Elastic Statistical Shape Analysis of Biological Structures with Case Studies: A Tutorial
Elastic Statistical Shape Analysis of Biological Structures with Case Studies: A Tutorial
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DOI：
10.1007/s11538-019-00609-w
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发表时间：
2019-07-01
影响因子：
3.5
通讯作者：
Kurtek, Sebastian
中科院分区：
文献类型：
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作者：
Min Ho Cho;Asiaee, Amir;Kurtek, Sebastian
我们描述了一个最新的曲线统计形状分析框架，并展示了它对各种生物数据集的适用性。所提出的方法是基于形状的函数表示，称为平方根速度函数和密切相关的弹性度量。这种方法的主要优点是它对重新参数化的不变性(除了标准的平移、旋转和缩放的保形变换)，以及计算对象之间的最优配准(点对应)的能力。在定义的形状之间距离的基础上，我们还描述了用于计算样本统计的工具，包括均值和协方差。基于协方差结构，还可以通过主成分分析来探索形状样本的变异性。最后，估计的均值和协方差可以用来定义形状空间上的包络高斯模型，这些模型很容易进行采样。我们提供了关于不同生物学数据集的多个案例研究，包括(1)叶轮廓，(2)颈内动脉，(3)扩散张量磁共振成像纤维束，(4)多形性胶质母细胞瘤，和(5)小鼠脊椎。另外，我们还提供了一个可用于生成本手稿中给出的结果的MatLab包。
We describe a recent framework for statistical shape analysis of curves and show its applicability to various biological datasets. The presented methods are based on a functional representation of shape called the square-root velocity function and a closely related elastic metric. The main benefit of this approach is its invariance to reparameterization (in addition to the standard shape-preserving transformations of translation, rotation and scale), and ability to compute optimal registrations (point correspondences) across objects. Building upon the defined distance between shapes, we additionally describe tools for computing sample statistics including the mean and covariance. Based on the covariance structure, one can also explore variability in shape samples via principal component analysis. Finally, the estimated mean and covariance can be used to define Wrapped Gaussian models on the shape space, which are easy to sample from. We present multiple case studies on various biological datasets including (1) leaf outlines, (2) internal carotid arteries, (3) Diffusion Tensor Magnetic Resonance Imaging fiber tracts, (4) Glioblastoma Multiforme tumors, and (5) vertebrae in mice. We additionally provide a MATLAB package that can be used to produce the results given in this manuscript.