Journal article
Local and global topology preservation in locally finite sets of tiles
Information sciences, Vol.137(1), pp.303-311
2001
DOI: 10.1016/S0020-0255(01)00107-4
Abstract
This paper deals with sets
P
of
tiles (compact, convex sets) in
R
2
or
R
3
. Tiles are a generalization of pixels or voxels; they can have arbitrary shapes, are allowed to have overlapping interiors, and need not cover the space. The union of all the tiles of
P
is denoted by
U(
P)
. The
neighborhood
N
P
(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
N
P
(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
N
P
(P)
.
Details
- Title: Subtitle
- Local and global topology preservation in locally finite sets of tiles
- Creators
- Punam K Saha - Medical Image Processing Group, University of Pennsylvania, Philadelphia, PA 19104-6021, USAAzriel Rosenfeld - Center for Automation Research, Computer Vision Laboratory, Institute for Advanced Computer Studies, University of Maryland, College Park, MD 20742-3275, USA
- Resource Type
- Journal article
- Publication Details
- Information sciences, Vol.137(1), pp.303-311
- Publisher
- Elsevier Inc
- DOI
- 10.1016/S0020-0255(01)00107-4
- ISSN
- 0020-0255
- eISSN
- 1872-6291
- Language
- English
- Date published
- 2001
- Academic Unit
- Electrical and Computer Engineering; Radiology
- Record Identifier
- 9984051529302771
Metrics
12 Record Views