Skeletons, Object Shape, Statistics
Skeletons, Object Shape, Statistics
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DOI：
10.3389/fcomp.2022.842637
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发表时间：
2022-10
影响因子：
2.6
通讯作者：
S. Pizer;J. S. Marron;J. Damon;Jared Vicory;A. Krishna;Zhiyuan Liu;Mohsen Taheri
中科院分区：
文献类型：
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作者：
S. Pizer;J. S. Marron;J. Damon;Jared Vicory;A. Krishna;Zhiyuan Liu;Mohsen Taheri
3D 以及 2D 中的对象和对象复合体都有许多可能的表示形式。其中骨骼表示具有特殊的优点和一些局限性。对于称为“s-reps”的特殊骨骼表示形式，这些优点包括非常适合表示板状物体群体以及对这些群体的统计应用。如果人们认识到 s-rep 存在于弯曲的形状空间中，那么完成这些统计应用是最好的。在这里，我们将阐述 s-reps 的定义、它们的优点和局限性、它们的数学特性、将 s-reps 拟合到单对象和多对象边界的方法、测量这些对象和多对象表示的统计数据的方法，以及涉及统计的此类应用的示例。虽然本文描述了这些方法的基本理论、思想和程序，并且已经产生了许多带有评估的应用，但在与其他形状表示的比较、新的应用领域和进一步的方法论发展方面仍然存在许多有趣的开放机会，其中许多都在这里明确讨论。
Objects and object complexes in 3D, as well as those in 2D, have many possible representations. Among them skeletal representations have special advantages and some limitations. For the special form of skeletal representation called “s-reps,” these advantages include strong suitability for representing slabular object populations and statistical applications on these populations. Accomplishing these statistical applications is best if one recognizes that s-reps live on a curved shape space. Here we will lay out the definition of s-reps, their advantages and limitations, their mathematical properties, methods for fitting s-reps to single- and multi-object boundaries, methods for measuring the statistics of these object and multi-object representations, and examples of such applications involving statistics. While the basic theory, ideas, and programs for the methods are described in this paper and while many applications with evaluations have been produced, there remain many interesting open opportunities for research on comparisons to other shape representations, new areas of application and further methodological developments, many of which are explicitly discussed here.