论文标题
具有视网膜血管网络应用的形状图的统计形状分析
Statistical Shape Analysis of Shape Graphs with Applications to Retinal Blood-Vessel Networks
论文作者
论文摘要
本文在形状图的统计形状分析中提供了理论和计算发展，并使用视网膜血管（RBV）网络的复杂数据分析了它们。形状图由连接其中一些节点的一组节点和边缘（平面表达曲线）表示。目标是利用节点的边缘和连接性和位置的形状为：（1）表征完整形状，（2）量化形状差异，（3）模型统计变异性。我们开发数学表示，弹性的Riemannian形状指标以及相关的统计分析工具。具体而言，我们得出了用于形状图形注册，大地测量，摘要和形状建模的工具。大地测量方便可视化最佳变形，PCA有助于降低尺寸和统计建模。这里的一个主要挑战是比较具有截然不同的复杂性（节点和边缘数量）的形状图。本文介绍了形状图的新型多尺度表示，以应对这一挑战。使用（1）``有效的电阻''的概念和（2）（2）弹性形状平均边缘曲线，一个人可以在保持整体结构的同时减少形状的图形复杂性。这样，我们可以通过将它们带到相似的复杂性来比较形状图。我们将这些想法从视网膜血管（RBV）网络中展示为从凝视和驱动数据持续式驱动数据盘中展示这些想法。
This paper provides theoretical and computational developments in statistical shape analysis of shape graphs, and demonstrates them using analysis of complex data from retinal blood-vessel (RBV) networks. The shape graphs are represented by a set of nodes and edges (planar articulated curves) connecting some of these nodes. The goals are to utilize shapes of edges and connectivities and locations of nodes to: (1) characterize full shapes, (2) quantify shape differences, and (3) model statistical variability. We develop a mathematical representation, elastic Riemannian shape metrics, and associated tools for such statistical analysis. Specifically, we derive tools for shape graph registration, geodesics, summaries, and shape modeling. Geodesics are convenient for visualizing optimal deformations, and PCA helps in dimension reduction and statistical modeling. One key challenge here is comparisons of shape graphs with vastly different complexities (in number of nodes and edges). This paper introduces a novel multi-scale representation of shape graphs to handle this challenge. Using the notions of (1) ``effective resistance" to cluster nodes and (2) elastic shape averaging of edge curves, one can reduce shape graph complexity while maintaining overall structures. This way, we can compare shape graphs by bringing them to similar complexity. We demonstrate these ideas on Retinal Blood Vessel (RBV) networks taken from the STARE and DRIVE databases.
