Fuzzy subspace clustering noisy image segmentation algorithm with adaptive local variance & non-local information and mean membership linking

The Fuzzy C-means (FCM) clustering algorithm is an effective method for image segmentation. Non-local spatial information considers more redundant information of the image thus is more robust to noise. However, under-segmentation of non-local spatial information may exist with higher noise density. The number of iteration steps is also significant in FCM, and employing membership linking can effectively reduce the number of iteration steps. Nonetheless, when there are outliers in the membership degree, the membership linking can make the algorithm converge prematurely before reaching the optimum, affecting segmentation performance. This paper presents a fuzzy subspace clustering noisy image segmentation algorithm with adaptive local variance & non-local information and mean membership linking (FSC_LNML). Firstly, local variance templates are utilized to eliminate the under-segmentation of non-local information, and local variance & non-local information are integrated into the FCM objective function to improve robustness. Secondly, the mean membership linking is employed as the denominator of the objective function to reduce the number of iterations and solve the problem that the algorithm converges early before reaching the optimum when the membership has an outlier. Thirdly, the absolute intensity difference between the original image and the local variance & non-local information and its inverse are used to adaptively constrain the original image and the local variance & non-local information. Finally, the concept of the subspace is introduced to adaptively assign appropriate weights to each dimension of the image to improve the segmentation performance of color images. The simulation results on noisy grayscale images and noisy color images show that the efficiency of the proposed method FSC_LNML is better than other fuzzy-based clustering algorithms. The convergence proof of the algorithm is also presented.