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.

中文翻译：

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自适应八叉树网格上的数字拓扑。

数字拓扑理论用于许多不同的图像处理和计算机图形算法。大多数现有理论适用于统一笛卡尔网格，并且它们不容易扩展到针对自适应笛卡尔网格的新算法。本文提供了自适应八叉树网格的经典数字拓扑框架的严格扩展，包括邻接、连通分量和简单点的表征。提供了激励示例、主要命题的证明和算法伪代码。