关键词: 微分同胚, 切空间, 李群, 邻域选择, MRI图像配准

Abstract: 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.

Key words: diffeomorphism, tangent space, Lie group, neighborhood selection, MRI image registration