ON LIMIT PROPERTIES IN DIGITIZATION SCHEMES.
Abstract
Continuity of curve digitizations is considered, and it is pointed out that no proposed digitization scheme satisfies continuity requirements. A general definition of digitization scheme is given, having those in the literature as special cases, and it is proved that for practical purposes, no digitization scheme is possible, in which limit curves always have unambiguous digitizations. A weaker definition of continuity is then given, and this property is proved to hold for a large class of digitization schemes. These concepts apply when a curve with some extremal property must be reconstructed from the digitization. The cases of a least perimeter polygon and of a least energy rod are considered in detail. In the first case, necessary and sufficient conditions are developed that assure a one-to-one correspondence between the given digitization and the minimal polygon. The convergence of an algorithm for finding the minimal polygon, is proved in the convex case. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1969
- Accession Number
- AD0690198
Entities
People
- G. Ugo Montanari
Organizations
- University of Maryland