An improved fuzzy c-means method based on multivariate skew-normal distribution for brain MR image segmentation

Accurate segmentation of magnetic resonance (MR) images is crucial for providing doctors with effective quantitative information for diagnosis. However, the presence of weak boundaries, intensity inhomogeneity, and noise in the images poses challenges for segmentation models to achieve optimal results. While deep learning models can offer relatively accurate results, the scarcity of labeled medical imaging data increases the risk of overfitting. To tackle this issue, this paper proposes a novel fuzzy c-means (FCM) model that integrates a deep learning approach. To address the limited accuracy of traditional FCM models, which employ Euclidean distance as a distance measure, we introduce a measurement function based on the skewed normal distribution. This function enables us to capture more precise information about the distribution of the image. Additionally, we construct a regularization term based on the Kullback-Leibler (KL) divergence of high-confidence deep learning results. This regularization term helps enhance the final segmentation accuracy of the model. Moreover, we incorporate orthogonal basis functions to estimate the bias field and integrate it into the improved FCM method. This integration allows our method to simultaneously segment the image and estimate the bias field. The experimental results on both simulated and real brain MR images demonstrate the robustness of our method, highlighting its superiority over other advanced segmentation algorithms.