dc.contributor.author |
Brimkov, VE |
en |
dc.contributor.author |
Klette, Reinhard |
en |
dc.date.accessioned |
2012-04-12T03:47:06Z |
en |
dc.date.issued |
2008 |
en |
dc.identifier.citation |
IEEE Transactions on Pattern Analysis and Machine Intelligence 30(4):577-590 2008 |
en |
dc.identifier.issn |
0162-8828 |
en |
dc.identifier.uri |
http://hdl.handle.net/2292/17145 |
en |
dc.description.abstract |
In this paper, we define and study digital manifolds of arbitrary dimension, and provide (in particular) a general theoretical basis for curve or surface tracing in picture analysis. The studies involve properties such as the one-dimensionality of digital curves and (n - 1)-dimensionality of digital hypersurfaces that makes them discrete analogs of corresponding notions in continuous topology. The presented approach is fully based on the concept of adjacency relation and complements the concept of dimension, as common in combinatorial topology. This work appears to be the first one on digital manifolds based on a graph-theoretical definition of dimension. In particular, in the n-dimensional digital space, a digital curve is a one-dimensional object and a digital hypersurface is an (n - 1)-dimensional object, as it is in the case of curves and hypersurfaces in the Euclidean space. Relying on the obtained properties of digital hypersurfaces, we propose a uniform approach for studying good pairs defined by separations and obtain a classification of good pairs in arbitrary dimension. We also discuss possible applications of the presented definitions and results. |
en |
dc.publisher |
IEEE Computer Society |
en |
dc.relation.ispartofseries |
IEEE Transactions on Pattern Analysis and Machine Intelligence |
en |
dc.rights |
Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. Details obtained from http://www.sherpa.ac.uk/romeo/issn/0162-8828/ |
en |
dc.rights.uri |
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm |
en |
dc.title |
Border and surface tracing - Theoretical foundations |
en |
dc.type |
Journal Article |
en |
dc.identifier.doi |
10.1109/TPAMI.2007.70725 |
en |
pubs.issue |
4 |
en |
pubs.begin-page |
577 |
en |
pubs.volume |
30 |
en |
dc.rights.holder |
Copyright: Institute of Electrical and Electronics Engineers (IEEE) |
en |
dc.identifier.pmid |
18276965 |
en |
pubs.end-page |
590 |
en |
dc.rights.accessrights |
http://purl.org/eprint/accessRights/RestrictedAccess |
en |
pubs.subtype |
Article |
en |
pubs.elements-id |
185909 |
en |
pubs.record-created-at-source-date |
2012-04-12 |
en |
pubs.dimensions-id |
18276965 |
en |