Share Email Print

Proceedings Paper

Problem of determining whether a parallel reduction operator for n-dimensional binary images always preserves topology
Author(s): T. Yung Kong
Format Member Price Non-Member Price
PDF $17.00 $21.00

Paper Abstract

Loosely speaking, a simple set of a finite binary image is a set of 1s whose deletion `preserves topology.' This concept can be made precise in different (and inequivalent) ways. Ronse established results which imply that, for finite 2-D binary images on a Cartesian grid and three different definitions of simple set, a set S of 1s is simple if every subset of S that lies in a 2- point by 2-point square is simple. In fact this is a special case of a general result which applies to arbitrary finite binary images -- not just 2-D images on a Cartesian grid -- and any definition of simple set which satisfies three axioms stated in this paper. For finite binary images on an n-dimensional Cartesian grid, we give appropriate definitions of simple set which satisfy all the axioms. When these definitions of simple set are used, verification that a parallel reduction operator for n-dimensional binary images preserves the topology of all possible input images may be achievable by checking only a finite number of cases.

Paper Details

Date Published: 1 December 1993
PDF: 9 pages
Proc. SPIE 2060, Vision Geometry II, (1 December 1993); doi: 10.1117/12.165013
Show Author Affiliations
T. Yung Kong, CUNY/Queens College (United States)

Published in SPIE Proceedings Vol. 2060:
Vision Geometry II
Robert A. Melter; Angela Y. Wu, Editor(s)

© SPIE. Terms of Use
Back to Top
Sign in to read the full article
Create a free SPIE account to get access to
premium articles and original research
Forgot your username?