Segmentation of bias field induced brain MR images using rough sets and stomped-t distribution

© 2019 Elsevier Inc. Over the past few decades, automatic segmentation of brain magnetic resonance (MR) images into different tissue classes has remained an important research area, particularly due to the presence of bias field artifact in MR images. In this regard, the stomped normal (StN) distribution is proved to generate an optimal representation of the intensity distribution in brain MR images, by incorporating the properties of rough sets in the probabilistic framework. The StN distribution is capable of successfully modelling the central tendency, dispersion, and width of the intensity distribution. However, it does not take into consideration the kurtosis of the distribution, which controls the concentration of values around the mean and shape of the tail of intensity distribution. In this regard, the paper presents a novel method for simultaneous segmentation and bias field correction in brain MR images. It integrates the concept of rough sets and the merit of a recently introduced probability distribution, called stomped-t (St-t) distribution. The St-t distribution incorporates the property of kurtosis in rough-probabilistic framework, where each tissue class is modelled using a crisp lower approximation and a probabilistic boundary region. The brain MR image is modelled using a mixture of finite number of St-t distributions and one uniform distribution. The uniform distribution takes into account cerebro-spinal fluid, pathologies, and other non-brain tissues. The proposed method employs both expectation-maximization algorithm and hidden Markov random field model for accurate and robust image segmentation. The performance of the proposed approach, along with a comparison with related methods, is illustrated on a set of synthetic and real brain MR images for different bias fields and noise levels.