基于形态外观流形的群形态计量学分析

Naixiang Lian, C. Davatzikos
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引用次数: 4

摘要

计算解剖学领域已经开发出严格的框架来分析解剖形状,基于模板的微分同构变换。然而,用于模板翘曲的算法、正则化参数和模板本身的差异,导致相同解剖结构的不同表示。这些参数的变化被认为是混杂因素,因为它们会产生非唯一的表示。最近,对传统计算解剖学框架的扩展,以解释这种混淆的变化,表明学习从大量表示中派生的等价类可以导致改进和更稳定的形态描述符。在此,我们遵循该方法,估计由模板翘曲过程的不同参数获得的形态外观流形。我们的方法与计算机视觉领域的工作相似,在计算机视觉领域,光线、姿势和其他参数的变化会导致图像外观的变化,以不同的方式代表完全相同的人物。然后将该框架用于生物医学图像的分组配准和统计分析,通过对选定的完整形态学描述符采用最小方差准则进行流形约束优化,即遍历每个个体的形态学外观流形,直到组方差最小。有效地,这一过程消除了上述混淆效应,并可能导致形态表征反映纯粹的生物变异,而不是由建模假设和参数设置引入的变异。利用主成分分析法对流形进行局部近似,处理了形态外观流形的非线性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Groupwise morphometric analysis based on morphological appearance manifold
The field of computational anatomy has developed rigorous frameworks for analyzing anatomical shape, based on diffeomorphic transformations of a template. However, differences in algorithms used for template warping, in regularization parameters, and in the template itself, lead to different representations of the same anatomy. Variations of these parameters are considered as confounding factors as they give rise to non-unique representation. Recently, extensions of the conventional computational anatomy framework to account for such confounding variations have shown that learning the equivalence class derived from the multitude of representations can lead to improved and more stable morphological descriptors. Herein, we follow that approach, estimating the morphological appearance manifold obtained by varying parameters of the template warping procedure. Our approach parallels work in the computer vision field, in which variations lighting, pose and other parameters leads to image appearancemanifolds representing the exact same figure in different ways. The proposed framework is then used for groupwise registration and statistical analysis of biomedical images, by employing a minimum variance criterion on selected complete morphological descriptor to perform manifold-constrained optimization, i.e. to traverse each individual's morphological appearance manifold until group variance is minimal. Effectively, this process removes the aforementioned confounding effects and potentially leads to morphological representations reflecting purely biological variations, instead of variations introduced by modeling assumptions and parameter settings. The nonlinearity of a morphological appearancemanifold is treated via local approximations of the manifold via PCA.
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