Digital Topology on Adaptive Octree Grids

Authors:
Ying Bai;Xiao Han;Jerry L. Prince
Affiliations:
Department of Electrical and Computer Engineering, Johns Hopkins University, Baltimore, USA 21218;CMS Software, Elekta Inc., St. Louis, USA 63043;Department of Electrical and Computer Engineering, Johns Hopkins University, Baltimore, USA 21218
Venue:
Journal of Mathematical Imaging and Vision
Year:
2009

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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.