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The Digital Topology of Sets of Convex Voxels

✍ Scribed by Punam K. Saha; Azriel Rosenfeld

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 101 KB
Volume: 62
Category: Article
ISSN: 1524-0703
DOI: 10.1006/gmod.2000.0527

No coin nor oath required. For personal study only.

✦ Synopsis

Classical digital geometry deals with sets of cubical voxels (or square pixels) that can share faces, edges, or vertices, but basic parts of digital geometry can be generalized to sets S of convex voxels (or pixels) that can have arbitrary intersections. In particular, it can be shown that if each voxel P of S has only finitely many neighbors (voxels of S that intersect P), and if any nonempty intersection of neighbors of P intersects P, then the neighborhood N (P) of every voxel P is simply connected and without cavities, and if the topology of N (P) does not change when P is deleted (i.e., P is a "simple" voxel), then deletion of P does not change the topology of S.

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