基于自适应切空间的MRI图像配准

摘要

微分同胚是一种光滑可逆的变换,在MRI图像配准中可以保证图像形变后的拓扑结构保持不变,同时避免出现不合理的物理现象.为了在空间变换中获得更合理的同胚映射,高维空间中数据的非线性结构被考虑,基于流形学习方法提出一种自适应切空间的MRI图像配准算法.首先,把MRI数据构造成对称正定(SPD)的协方差矩阵,然后形成李群;接着,利用样本点邻域的局部切空间来表示李群的几何结构的非线性;接下来,在流形上用自适应邻域选择的方法形成的线性子空间去逼近局部切空间,提高切空间的局部线性化程度,从而最大限度地保留流形的局部非线性结构,得到最优的同胚映射.仿真数据和临床数据的实验结果显示,与传统的非参数微分同胚配准算法相比,该算法在高维稠密形变场上获得更高的拓扑保持度,最终提高图像配准精度.%The diffeomorphism is a differential transformation with smooth and invertible properties,which leading to topology preservation between anatomic individuals while avoiding physically implausible phenomena during MRI image registration.In order to yield a more plausible diffeomorphism for spatial transformation,nonlinear structure of high-dimensional data was considered,and an MRI image registration using manifold learning based on adaptive tangent space was put forward.Firstly,Symmetric Positive Definite (SPD) covariance matrices were constructed by voxels from an MRI image,then to form a Lie group manifold.Secondly,tangent space on the Lie group was used to locally approximate nonlinear structure of the Lie group manifold.Thirdly,the local linear approximation was adaptively optimized by selecting appropriate neighborhoods for each sample voxel,therefore the linearization degree of tangent space was improved,the local nonlinearization structure of manifold was highly preserved,and the best optimal diffeomorphism could be obtained.Numerical comparative experiments were conducted on both synthetic data and clinical data.Experimental results show that compared with the existing algorithm,the proposed algorithm obtains a higher degree of topology preservation on a dense high-dimensional deformation field,and finally improves the registration accuracy.