Geometric and Statistical Models for Analysis of Two-Object Complexes
Geometric and Statistical Models for Analysis of Two-Object Complexes
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DOI：
10.1007/s11263-023-01800-2
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发表时间：
2023-04
影响因子：
19.5
通讯作者：
Zhiyuan Liu;J. Damon;J. S. Marron;S. Pizer;PhD Laurent Najman
中科院分区：
文献类型：
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作者：
Zhiyuan Liu;J. Damon;J. S. Marron;S. Pizer;PhD Laurent Najman
涉及附近物体的相关形状特征通常包含重要的解剖信息。然而，在多目标复合体的联合分析中，很难捕获物体内部和物体之间的形状信息。本文提出(1)基于一种称为链接结构的显式数学模型捕获物体之间的形状；(2)使用局部仿射帧捕获对刚性变换不变的形状特征；(3)使用一种称为NEUJIVE的统计方法捕获物体内部和物体之间（CoWBO）形状特征的相关性。由此产生的相关形状特征可以从不同的角度对多目标复合物进行全面的理解。首先，这些特征明确地说明了物体之间的位置和几何关系，这些关系在解剖学上是重要的。其次，局部仿射帧产生丰富的内部几何特征，这些特征不受全局对齐的影响。第三，对物体内部和物体之间形状的联合分析产生了鲁棒和有用的特征。为了证明所提出的方法，我们使用提取的两个功能相关的大脑结构——海马体和尾状体的形状特征来对自闭症患者和对照组进行分类。我们发现在各种形状特征的选择中，CoWBO特征的分类性能最好。此外，在所提出的方法形成的特征空间中，组间差异具有统计学意义。
Correlated shape features involving nearby objects often contain important anatomic information. However, it is difficult to capture shape information within and between objects for a joint analysis of multi-object complexes. This paper proposes (1) capturing between-object shape based on an explicit mathematical model called a linking structure, (2) capturing shape features that are invariant to rigid transformation using local affine frames and (3) capturing Correlation of Within- and Between-Object (CoWBO) shape features using a statistical method called NEUJIVE. The resulting correlated shape features give comprehensive understanding of multi-object complexes from various perspectives. First, these features explicitly account for the positional and geometric relations between objects that can be anatomically important. Second, the local affine frames give rise to rich interior geometric features that are invariant to global alignment. Third, the joint analysis of within- and between-object shape yields robust and useful features. To demonstrate the proposed methods, we classify individuals with autism and controls using the extracted shape features of two functionally related brain structures, the hippocampus and the caudate. We found that the CoWBO features give the best classification performance among various choices of shape features. Moreover, the group difference is statistically significant in the feature space formed by the proposed methods.