论文标题
离散轮廓树的一些理论结果
Some theoretical results on discrete contour trees
论文作者
论文摘要
已经开发了轮廓树来可视化或编码成像技术和科学模拟中的标量数据。轮廓是在连续的标量字段上定义的。对于离散数据，首先插值连续函数，然后在其中定义轮廓。在本文中，我们在标量图上定义了一个离散的轮廓树，称为ISO-Tree，并讨论其属性。我们表明，ISO-TREE模型可用于所有维度的数据，并开发一个正式化离散轮廓结构的公理系统。我们还报告了ISO-Trees和增强轮廓树之间的同构，表明轮廓树算法可用于计算离散的轮廓树，反之亦然。
Contour trees have been developed to visualize or encode scalar data in imaging technologies and scientific simulations. Contours are defined on a continuous scalar field. For discrete data, a continuous function is first interpolated, where contours are then defined. In this paper we define a discrete contour tree, called the iso-tree, on a scalar graph, and discuss its properties. We show that the iso-tree model works for data of all dimensions, and develop an axiomatic system formalizing the discrete contour structures. We also report an isomorphism between iso-trees and augmented contour trees, showing that contour tree algorithms can be used to compute discrete contour trees, and vice versa.
