Journal article
Strongly normal sets of convex polygons or polyhedra
Pattern recognition letters, Vol.19(12), pp.1119-1124
1998
DOI: 10.1016/S0167-8655(98)00088-9
Abstract
A set
P
of nondegenerate convex polygons
P in
R
2
, or polyhedra
P in
R
3
, will be called
normal if the intersection of any two of the
Ps of
P
is a face (in the case of polyhedra), an edge, a vertex or empty.
P
is called
strongly normal (SN) if it is normal and, for all
P,
P
1, …,
P
n
, if each
P
i
intersects
P and
I=
P
1∩⋯∩
P
n
is nonempty, then
I intersects
P. The union of the
P
i∈
P
that intersect
P
∈
P
is called the
neighborhood of
P in
P
, and is denoted by
N
P
(
P). We prove that
P
is SN iff for any
P
′
⊆
P
and
P
∈
P
′,
N
P
′
(
P) is simply connected. Thus SN characterizes sets
P
of polyhedra (or polygons) in which the neighborhood of any polyhedron, relative to any subset
P
′ of
P
, is simply connected. Tessellations of
R
2 or
R
3 into convex polygons or polyhedra are normal, but they may not be SN; for example, the square and hexagonal regular tessellations of
R
2 are SN, but the triangular regular tessellation is not.
Details
- Title: Subtitle
- Strongly normal sets of convex polygons or polyhedra
- Creators
- Punam K Saha - Medical Image Processing Group, University of Pennsylvania, Philadelphia, PA 19104-6021, USAAzriel Rosenfeld - Computer Vision Laboratory, Center for Automation Research, University of Maryland, College Park, MD 20742-3275, USA
- Resource Type
- Journal article
- Publication Details
- Pattern recognition letters, Vol.19(12), pp.1119-1124
- DOI
- 10.1016/S0167-8655(98)00088-9
- ISSN
- 0167-8655
- eISSN
- 1872-7344
- Publisher
- Elsevier B.V
- Language
- English
- Date published
- 1998
- Academic Unit
- Radiology; Electrical and Computer Engineering
- Record Identifier
- 9984051878602771
Metrics
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