Color image segmentation is an important technique in image processing, pattern recognition and computer vision. Many segmentation algorithms have been proposed. However, it is still a complex task especially when there are noises in the images, which have not been studied in much detail.
Neutrosophic set (NS) studies the origin, nature, and scope of neutralities. In this paper, we apply NS in the color image and define some new concepts. A directional α-mean operation is proposed to reduce the set indeterminacy. The fuzzy c-means clustering method is improved by integrating with NS and employed for the color image segmentation. The computation of membership and the clustering termination criterion are redefined accordingly. Moreover, a validity criterion is employed to determine the optimal clustering number. Numerical experiments serve to illustrate the effectiveness and reliability of the proposed approach. Experimental results demonstrate that our approach can segment color images automatically and effectively, produce good results as favorably compared to some existing algorithms. The optimal clustering number is determined automatically and no prior knowledge is required. Especially, it can segment both images with the simple and distinct objects and the images with complex and noisy objects, which is the most difficult task for color image segmentation.