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自适应八叉树网格上的数字拓扑

Digital Topology on Adaptive Octree Grids.

作者信息

Bai Ying, Han Xiao, Prince Jerry L

机构信息

Department of Electrical and Computer Engineering Johns Hopkins University, Baltimore MD 21218.

出版信息

J Math Imaging Vis. 2009 Jun 1;34(2):165-184. doi: 10.1007/s10851-009-0140-7.

DOI:10.1007/s10851-009-0140-7
PMID:20072715
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC2805029/
Abstract

The theory of digital topology is used in many different image processing and computer graphics algorithms. Most of the existing theories apply to uniform cartesian grids, and they are not readily extensible to new algorithms targeting at adaptive cartesian grids. This article provides a rigorous extension of the classical digital topology framework for adaptive octree grids, including the characterization of adjacency, connected components, and simple points. Motivating examples, proofs of the major propositions, and algorithm pseudocodes are provided.

摘要

数字拓扑理论被应用于许多不同的图像处理和计算机图形算法中。现有的大多数理论适用于均匀笛卡尔网格，并且它们不容易扩展到针对自适应笛卡尔网格的新算法。本文为自适应八叉树网格提供了经典数字拓扑框架的严格扩展，包括邻接性、连通分量和简单点的特征描述。文中给出了动机示例、主要命题的证明以及算法伪代码。

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