Du Jia, Goh Alvina, Qiu Anqi
Division of Bioengineering, National University of Singapore, Singapore.
Inf Process Med Imaging. 2011;22:448-62. doi: 10.1007/978-3-642-22092-0_37.
We propose a novel large deformation diffeomorphic registration algorithm to align high angular resolution diffusion images (HARDI) characterized by Orientation Distribution Functions (ODF). Our proposed algorithm seeks an optimal diffeomorphism of large deformation between two ODF fields in a spatial volume domain and at the same time, locally reorients an ODF in a manner such that it remains consistent with the surrounding anatomical structure. We first extend ODFs traditionally defined in a unit sphere to a generalized ODF defined in R3. This makes it easy for an affine transformation as well as a diffeomorphic group action to be applied on the ODF. We then construct a Riemannian space of the generalized ODFs and incorporate its Riemannian metric for the similarity of ODFs into a variational problem defined under the large deformation diffeomorphic metric mapping (LDDMM) framework. We finally derive the gradient of the cost function in both Riemannian spaces of diffeomorphisms and the generalized ODFs, and present its numerical implementation. Both synthetic and real brain HARDI data are used to illustrate the performance of our registration algorithm.
我们提出了一种新颖的大变形微分同胚配准算法，用于对齐以方向分布函数（ODF）为特征的高角分辨率扩散图像（HARDI）。我们提出的算法在空间体积域中寻找两个ODF场之间大变形的最优微分同胚，同时以一种使其与周围解剖结构保持一致的方式对ODF进行局部重新定向。我们首先将传统上在单位球中定义的ODF扩展到在R3中定义的广义ODF。这使得仿射变换以及微分同胚群作用易于应用于ODF。然后，我们构建广义ODF的黎曼空间，并将其用于ODF相似性的黎曼度量纳入在大变形微分同胚度量映射（LDDMM）框架下定义的变分问题中。我们最终在微分同胚和广义ODF的黎曼空间中推导成本函数的梯度，并给出其数值实现。合成和真实的脑HARDI数据均用于说明我们配准算法的性能。
