Brain MR image segmentation based on local Gaussian mixture model and nonlocal spatial regularization

•We proposed a novel variational approach for brain image segmentation.•A local data fitting term and a nonlocal spatial regularization term are combined.•The data fitting term is based on local Gaussian mixture model.•The nonlocal regularization term is helpful for the preservation of image structures.•By experiments on simulated images and clinic images, we obtained promising results.

Brain Magnetic Resonance (MR) images often suffer from the inhomogeneous intensities caused by the bias field and heavy noise. The most widely used image segmentation algorithms, which typically rely on the homogeneity of image intensities in different regions, often fail to provide accurate segmentation results due to the existence of bias field and heavy noise. This paper proposes a novel variational approach for brain image segmentation with simultaneous bias correction. We define an energy functional with a local data fitting term and a nonlocal spatial regularization term. The local data fitting term is based on the idea of local Gaussian mixture model (LGMM), which locally models the distribution of each tissue by a linear combination of Gaussian function. By the LGMM, the bias field function in an additive form is embedded to the energy functional, which is helpful for eliminating the influence of the intensity inhomogeneity. For reducing the influence of noise and getting a smooth segmentation, the nonlocal spatial regularization is drawn upon, which is good at preserving fine structures in brain images. Experiments performed on simulated as well as real MR brain data and comparisons with other related methods are given to demonstrate the effectiveness of the proposed method.