针对传统高斯混合模型应用于彩色图像分割时计算复杂度高等问题, 提出一种多阶抽样的高斯混合模型的彩色图像分割算法。首先，给出采样数定理及其证明，并推导出与聚类类别数和最小聚类相关的最小采样数目；其次，设计一罚函数判断抽样优劣，消除抽样对聚类模型影响，根据最小采样数数目，对像素点进行均匀采样，并利用高斯混合模型对采样像素点进行聚类；最后，定义像素点和类之间的距离，对剩余的像素点按距离最近原则进行划分。实验结果表明算法具有有效性。

The application of classical Gaussian mixture model to image segmentation has highly computational complexity. A image segmentation method based on Gaussian mixture model with multi-sampling is proposed in order to solve this problem. First, the sampling theorem is given and proved,and the minimum sample size is derived according to the smallest cluster and cluster number. Second, a penalty function, which is to judge the good sample, has been designed to eliminate the error of clustering model,and image pixels are sampled based on the minimum sample size to be clustered according to Gaussian mixture model. Finally, by the means of the definition on the distance between a pixel point and the categories, the remaining points is assigned respective cluster depending on the principles of the nearest distance. The experimental results show the effectiveness of the algorithm.