A Nonconservative Lagrangian Framework for Statistical Fluid Registration-SAFIRA
A Nonconservative Lagrangian Framework for Statistical Fluid Registration-SAFIRA
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DOI：
10.1109/tmi.2010.2067451
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发表时间：
2011-02-01
影响因子：
10.6
通讯作者：
Thompson, Paul M.
中科院分区：
文献类型：
--
作者：
Brun, Caroline C.;Lepore, Natasha;Thompson, Paul M.
在本文中，我们使用非保守拉格朗日力学方法制定了一种用于 3D 脑图像流体配准的新统计算法。该算法被命名为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[9]，其中通过惩罚与零应变率的偏差来规范变形。在[9]中，规范变形的术语包括变形矩阵（Sigma）和矢量场（q）的协方差。在这里，我们使用拉格朗日框架重新表述该算法，表明正则化项本质上允许在流动过程中发生非保守工作。给定一组受试者的 3D 大脑图像，使用非统计实现在第一轮配准中计算矢量场及其相应的变形矩阵。然后获得变形矩阵和矢量场的协方差矩阵，并将其合并（单独或联合）在非保守项中，创建 SAFIRA 的四个版本。我们在健康同卵双胞胎和异卵双胞胎的 92 份 3D 脑部扫描中评估并比较了我们的算法的性能；还显示了同一受试者中线描绘的胼胝体形状的二维验证。在对每种方法进行初步测试后，我们使用基于张量的形态测量（TBM）（一种分析大脑结构局部体积差异的技术）比较了它们的检测能力。我们使用从图像和变形场导出的各种统计指标来比较每个算法变体的准确性。所有这些测试也是使用传统的流体方法进行的，该方法在 TBM 研究中已得到相当广泛的应用。当用于新大脑图像的自动体积量化时，结合了基于矢量的大脑变异经验统计的版本始终比其对应版本更准确。这表明这种方法对于大规模神经影像研究具有优势。
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 [9], where the deformation was regularized by penalizing deviations from a zero rate of strain. In [9], the terms regularizing the deformation included the covariance of the deformation matrices (Sigma) 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.