （represented by the standard deviation between the memberships） and the spa- tial dependence of pixels （indicated by the density of neighborhood pixels）. There are four steps to conduct the soft partition： 1） Get a membership matrix by FCM clustering. 2） Calculate the standard deviation of class membership for each pixel from the membership matrix. 3） Compute the density of neighboring elements for each class in the pixel＇s neighbor and these elements are weighted by their membership. 4） Take the results from step 2 and 3 as references to allocate the centre pixel. To release from manual operation, some important adjustable parameters （e. g. neighborhood window size, etc. ） are determined by adaptive calculation. Experiments indicate that the average area of clustering patches can be applied to derive the base number of window size for calculating the density of neighboring elements. MATLAB simulation tests show that the accuracy of allocation by SPFcM is 9% higher than that by the hard one involved with the maxi- mum membership.