Hybrid Methods of Spatial Credibilistic Clustering and Particle Swarm Optimization in High Noise Image Segmentation

information from the original image as compared with crisp or hard segmentation methods. In practice, noisy images (even high noise images) are very common. It's very essential and critical to deal with such images to process real-image segmentation and pattern recognition. In this paper, differences of credibilistic clustering algorithm (CCA) and fuzzy c-means algorithm (FCM) in dealing with noisy images are studied and the research shows that in most cases, CCA performs better than FCM in high noise image segmentation. Based on that, a new kind of fuzzy clustering methods is presented. It combines spatial credibilistic clustering algorithm (SCCA) with particle swarm optimization (PSO) and takes full advantages of them. The advantages that come from CCA in noise image segmentation also help in SCCA, and the imposition of spatial information enlarges the advantage. The addition of PSO helps to improve global search performance; thereby the novel methods overcome the drawback of single clustering methods local optimal solutions. Computational experiments show that the proposed methods give the best segmentation results when compared with FCM, CCA, spatial fuzzy c-means algorithm (SFCM), SCCA and the PSO incorporated versions of FCM, CCA, and SFCM. However, the conventional FCM doesn't consider any spatial information in the image context, which makes it very sensitive to noise and other imaging artifacts. But noisy images (even high noise images) are very common in practice, and they must be segmented quite well for pattern recognition or other computer vision based operations. To better deal with noisy images, lots of researchers have put forward various kinds of methods to incorporate local spatial information into the original FCM algorithm. Some researchers [2]-[8] incorporated spatial information by modifying the membership functions or objective functions directly, and others [9]-[11] incorporated spatial information by introducing extra median images. The incorporation of spatial information makes the algorithm less prone to noise and terminates faster than the conventional FCM. Also, the constraint of FCM is a probabilistic constraint that the memberships of a pixel across clusters must sum to 1. This constraint does give meaningful results in applications where it is appropriate to interpret memberships as probabilities or degrees of sharing. However, since the memberships generated by this constraint are relative numbers, they are not suitable for applications in which the memberships are supposed to represent “typicality”, or compatibility with an elastic constraint [12][13]. When performing noise image segmentation, this kind of membership will make noise pixels, which are far from all cluster centers, affect all cluster centers almost equally, especially when dealing with high noise images, all cluster centers will be pulled towards the center of all noise pixels. To overcome the disadvantage of probabilistic constraint, the approach of credibilistic clustering was developed by Zhou et al. [14], which uses the credibility weights to measure the compactness of the data, and the memberships derived from credibilistic clustering algorithm (CCA) actually represent the “typicality” or compatibility of feature points. But there is no reference to discuss or study the differences of CCA and FCM in noise image segmentation and why CCA performs better. In this paper, we give an explanation of this by studying the differences of the memberships of CCA and FCM as well as discussing three different conditions. Based on this, we can declare that CCA is more suitable to noise image segmentation