A spatially constrained skew Student’s-t mixture model for brain MR image segmentation and bias field correction

Abstract

Accurate segmentation of brain magnetic resonance images is a key step in quantitative analysis of brain images. Finite mixture model is one of the most widely used methods in brain magnetic resonance image segmentation. However, due to the presence of intensity inhomogeneity artifact and noise, the image histogram distribution of brain MR images may follow a heavy tailed distribution or asymmetric distribution, which makes traditional finite mixture model, such as Gaussian mixture model, hard to achieve accurate segmentation results. To alleviate these problems, a novel spatially constrained finite skew student’s-t mixture model is proposed in this paper. Firstly, we propose anisotropic two-level spatial information, which combines the prior and posterior probabilities, to reduce the impact of noise. The proposed spatial information can preserve rich details, such as edges and corners. Secondly, we couple the anisotropic spatial information into the skew student’s-t distribution to fit the intensity distribution of observation data with heavy tail distribution or asymmetric distribution. Thirdly, we use a linear combination of a set of orthogonal basis functions to model the intensity inhomogeneities. Finally, the objective function integrates both tissue segmentation and the bias field estimation. In the implementation, we used an improved expectation maximization (EM) algorithm to estimate the model parameters. The experimental results of our model on synthetic data and brain magnetic resonance images are better than other state-of-the-art segmentation methods.