Lepore Natasha, Brun Caroline A, Chiang Ming-Chang, Chou Yi-Yu, Dutton Rebecca A, Hayashi Kiralee M, Lopez Oscar L, Aizenstein Howard J, Toga Arthur W, Becker James T, Thompson Paul M
Laboratory of Neuro Imaging, Department of Neurology, David Geffen School of Medicine at UCLA, Los Angeles, CA 90095, USA.
Med Image Comput Comput Assist Interv. 2006;9(Pt 1):191-8. doi: 10.1007/11866565_24.
Tensor-based morphometry (TBM) is widely used in computational anatomy as a means to understand shape variation between structural brain images. A 3D nonlinear registration technique is typically used to align all brain images to a common neuroanatomical template, and the deformation fields are analyzed statistically to identify group differences in anatomy. However, the differences are usually computed solely from the determinants of the Jacobian matrices that are associated with the deformation fields computed by the registration procedure. Thus, much of the information contained within those matrices gets thrown out in the process. Only the magnitude of the expansions or contractions is examined, while the anisotropy and directional components of the changes are ignored. Here we remedy this problem by computing multivariate shape change statistics using the strain matrices. As the latter do not form a vector space, means and covariances are computed on the manifold of positive-definite matrices to which they belong. We study the brain morphology of 26 HIV/AIDS patients and 14 matched healthy control subjects using our method. The images are registered using a high-dimensional 3D fluid registration algorithm, which optimizes the Jensen-Rényi divergence, an information-theoretic measure of image correspondence. The anisotropy of the deformation is then computed. We apply a manifold version of Hotelling's T2 test to the strain matrices. Our results complement those found from the determinants of the Jacobians alone and provide greater power in detecting group differences in brain structure.
基于张量的形态测量学（TBM）在计算解剖学中被广泛应用，作为理解结构性脑图像之间形状变化的一种手段。通常使用一种三维非线性配准技术将所有脑图像与一个共同的神经解剖模板对齐，并对变形场进行统计分析以识别解剖结构上的组间差异。然而，这些差异通常仅根据与配准过程计算出的变形场相关联的雅可比矩阵的行列式来计算。因此，这些矩阵中包含的许多信息在这个过程中被舍弃了。只检查了扩张或收缩的幅度，而变化的各向异性和方向分量被忽略了。在这里，我们通过使用应变矩阵计算多变量形状变化统计量来解决这个问题。由于应变矩阵并不构成一个向量空间，所以在它们所属的正定矩阵流形上计算均值和协方差。我们使用我们的方法研究了26名艾滋病毒/艾滋病患者和14名匹配的健康对照受试者的脑形态。使用一种高维三维流体配准算法对图像进行配准，该算法优化了詹森 - 雷尼散度，这是一种图像对应性的信息论度量。然后计算变形的各向异性。我们将霍特林T2检验的流形版本应用于应变矩阵。我们的结果补充了仅从雅可比行列式中发现的结果，并在检测脑结构的组间差异方面提供了更大的功效。
