A lie group semi-supervised FCM clustering method for image segmentation

Abstract

As an unsupervised clustering method with low overhead, Fuzzy C-means (FCM) clustering has been widely used in a variety of image segmentation tasks. However, existing FCM clustering methods are sensitive to image noises and are either suffer from losing of image detail or falling into local optima in identifying cluster centers. Aiming at these problems, this paper proposes a Lie group semi-supervised FCM (LieSSFCM) clustering method for image segmentation. The method maps the input image from Euclidean space to Lie group manifold by representing each image pixel as a matrix Lie group and calculates geodesic distances between group elements and cluster centers on Lie group manifold. Prior information of the image and neighborhood relationships of pixels are used to guide the initialization and constrain the update of cluster centers and the corresponding fuzzy membership matrix. The proposed LieSSFCM has been validated against two medical image datasets and was compared with seven FCM clustering methods. Experimental results along with a systematic evaluation demonstrated that the method was superior in segmentation accuracy both visually and statistically, robustness to noises, adaptability to different tasks, and stability while maintaining a moderate computational complexity.