Significantly Fast and Robust Fuzzy C-Means Clustering Algorithm Based on Morphological Reconstruction and Membership Filtering

As fuzzy c-means clustering (FCM) algorithm is sensitive to noise, local spatial information is often introduced to an objective function to improve the robustness of the FCM algorithm for image segmentation. However, the introduction of local spatial information often leads to a high computational complexity, arising out of an iterative calculation of the distance between pixels within local spatial neighbors and clustering centers. To address this issue, an improved FCM algorithm based on morphological reconstruction and membership filtering (FRFCM) that is significantly faster and more robust than FCM is proposed in this paper. First, the local spatial information of images is incorporated into FRFCM by introducing morphological reconstruction operation to guarantee noise-immunity and image detail-preservation. Second, the modification of membership partition, based on the distance between pixels within local spatial neighbors and clustering centers, is replaced by local membership filtering that depends only on the spatial neighbors of membership partition. Compared with state-of-the-art algorithms, the proposed FRFCM algorithm is simpler and significantly faster, since it is unnecessary to compute the distance between pixels within local spatial neighbors and clustering centers. In addition, it is efficient for noisy image segmentation because membership filtering are able to improve membership partition matrix efficiently. Experiments performed on synthetic and real-world images demonstrate that the proposed algorithm not only achieves better results, but also requires less time than the state-of-the-art algorithms for image segmentation.