The brain magnetic resonance (MR) image has an embedded bias field. This field needs to be corrected to obtain the actual MR image for classification. Bias field, being a slowly varying nonlinear field, needs to be estimated. In this paper, we have proposed three schemes and in turn three algorithms to segment the given MR image while estimating the bias field. The problem is compounded when the MR image is corrupted with noise in addition to the inherent bias field. The notions of possibilistic and fuzzy membership have been combined to take care of the modeling of the bias field and noise. The weighted typicality measure together with the weighted fuzzy membership has been used to model the image. The above resulted in the proposed Bias Corrected Possibilistic Fuzzy C-Means (BCPFCM) strategy and the algorithm. Further reinforcing the neighbourhood data to the modeling aspect has resulted in the two other strategies namely Bias Corrected Possibilistic Neighborhood Fuzzy C-Means (BCPNFCM) and Bias Corrected Separately weighted Possibilistic Neighborhood Fuzzy C-Means (BCSPNFCM). The proposed algorithms have successfully been tested with synthetic data with bias field of low and high spatial frequency. Noisy brain MR images with Gaussian Noise of varying strength have been considered from the BrainWeb database. The algorithms have also been tested on real brain MR data set with axial and sagittal view and it has been found that the proposed algorithms produced segmentation results with less percentage of misclassification errors as compared to the Bias Corrected Fuzzy C-Means (BCFCM) algorithm proposed by Ahmed et al. [4]. The performance of the proposed algorithms has been compared with algorithms from other paradigm in the context of Tanimoto's index. 
Modified possibilistic fuzzy C-means algorithms for segmentation of magnetic resonance image