dc.contributor.author |
Klette, Reinhard |
en |
dc.date.accessioned |
2008-08-21T01:56:05Z |
en |
dc.date.available |
2008-08-21T01:56:05Z |
en |
dc.date.issued |
2000 |
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dc.identifier.citation |
Communication and Information Technology Research Technical Report 60, (2000) |
en |
dc.identifier.issn |
1178-3685 |
en |
dc.identifier.uri |
http://hdl.handle.net/2292/2723 |
en |
dc.description |
You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) days from the most recent time that you verified that this technical report is still available from the original CITR web site; http://citr.auckland.ac.nz/techreports/ under terms that include this permission. All other rights are reserved by the author(s). |
en |
dc.description.abstract |
The history of cell complexes is closely related to the birth and development of topology in general. Johann Benedict Listing (1802-1882) introduced the term "topology" into mathematics in a paper published in 1847, and he also defined cell complexes for the first time in a paper published in 1862. Carl Friedrich Gauss (1777-1855) is often cited as the one who initiated these ideas, but he did not publish either on topology or on cell complexes. The pioneering work of Leonhard Euler (1707-1783) on graphs is also often cited as the birth of topology, and Euler's work was cited by Listing in 1862 as a stimulus for his research on cell complexes. There are different branches in topology which have little in common: point set topology, algebraic topology, differential topology etc. Confusion may arise if just "topology" is specied, without clarifying the used concept. Topological subjects in mathematics are often related to continuous models, and therefore quite irrelevant to computer based solutions in image analysis. Compared to this, only a minority of topology publications in mathematics addresses discrete spaces which are appropriate for computer-based image analysis. In these cases, often the notion of a cell complex plays a crucial role. This paper briefly reports on a few of these publications, which might be helpful or at least of interest for recent studies in topological issues in image analysis. It is not a balanced review, due to a certain randomness in the selection process of cited work. This paper is also not intended to cover the very lively progress in cell complex studies within the context of image analysis during the last two decades. Basically it stops its historic review at the time when this subject in image analysis research gained speed in 1980-1990. As a general point of view, the paper indicates that image analysis contributes to a fusion of two topological concepts, the geometric or abstract cell complex approach and point set topology, which leads to an in-depth study of topologies defined on geometric or abstract cell complexes. |
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dc.publisher |
CITR, The University of Auckland, New Zealand |
en |
dc.relation.ispartofseries |
Communication and Information Technology Research (CITR) Technical Report Series |
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dc.rights |
Copyright CITR, The University of Auckland. You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) days from the most recent time that you verified that this technical report is still available from the original CITR web site under terms that include this permission. All other rights are reserved by the author(s). |
en |
dc.rights.uri |
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm |
en |
dc.source.uri |
http://citr.auckland.ac.nz/techreports/2000/CITR-TR-60.pdf |
en |
dc.title |
Cell Complexes through Time |
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dc.type |
Technical Report |
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dc.subject.marsden |
Fields of Research::280000 Information, Computing and Communication Sciences |
en |