Department of Radiology, University of Pennsylvania, Philadelphia, PA, United States.
Med Image Anal. 2011 Dec;15(6):814-29. doi: 10.1016/j.media.2011.06.003. Epub 2011 Jul 28.
Computational anatomy quantifies anatomical shape based on diffeomorphic transformations of a template. However, different templates warping algorithms, regularization parameters, or templates, lead to different representations of the same exact anatomy, raising a uniqueness issue: variations of these parameters are confounding factors as they give rise to non-unique representations. Recently, it has been shown that learning the equivalence class derived from the multitude of representations of a given anatomy can lead to improved and more stable morphological descriptors. Herein, we follow that approach, by approximating this equivalence class of morphological descriptors by a (nonlinear) morphological appearance manifold fitting to the data via a locally linear model. Our approach parallels work in the computer vision field, in which variations lighting, pose and other parameters lead to image appearance manifolds representing the exact same figure in different ways. The proposed framework is then used for group-wise registration and statistical analysis of biomedical images, by employing a minimum variance criterion to perform manifold-constrained optimization, i.e. to traverse each individual's morphological appearance manifold until group variance is minimal. The hypothesis is that this process is likely to reduce aforementioned confounding effects and potentially lead to morphological representations reflecting purely biological variations, instead of variations introduced by modeling assumptions and parameter settings.
计算解剖学基于模板的可变形变换来量化解剖形状。然而，不同的模板变形算法、正则化参数或模板会导致对同一解剖结构的不同表示，从而产生唯一性问题：这些参数的变化是混杂因素，因为它们会产生非唯一的表示。最近，已经表明，通过学习从给定解剖结构的众多表示中导出的等价类，可以得到改进的和更稳定的形态描述符。在这里，我们遵循这种方法，通过通过局部线性模型将形态描述符的等价类近似为（非线性）形态外观流形，以拟合数据。我们的方法与计算机视觉领域的工作类似，在该领域中，光照、姿势和其他参数的变化会导致以不同方式表示完全相同图形的图像外观流形。然后，通过使用最小方差准则来执行流形约束优化，即遍历每个人的形态外观流形，直到组方差最小，从而将所提出的框架用于生物医学图像的组间配准和统计分析。假设该过程可能会减少上述混杂效应，并可能导致反映纯粹生物学变化的形态表示，而不是由建模假设和参数设置引入的变化。
