基于核函数与马氏距离的FCM图像分割算法

针对模糊聚类算法邻域信息与空间信息利用率低易受噪声影响的问题，提出一种结合核函数与马氏距离的FCM算法，即FCMKM算法。首先，将图像像素点由低维空间通过核函数非线性映射到高维空间；然后，利用马氏距离替换原有的欧氏距离作为高维空间距离量度；最后，利用改进后的算法对图像进行分割。为验证FCMKM算法的性能，选取Bezdek划分系数、Xie-Beni系数、重构错误率、运行时间、迭代次数五个评测指标作为对比实验的评价标准。实验结果表明，与传统FCM算法、基于核函数的FCM算法、基于马氏距离的FCM算法相比，FCMKM算法能有效地提高模糊聚类算法的抗噪性。

Image segmentation of FCM algorithm based on kernel function and Markov distance

In order to solve the problem that the low utilization rate of the neighborhood information and spatial information led to vulnerability to noise of fuzzy clustering algorithm, this paper proposed a fuzzy C-means algorithm combining kernel function and Mahalanobis distance(FCMKM). Firstly, it non-linearly mapped the image pixels from low-dimensional space to high-dimensional space through the kernel function. Then, it replaced the original Euclidean distance with Mahalanobis distance as a high-dimensional spatial distance measurement. Finally, it used the improved algorithm to segment the image. The paper selected five evaluation indexes Bezdek partition coefficient, Xie-Beni coefficient, reconstruction error rate, running time and iteration number as evaluation criteria of comparative experiments to verify the performance of the FCMKM algorithm. Experimental results show that compared with traditional FCM algorithm, kernel function based FCM algorithm and Markov distance based FCM algorithm, FCMKM algorithm can effectively improve the anti-noise performance of fuzzy clustering algorithm.