由于人体脑血管结构复杂, 空间比例小, 三维分割和重构十分困难, 本文面向时飞磁共振血管造影(TOF MRA)数据提出了一种新的瑞利高斯有限混合模型来实现脑血管的自动提取和分割。首先, 对已有的混合模型进行了分析; 然后, 采用最大强度投影法(MIP)预处理脑部数据后采用高斯分布拟合血管类, 采用瑞利分布和高斯分布拟合非血管类。提出的模型构造简单, 参数向量较少; 在血管与非血管的混合区域, 模型与灰度直方图具有较好的拟合性。模型在传统期望最大化(EM)算法中加入随机扰动项构造随机期望最大化(SEM)算法来实现混合模型的参数估计, 降低了算法对初值的依赖, 同时提高了鲁棒性。实验证明, 与已有双高斯模型相比, 血管点数增加了27%, 可细分到三级血管且细节的连通性更好。本模型可更准确地拟合数据的灰度分布曲线, 有效地分割脑血管主分支及周围较细小分支, 泛化性较好并可应用于相似系统中。

As the brain vessel of human has complex topological structure and smaller space proportion,it is hard to be segmented and reconstructed in three dimensions. Therefore, this paper proposes an automatic statistical intensity based approach for extracting the 3D cerebrovascular system from time-of-flight (TOF) Magnetic Resonance Angiography (MRA) data. First, the Finite Mixture Model (FMM) is analyzed, and it is used to fit the intensity histogram of the brain image sequence preprocessed by the Maximum Intensity Projection(MIP). Then, the Gaussian distribution is used to fit the vessel, and the Gaussian distribution and Rayleigh distribution are used to fit other low intensity tissues. Since the model is easy to realize and has a short parameter vector, it decreases the parameter drift problem and can fit the intensity histogram well, especially in the cross region between the cerebrovascular and other tissues. Moreover, the stochastic disturbance is added in the traditional Expectation Maximization(EM) to construct Stochastic Estimation Maximization (SEM) algorithm to estimate the parameter vector, by which the method shows low initial value dependence and a high robust. As compared with the experiments, this model can segment more 27% cerebrovascular voxels than two Gaussian models do and it can segment in three level for the small cerebrovascular branches with a better connectivity. The model can fit a gray distribition curve of the data accurately, segment the main branch of brain vessel and slight vessel branch and can be used in other similar systems.