On the detection of simple points in higher dimensions using cubical homology
Simple point detection is an important task for several problems in discrete geometry, such as topology preserving thinning in image processing to compute discrete skeletons. In this paper, the approach to simple point detection is based on techniques from cubical homology, a framework ideally suite...
| Veröffentlicht in: | IEEE transactions on image processing : a publication of the IEEE Signal Processing Society. - 1992. - 15(2006), 8 vom: 10. Aug., Seite 2462-9 |
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| 1. Verfasser: | |
| Weitere Verfasser: | , , |
| Format: | Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
2006
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| Zugriff auf das übergeordnete Werk: | IEEE transactions on image processing : a publication of the IEEE Signal Processing Society |
| Schlagworte: | Evaluation Study Journal Article Research Support, N.I.H., Extramural Research Support, U.S. Gov't, Non-P.H.S. |
| Zusammenfassung: | Simple point detection is an important task for several problems in discrete geometry, such as topology preserving thinning in image processing to compute discrete skeletons. In this paper, the approach to simple point detection is based on techniques from cubical homology, a framework ideally suited for problems in image processing. A (d-dimensional) unitary cube (for a d-dimensional digital image) is associated with every discrete picture element, instead of a point in epsilon(d) (the d-dimensional Euclidean space) as has been done previously. A simple point in this setting then refers to the removal of a unitary cube without changing the topology of the cubical complex induced by the digital image. The main result is a characterization of a simple point p (i.e., simple unitary cube) in terms of the homology groups of the (3d - 1) neighborhood of p for arbitrary, finite dimensions |
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| Beschreibung: | Date Completed 12.09.2006 Date Revised 10.12.2019 published: Print Citation Status MEDLINE |
| ISSN: | 1941-0042 |