A Measurement Error Model Based on Finite Mixture of the Skew-Normal Distributions for Brain MR Image Segmentation

The accuracy of medical image segmentation plays a crucial role in assisting with diagnosis. One commonly used method is the Gaussian mixture model (GMM) due to its high accuracy and low complexity. However, GMM faces challenges when dealing with images that follow asymmetrical distributions, as it is primarily designed for symmetrical distributions. Additionally, GMM does not account for measurement errors, which can hinder accurate distribution fitting when images contain various measurement errors. Furthermore, GMM does not incorporate spatial information, making it susceptible to noise during image segmentation. To address these issues, we propose a finite mixture measurement error model based on skew-normal distributions. This model allows for varying variances of measurement errors among different subjects. Furthermore, we introduce a novel anisotropic spatial information constraint term to preserve object details while reducing the impact of noise. Finally, we propose an EM type algorithm to estimate the parameters and maximize the likelihood. Experimental results using brain MR images demonstrate that our proposed method outperforms existing techniques in terms of segmentation accuracy.