为了更有效地对被噪声污染的脑部MR图像进行分割，提出了一种基于模糊核聚类和模糊Markov随机场的脑部MR图像分割算法。该算法在使用高斯径向基函数的核聚类目标函数中，引入了基于Markov随机场的补偿项，作为分割算法的空间约束。这种空间补偿项用Gibbs分布描述，实际上是一种归一化的核函数，其和用来度量灰度特征的核函数的形式是相似的，并且这种空间约束利用了分割结果的模糊信息。这种基于核函数和Markov随机场模型的算法克服了传统聚类以及核聚类算法的缺陷，不仅提出了更加合理的空间约束, 而且改善了原有的分割模型，因此可以得到更加分段光滑的聚类结果。通过对合成图像、模拟MR图像以及临床MR图像进行的分割实验以及和标准分割结果的比较表明，该算法优于相关算法，可以有效地分割被污染的MR图像。

In order to more effectively segment noise-corrupted brain MRI images, a kernelized clustering algorithm using fuzzy Markov random field (MRF) model is proposed. The proposed algorithm is implemented by incorporating the MRF based spatial constraints as a regularization term to the objective function of the kernelized fuzzy C-means clustering（FCM）. The spatial connectivity modeled by the Gibbs distribution is actually formulated as a normalized Gaussian radius basis function (GRBF), and very similar to the kernel function used to measure the intensity feature of image data. Due to the introduction of fuzzy information in the spatial constraints, the MRF and GRBF based clustering algorithm improves the segmentation model and usually outperforms the conventional intensity based FCM method and the corresponding kernelized clustering method. The modified algorithm can incline the solution to a piecewise smoother segmentation result. Experiments on synthetic data, simulated and real clinical MR images and the result comparisons with ground truth show the proposed algorithm is superior to its rivals and is effective to segment MR data corrupted by noise.