An improved anisotropic hierarchical fuzzy c-means method based on multivariate student t-distribution for brain MRI segmentation

• Reducing the effect of noise and preserving more details.
• Using multivariate t-distribution to improve the robustness.Using hierarchical FCM to reduce the effect of outliers.
• The method can obtain more accurate segmented results and estimated bias field.

Accurate segmentation for magnetic resonance (MR) images is an essential step in quantitative brain image analysis. However, due to the existence of intensity inhomogeneity (also named as bias field) and noise in the MR images, many segmentation methods are suffer from limited robustness and hard to find accurate results. This paper proposes an improved anisotropic multivariate student t-distribution based hierarchical fuzzy c-means method (IAMTHFCM). Firstly, improved anisotropic spatial information, defined in the neighborhoods of each pixel, is proposed to overcome the effect of the noise and preserve more detail information, especially for points with less repetitive patterns, such as corner and end points. Secondly, the improved anisotropic spatially information is utilized into a negative multivariate student t-distribution based log-posterior as the dissimilarity function to improve the robustness and accuracy. Thirdly, we use the hierarchical strategy to construct a more flexible objective function by considering the improved dissimilarity function itself as a sub-FCM, to make the method more robust and accurate to outliers and weak edges. Finally, the intensity inhomogeneities is modeled as a linear combination of a set of orthogonal basis functions, and parameterized by the coefficients of the orthogonal basis functions. Then the objective function is integrated with the bias field estimation and makes the proposed method can estimate the bias field meanwhile segmenting images. The segmentation and the bias field estimation can obtain benefit from each other. Our statistical results on both synthetic and clinical images show that the proposed method can overcome the difficulties caused by noise and bias fields and obtain more accurate results.