Hao Xiang, Whitaker Ross T, Fletcher P Thomas
Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT, USA.
Inf Process Med Imaging. 2011;22:13-24. doi: 10.1007/978-3-642-22092-0_2.
We present a new geodesic approach for studying white matter connectivity from diffusion tensor imaging (DTI). Previous approaches have used the inverse diffusion tensor field as a Riemannian metric and constructed white matter tracts as geodesics on the resulting manifold. These geodesics have the desirable property that they tend to follow the main eigenvectors of the tensors, yet still have the flexibility to deviate from these directions when it results in lower costs. While this makes such methods more robust to noise, it also has the serious drawback that geodesics tend to deviate from the major eigenvectors in high-curvature areas in order to achieve the shortest path. In this paper we formulate a modification of the Riemannian metric that results in geodesics adapted to follow the principal eigendirection of the tensor even in high-curvature regions. We show that this correction can be formulated as a simple scalar field modulation of the metric and that the appropriate variational problem results in a Poisson's equation on the Riemannian manifold. We demonstrate that the proposed method results in improved geodesics using both synthetic and real DTI data.
我们提出了一种用于从扩散张量成像（DTI）研究白质连通性的新测地线方法。先前的方法将逆扩散张量场用作黎曼度量，并将白质束构建为所得流形上的测地线。这些测地线具有这样的理想特性，即它们倾向于沿着张量的主特征向量，但当这样做能降低成本时，仍具有偏离这些方向的灵活性。虽然这使得此类方法对噪声更具鲁棒性，但它也有一个严重的缺点，即测地线为了达到最短路径，在高曲率区域往往会偏离主特征向量。在本文中，我们制定了一种黎曼度量的修正方法，即使在高曲率区域，也能使测地线适应沿着张量的主特征方向。我们表明，这种修正可以被表述为度量的一个简单标量场调制，并且适当的变分问题会在黎曼流形上产生一个泊松方程。我们使用合成和真实的DTI数据证明了所提出的方法能产生改进的测地线。
