A Robust Spatial Information-Theoretic GMM Algorithm for Bias Field Estimation and Brain MRI Segmentation

Due to their simplicity and flexibility, the unsupervised statistical models such as Gaussian mixture model (GMM) are powerful tools to address the brain magnetic resonance (MR) images segmentation problems. However, the GMM is based only on the intensity information, which makes it sensitive to noise. Lots of GMM-based segmentation algorithms have the low segmentation accuracy because of the influence caused by noise and intensity inhomogeneity. To further improve the segmentation accuracy, a robust spatial information-theoretic GMM algorithm is proposed in this paper to simultaneously estimate the intensity inhomogeneity and segment brain MR images. First, a novel spatial factor containing the non-local spatial information is incorporated to reduce the impact of noise. The proposed spatial factor not only takes into account the local neighboring information, but also considers the spatial structure information of pixels. Thus, our algorithm can retain more image details while reducing the influence of noise. Second, the mutual information (MI) maximization method is used to identify and eliminate outliers. Finally, to overcome the impact of intensity inhomogeneity, we use a linear combination of a set of orthogonal polynomials to approximate the bias field. The objective function is integrated with the bias field estimation model to segment the images and estimate the bias field simultaneously. The experimental results on both synthetic and clinical brain MR images show that the proposed algorithm can overcome the influence of noise and intensity inhomogeneity, and achieve more accurate segmentation results.