论文标题
表示弹性图的形状分析的表示，指标和统计数据
Representations, Metrics and Statistics For Shape Analysis of Elastic Graphs
论文作者
论文摘要
对象的统计形状分析的过去方法主要集中在同一拓扑类中的对象上，例如标量函数，欧几里得曲线或表面等。对于以更复杂的方式不同的对象，当前文献仅提供拓扑方法。本文介绍了一种深远的几何方法，用于分析图形对象的形状，例如路网，血管，脑纤维区等。它代表了这些物体，在几何和拓扑中都表现出差异，如由曲线组成的图形差异，该曲线由曲线组成，并具有任意形状（EDGES）和在任意连接连接（nodes）（nodes）（nodes）中。为了执行统计分析，需要数学表示，指标和其他几何工具，例如地球，均值和协方差。本文利用商结构来开发有效的算法来计算这些数量，从而导致有用的统计工具，包括主成分分析和图形形状的分析统计测试和建模。使用来自神经元和脑动脉网络的各种模拟以及实际数据来证明该框架的功效。
Past approaches for statistical shape analysis of objects have focused mainly on objects within the same topological classes, e.g., scalar functions, Euclidean curves, or surfaces, etc. For objects that differ in more complex ways, the current literature offers only topological methods. This paper introduces a far-reaching geometric approach for analyzing shapes of graphical objects, such as road networks, blood vessels, brain fiber tracts, etc. It represents such objects, exhibiting differences in both geometries and topologies, as graphs made of curves with arbitrary shapes (edges) and connected at arbitrary junctions (nodes). To perform statistical analyses, one needs mathematical representations, metrics and other geometrical tools, such as geodesics, means, and covariances. This paper utilizes a quotient structure to develop efficient algorithms for computing these quantities, leading to useful statistical tools, including principal component analysis and analytical statistical testing and modeling of graphical shapes. The efficacy of this framework is demonstrated using various simulated as well as the real data from neurons and brain arterial networks.
