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Intensity inhomogeneities cause considerable difficulties in the quantitative analysis of magnetic resonanceimages (MRIs). Consequently, intensity inhomogeneities estimation is a necessary step before quantitative analysis of MR data can be undertaken. This study proposes a new energy minimisation framework for simultaneous estimation of the intensity inhomogeneities and segmentation. The method was formulated by modifying the objective function of the standard fuzzy c-means algorithm to compensate for intensity inhomogeneities by using basis functions and to compensate for noise by using improved non-local information. The energy function depends on the coefficients of the basis functions, the membership ratios, the centroid of the tissues and an improved non-local information in the image. Intensity inhomogeneities estimation and image segmentation are simultaneously achieved by calculating the result of minimising this energy. The non-local framework has been widely used to provide non-local information; however, the traditional framework only considers the neighbouring patch information, which will lose information of the corner and end points. This study presents an improved non-local framework, which can contain the corner and end points region information. Experimental results on both real MRIs and simulated MR data show that the authors method can obtain more accurate results when segmenting images with bias field and noise.