基于学生t分布的鲁棒分层模糊算法及其在图像分割中的应用

著名的模糊C均值算法（FCM）一直被视为图像分割应用中一个强有力的工具.然而，由于FCM中距离函数选择问题使得其对图像噪声的鲁棒性不足.本文提出了一个新的分层模糊C均值算法，使得传统的模糊C均值算法对于图像噪声和离群点有更好的鲁棒性.在此基础上引入了一个更加灵活的函数，即将距离函数本身看作是一个子学生t分布函数.使分层模型具有更好的通用性和灵活性.本文提出的算法可以扩展到其他基于FCM模型的算法实现，以获得更优的鲁棒性.实验结果表明本文提出新的分层模糊C均值算法的鲁棒性确实有效.

A Robust Hierarchical Fuzzy Algorithm with Student's t-Distribution for Image Segmentation Application

The well-known fuzzy c-means algorithm (FCM) has been regarded as a useful tool for image segmentation application.However,it is still insufficient in the robustness to image noise due to the distance function selection in FCM.In this paper,we propose a new hierarchical fuzzy algorithm to make the traditional fuzzy c-means more robust to image noise and outliers.We introduce a more flexible function which considers the distance function itself as a sub-FCM with student's t-distribution.Thus,our hierarchical model is general and flexible enough to deal with outliers and noises.Our algorithm can be extended to any other FCM-based models to achieve superior performance.Experimental results demonstrate the improved robustness and effectiveness of the proposed algorithm.