The Morphological Processing of Binary Images
Abstract
The morphological processing of binary images is treated in depth from the viewpoint of ordered topology. The basic ideas of Nachbin arid Birkhoff concerning when a partial ordering of a set that has a topology is compatible with that topology are used to obtain a definition of an order resolvable topological ordered space. This abstraction is then used to define semicontinuity in a sufficiently general way to unify its treatment in mathematical morphology. This is followed by a detailed review of the basic concepts of closed-set morphology. In this review, a more thorough treatment than is available elsewhere is given of the several limit concepts used in morphology; likewise, the continuity properties of the erosion, dilation, and homothesis operations are more thoroughly treated than is usual. The morphological transformation and transformation space theory of closed-set morphology is presented in a systematic way that incorporates the relevant contributions of Matheron and Maragos, as well as the recent important work of Banon and Barrera. Finally, a class of countable closed-set bases for the underlying hit-miss topology is used to derive a novel representation of morphological transformations. Mathematical morphology, Hit-miss topology, Myopic topology, Compact ordered spaces, Poset/lattice topology, Minkowski sum, dilation, Minkowski difference, Erosion, Translation-invariant set mappings, Kernel representations, Morphological transformations.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1993
- Accession Number
- ADA274310
Entities
People
- Dennis W. Mcguire
Organizations
- United States Army Research Laboratory