Nested Sphere Statistics of Skeletal Models
Nested Sphere Statistics of Skeletal Models
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DOI：
10.1007/978-3-642-34141-0_5
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
S. Pizer;Sungkyu Jung;D. Goswami;Jared Vicory;Xiaojie Zhao;Ritwik Chaudhuri;J. Damon;S. Huckemann;J. S. Marron
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文献类型：
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作者：
S. Pizer;Sungkyu Jung;D. Goswami;Jared Vicory;Xiaojie Zhao;Ritwik Chaudhuri;J. Damon;S. Huckemann;J. S. Marron
我们寻求一种形式的对象模型，准确和完整地捕捉大多数非分支解剖对象的内部，同时是非常适合对人口的概率分析，这样的对象。我们表明，某些近中，骨骼模型满足这些要求。这些模型首先在数学上定义在连续的三维空间，然后离散表示形成的一个元组的辐条向量。我们描述了以足够稳定的方式将这些骨架模型拟合到对象的手动或自动分割中的方法，以支持统计分析，并且我们概述了修改这些拟合的方法，以在对象的训练群体中提供轮辐向量的良好对应性。理解将发展，这些离散的骨架模型生活在一个抽象的空间，由一个笛卡尔产品的欧几里德空间和一个集合的球形空间。基于这种理解以及对象在各种刚性和非刚性变换下的变化方式，一种类似于主成分分析的称为复合主嵌套球体的方法将被视为适用于学习关于新的且更具代表性的平均对象的更有效的对象变化模式集合。比其他表示和其他统计分析方法提供的那些。该方法是通过应用程序来说明Escampi。
We seek a form of object model that exactly and completely captures the interior of most non-branching anatomic objects and simultaneously is well suited for probabilistic analysis on populations of such objects. We show that certain nearly medial, skeletal models satisfy these requirements. These models are first mathematically defined in continuous three-space, and then discrete representations formed by a tuple of spoke vectors are derived. We describe means of fitting these skeletal models into manual or automatic segmentations of objects in a way stable enough to support statistical analysis, and we sketch means of modifying these fits to provide good correspondences of spoke vectors across a training population of objects. Understanding will be developed that these discrete skeletal models live in an abstract space made of a Cartesian product of a Euclidean space and a collection of spherical spaces. Based on this understanding and the way objects change under various rigid and nonrigid transformations, a method analogous to principal component analysis calledcomposite principal nested sphereswill be seen to apply to learning a more efficient collection of modes of object variation about a new and more representative mean object than those provided by other representations and other statistical analysis methods. The methods are illustrated by application to hippocampi.