Brain MR image segmentation based on an adaptive combination of global and local fuzzy energy

This paper presents a novel fuzzy algorithm for segmentation of brain MR images and simultaneous estimation of intensity inhomogeneity. The proposed algorithm defines an objective function including a local fuzzy energy and a global fuzzy energy. Based on the assumption that the local image intensities belonging to each different tissue satisfy Gaussian distributions with different means, we derive the local fuzzy energy by utilizing maximum a posterior probability (MAP) and Bayes rule. The global fuzzy energy is defined by measuring the distance between the original image and the corresponding inhomogeneity-free image. We combine the global fuzzy energy with the local fuzzy energy using an adaptive weight function whose value varies with the local contrast of the image. This combination enables the proposed algorithm to address intensity inhomogeneity and to improve the accuracy of segmentation and its robustness to initialization. Besides, the proposed algorithm incorporates neighborhood spatial information into the membership function to reduce the impact of noise. Experimental results for synthetic and real images validate the desirable performances of the proposed algorithm.