Tensor splines for interpolation and approximation of DT-MRI with applications to segmentation of isolated rat hippocampi
Tensor splines for interpolation and approximation of DT-MRI with applications to segmentation of isolated rat hippocampi
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DOI：
10.1109/tmi.2007.903195
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发表时间：
2007-11-01
影响因子：
10.6
通讯作者：
Forder, John R.
中科院分区：
文献类型：
--
作者：
Barmpoutis, Angelos;Vemuri, Baba C.;Forder, John R.
在本文中，我们提出了用于扩散张量（对称正定（SPD）矩阵）统计鲁棒插值和近似的新算法，并使用它们来开发现有标量场分割概率算法的重要扩展，以便分割扩散张量磁共振成像（DT-MRI）数据集。使用 SPD 矩阵空间上的黎曼度量，我们提出了一种新颖且鲁棒的 B 样条算法的高阶（三次）连续张量积来近似 SPD 扩散张量场。得到的近似值被适当地称为张量样条。接下来，我们通过联合估计标签（分配给每个体素）场来分割扩散张量场，该标签由高斯马尔可夫测量场（GMMF）和代表标记区域的每个平滑张量样条模型的参数建模。给出了来自离体大鼠海马体的合成数据和真实扩散张量场的插值、近似和分割结果，并进行了验证。我们还对我们的算法与现有方法进行了比较，并显示在存在噪声和异常值的情况下显着改进的结果。
In this paper, we present novel algorithms for statistically robust interpolation and approximation of diffusion tensors-which are symmetric positive definite (SPD) matrices-and use them in developing a significant extension to an existing probabilistic algorithm for scalar field segmentation, in order to segment diffusion tensor magnetic resonance imaging (DT-MRI) datasets. Using the Riemannian metric on the space of SPD matrices, we present a novel and robust higher order (cubic) continuous tensor product of B-splines algorithm to approximate the SPD diffusion tensor fields. The resulting approximations are appropriately dubbed tensor splines. Next, we segment the diffusion tensor field by jointly estimating the label (assigned to each voxel) field, which is modeled by a Gauss Markov measure field (GMMF) and the parameters of each smooth tensor spline model representing the labeled regions. Results of interpolation, approximation, and segmentation are presented for synthetic data and real diffusion tensor fields from an isolated rat hippocampus, along with validation. We also present comparisons of our algorithms with existing methods and show significantly improved results in the presence of noise as well as outliers.