Local and Global Topology Preservation in Locally Finite Sets of Tiles
Abstract
This paper deals with sets P of tiles (compact, convex sets) in R(n). Tiles are a generalization of pixels or voxels (in R2 or R3); they can have arbitrary shapes and are allowed to overlap. The union of all the tiles of P is denoted by U(P). The neighborhood Np(P) of a tile P is the union of the tiles of P that intersect P. P is called simple if deletion of P from P does not change the topology (in the homotopy sense) of U(P). We show in this paper that if P satisfies a property called strong normality (SN), and deletion of P preserves the topology of Np (P), then P is simple. This may not be true if P is not SN; and even if P is SN, P may be simple even if deletion of P does not preserve the topology of Np(P).
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1998
- Accession Number
- ADA353732
Entities
People
- Azriel Rosenfeld
- Punam K. Saha
Organizations
- University of Maryland