Fast and Robust Fuzzy C-Means Algorithms for Automated Brain MR Image Segmentation

IntroductIon By definition, image segmentation represents the partitioning of an image into nonoverlapping, consistent regions, which appear to be homogeneous with respect to some criteria concerning gray level intensity and/or texture. The fuzzy c-means (FCM) algorithm is one of the most widely used method for data clustering, and probably also for brain image segmentation (Bezdek & Pal., 1991). However, in this latter case, standard FCM is not efficient by itself, as it is unable to deal with that relevant property of images that neighbor pixels are strongly correlated. Ignoring this specific-ity leads to strong noise sensitivity and several other imaging artifacts. Recently, several solutions were given to improve the performance of segmentation. Most of them involve using local spatial information: the own gray level of a pixel is not the only information that contributes to its assignment to the chosen cluster. Its neighbors also have their influence while getting a label. Pham and Prince (1999) modified the FCM objective function by including a spatial penalty, enabling the iterative algorithm to estimate spatially smooth membership functions. Ahmed, Yamany, Mohamed, Farag, and Moriarty (2002) introduced a neighborhood averaging additive term into the objective function of FCM, calling the algorithm bias corrected FCM (BCFCM). This approach has its own merits in bias field estimation , but it computes the neighborhood term in every iteration step, giving the algorithm a serious computational load. Moreover, the zero gradient condition at the estimation of the bias term produces a significant amount of misclassifications (Siyal & Yu, 2005). Ch-uang, Tzeng, Chen, Wu, and Chen (2006) proposed averaging the fuzzy membership function values and reassigning them according to a tradeoff between the original and averaged membership values. This approach can produce accurate clustering if the tradeoff is well adjusted empirically, but it is enormously time consuming. In order to reduce the execution time, Szi-lágyi, Benyó, Szilágyi, and Adam (2003), and Chen and Zhang (2004) proposed to evaluate the neighborhoods of each pixel as a prefiltering step, and perform FCM afterwards. The averaging and median filters, followed by FCM clustering, are referred to as FCM_S1 and FCM_S2, respectively (Chen & Zhang, 2004). Szilá-gyi et al. (2003) also pointed out that once having the neighbors evaluated, and thus for each pixel having extracted a one-dimensional feature vector, FCM can be performed on the basis of the gray level histogram, clustering the gray levels instead of the pixels, which significantly reduces …