The standard fuzzy C-means (FCM) algorithm does not fully utilize the spatial information for image segmentation and is sensitive to noise especially in the presence of intensity inhomogeneity in magnetic resonance imaging (MRI) images. The underlying reason is that a single fuzzy membership function in FCM algorithm cannot properly represent pattern associations to all clusters. In this paper, we present a spatial fuzzy C-means (SpFCM) algorithm for the segmentation of MRI images. The algorithm utilizes spatial information from the neighbourhood of each pixel under consideration and is realized by defining a probability function. A new membership function is introduced using this spatial information to generate local membership values for each pixel. Finally, new clustering centers and weighted joint membership functions are presented based on the local and global membership functions. The resulting SpFCM algorithm solves the problem of sensitivity to noise and intensity inhomogeneity in MRI data and thereby improves the segmentation results. The experimental results on several simulated and real-patient MRI brain images show that the SpFCM algorithm has superior performance on image segmentation when compared to some FCM-based algorithms.
Surface fitting is one of the well‐known retrospective methods for bias field estimation from magnetic resonance imaging (MRI) images. Bias field in MRI images is primarily caused because of radio frequency–coil nonuniformity, improper image acquisition process, patient movement, and so on. The bias field can be characterized by any slow variant and smooth function because of its slow variant nature. In this paper, we present a comparative study between polynomial and Gaussian surface fitting methods. In particular, we have used both the second‐ and third‐order polynomial functions to estimate the bias field. In this study, we approximate the bias field in two different ways. In the first method, the surfaces are fitted on the anatomical tissue regions individually and then fused to estimate the bias field. Conversely, in the second method, we have done the same over the entire image region. We have tested on three volumes of simulated and one volume of real‐patient MRI brain images and validated the results by both the qualitative and quantitative analyses. The quantitative analyses are presented in standard deviation and coefficient of joint variation. The analysis of the simulation results show that the Gaussian surface fitting method yields better results in both the cases, where the surface fitting is done on entire image and individual tissue regions.
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