Laboratory of Neuro Imaging, UCLA School of Medicine, Los Angeles, CA 90095, USA.
IEEE Trans Med Imaging. 2011 Feb;30(2):184-202. doi: 10.1109/TMI.2010.2067451. Epub 2010 Sep 2.
In this paper, we used a nonconservative Lagrangian mechanics approach to formulate a new statistical algorithm for fluid registration of 3-D brain images. This algorithm is named SAFIRA, acronym for statistically-assisted fluid image registration algorithm. A nonstatistical version of this algorithm was implemented , where the deformation was regularized by penalizing deviations from a zero rate of strain. In , the terms regularizing the deformation included the covariance of the deformation matrices (Σ) and the vector fields (q) . Here, we used a Lagrangian framework to reformulate this algorithm, showing that the regularizing terms essentially allow nonconservative work to occur during the flow. Given 3-D brain images from a group of subjects, vector fields and their corresponding deformation matrices are computed in a first round of registrations using the nonstatistical implementation. Covariance matrices for both the deformation matrices and the vector fields are then obtained and incorporated (separately or jointly) in the nonconservative terms, creating four versions of SAFIRA. We evaluated and compared our algorithms' performance on 92 3-D brain scans from healthy monozygotic and dizygotic twins; 2-D validations are also shown for corpus callosum shapes delineated at midline in the same subjects. After preliminary tests to demonstrate each method, we compared their detection power using tensor-based morphometry (TBM), a technique to analyze local volumetric differences in brain structure. We compared the accuracy of each algorithm variant using various statistical metrics derived from the images and deformation fields. All these tests were also run with a traditional fluid method, which has been quite widely used in TBM studies. The versions incorporating vector-based empirical statistics on brain variation were consistently more accurate than their counterparts, when used for automated volumetric quantification in new brain images. This suggests the advantages of this approach for large-scale neuroimaging studies.
在本文中，我们使用非保守拉格朗日力学方法来构建一种新的统计算法，用于 3D 脑图像的流体配准。该算法名为 SAFIRA，是统计辅助流体图像配准算法的缩写。实现了该算法的非统计版本，其中通过惩罚应变率为零的偏差来正则化变形。在[1]中，正则化变形的项包括变形矩阵（Σ）和向量场（q）的协方差。在这里，我们使用拉格朗日框架重新表述了该算法，表明正则化项本质上允许在流动过程中发生非保守功。对于来自一组受试者的 3D 脑图像，使用非统计实现计算第一轮配准的向量场及其相应的变形矩阵。然后获得并纳入变形矩阵和向量场的协方差矩阵（分别或共同）到非保守项中，创建了 SAFIRA 的四个版本。我们在 92 个健康的同卵和异卵双胞胎的 3D 脑扫描上评估和比较了我们的算法性能；还对同一受试者中线勾画的胼胝体形状进行了 2D 验证。在进行了每项方法的初步测试以证明其有效性后，我们使用基于张量的形态测量学（TBM）比较了它们的检测能力，这是一种分析大脑结构局部体积差异的技术。我们使用从图像和变形场中得出的各种统计指标比较了每个算法变体的准确性。所有这些测试也都使用传统的流体方法运行，该方法在 TBM 研究中被广泛使用。在用于新大脑图像的自动体积量化时，纳入基于向量的大脑变异经验统计信息的版本始终比其对应版本更准确。这表明该方法在大规模神经影像学研究中的优势。
