Robust Tensor Splines for Approximation of Diffusion Tensor MRI Data.
Robust Tensor Splines for Approximation of Diffusion Tensor MRI Data.
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用于近似扩散张量 MRI 数据的鲁棒张量样条。
DOI：
10.1109/cvprw.2006.179
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
Forder,JohnR
中科院分区：
文献类型：
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作者：
Barmpoutis,Angelos;Vemuri,BabaC;Forder,JohnR
在本文中，我们提出了一种新的和强大的样条逼近算法给定的噪声对称正定（SPD）张量场。这种张量场通常以扩散张量（DT）MRI数据集的形式出现在医学成像领域中。我们开发了一个统计上强大的算法，用于构建一个张量积的B-样条-近似和插值这些数据-使用黎曼度量的SPD张量的流形。我们的方法涉及两个步骤的过程，其中第一步使用黎曼距离，以评估张量样条通过计算扩散张量的加权固有平均值，第二步涉及最小化的黎曼距离之间的评估样条曲线和给定的数据。这两个步骤交替进行，以实现所需的张量样条近似给定的张量场。我们提出了我们的算法与四个现有的张量插值方法应用于DT-MRI数据从固定的心脏切片的兔子，并显示显着改善的结果中存在的噪声和离群值的比较。我们还提出了我们的算法使用合成生成的噪声张量场数据与离群值的验证结果。这种插值工作有许多应用，例如，DT-MRI注册，DT-MRI图谱构建等。本研究部分由NIH ROI NS 42075和佛罗里达大学放射学系资助。
In this paper, we present a novel and robust spline approximation algorithm given a noisy symmetric positive definite (SPD) tensor field. Such tensor fields commonly arise in the field of Medical Imaging in the form of Diffusion Tensor (DT) MRI data sets. We develop a statistically robust algorithm for constructing a tensor product of B-splines - for approximating and interpolating these data - using the Riemannian metric of the manifold of SPD tensors. Our method involves a two step procedure wherein the first step uses Riemannian distances in order to evaluate a tensor spline by computing a weighted intrinsic average of diffusion tensors and the second step involves minimization of the Riemannian distance between the evaluated spline curve and the given data. These two steps are alternated to achieve the desired tensor spline approximation to the given tensor field. We present comparisons of our algorithm with four existing methods of tensor interpolation applied to DT-MRI data from fixed heart slices of a rabbit, and show significantly improved results in the presence of noise and outliers. We also present validation results for our algorithm using synthetically generated noisy tensor field data with outliers. This interpolation work has many applications e.g., in DT-MRI registration, in DT-MRI Atlas construction etc. This research was in part funded by the NIH ROI NS42075 and the Department of Radiology, University of Florida.