9 April 1993 Indecomposability problem in mathematical morphology
Author Affiliations +
Proceedings Volume 1832, Vision Geometry; (1993) https://doi.org/10.1117/12.142162
Event: Applications in Optical Science and Engineering, 1992, Boston, MA, United States
Abstract
The indecomposable sets are those which cannot be expressed as a Minkowski sum in any nontrivial manner. In this paper we concentrate on the indecomposability problem for sets in the domain of binary images. We show that, it is possible to express a binary image as a hypercomplex algebraic number. More interestingly, if we restrict our domain of binary images then Minkowski addition (direct sum) (also called dilation) turns out to be the addition of two such hypercomplex numbers. In that process the indecomposability problem is transformed into a number theoretic problem. As a by-product our treatment of the problem produces an efficient algorithm for computing Minkowski addition of two binary images.
© (1993) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Pijush K. Ghosh, Pijush K. Ghosh, Robert M. Haralick, Robert M. Haralick, "Indecomposability problem in mathematical morphology", Proc. SPIE 1832, Vision Geometry, (9 April 1993); doi: 10.1117/12.142162; https://doi.org/10.1117/12.142162
PROCEEDINGS
10 PAGES


SHARE
RELATED CONTENT

Parallel Architecture for Mathematical Morphology
Proceedings of SPIE (October 31 1989)
Applications of matrix morphology
Proceedings of SPIE (October 31 1990)
Marching Chains algorithm for Alexandroff-Khalimsky spaces
Proceedings of SPIE (November 23 2002)

Back to Top