国家重点研发计划(2018YFA0701700, 2018YFA0701701); 国家自然科学基金(62002253)
模糊C均值(FCM)聚类算法凭借其学习成本低、算法开销少的特点, 已经成为常用的图像分割技术之一. 然而, 传统FCM算法存在对图像中噪声敏感的问题. 近年来, 各种对传统FCM算法的改进虽然提高了算法的噪声鲁棒性, 但是往往以损失图像上的细节为代价. 提出一种基于李群理论的改进FCM算法并将其应用于图像分割中. 所提算法针对图像的所有像素构建矩阵李群特征, 用以归纳每个像素的底层图像特征以及与其邻域窗口内其他像素的关系, 从而将传统FCM算法聚类分析中求取像素点之间的欧氏距离转变为在李群流形上求取像素点李群特征之间的测地线距离. 针对在李群流形上更新聚类中心和模糊隶属度矩阵的问题, 所提算法使用一种自适应模糊加权的目标函数, 提高算法的泛化性和稳定性. 通过在3组医学图像上与传统FCM算法以及几种经典改进算法的实验对比验证了所提方法的有效性.
Fuzzy C-means (FCM) clustering algorithm has become one of the commonly used image segmentation techniques with its low learning cost and algorithm overhead. However, the conventional FCM clustering algorithm is sensitive to noise in images. Recently, many of improved FCM algorithms have been proposed to improve the noise robustness of the conventional FCM clustering algorithm, but often at a cost of detail loss on the image. This study presents an improved FCM clustering algorithm based on Lie group theory and applies it to image segmentation. The proposed algorithm constructs matrix Lie group features for the pixels of an image, which summarizes the low-level image features of each pixel and its relationship with other pixels in the neighborhood window. By doing this, the proposed method transforms the clustering problem of measuring the Euclidean distances between pixels into calculating the geodesic distances between Lie group features of pixels on the Lie group manifold. Aiming at the problem of updating the clustering center and fuzzy membership matrix on the Lie group manifold, the proposed method uses an adaptive fuzzy weighted objective function, which improves the generalization and stability of the algorithm. The effectiveness of the proposed method is verified by comparing with conventional FCM and several classic improved algorithms on the experiments of three types of medical images.