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dc.contributor.author |
Boutin, M. |
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dc.contributor.author |
Huang, S. |
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dc.date.accessioned |
2019-02-19T19:04:43Z |
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dc.date.available |
2019-02-19T19:04:43Z |
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dc.date.issued |
2013 |
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dc.identifier.citation |
The Pascal Triangle of a Discrete Image: Definition, Properties and Application to Shape Analysis / M. Boutin, S. Huang // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 8 назв. — англ. |
uk_UA |
dc.identifier.issn |
1815-0659 |
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dc.identifier.other |
2010 Mathematics Subject Classification: 30E05; 57S25; 68T10 |
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dc.identifier.other |
DOI: http://dx.doi.org/10.3842/SIGMA.2013.031 |
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dc.identifier.uri |
http://dspace.nbuv.gov.ua/handle/123456789/149235 |
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dc.description.abstract |
We define the Pascal triangle of a discrete (gray scale) image as a pyramidal arrangement of complex-valued moments and we explore its geometric significance. In particular, we show that the entries of row k of this triangle correspond to the Fourier series coefficients of the moment of order k of the Radon transform of the image. Group actions on the plane can be naturally prolonged onto the entries of the Pascal triangle. We study the prolongation of some common group actions, such as rotations and reflections, and we propose simple tests for detecting equivalences and self-equivalences under these group actions. The motivating application of this work is the problem of characterizing the geometry of objects on images, for example by detecting approximate symmetries. |
uk_UA |
dc.description.sponsorship |
This paper is a contribution to the Special Issue “Symmetries of Dif ferential Equations: Frames, Invariants
and Applications”. The full collection is available at http://www.emis.de/journals/SIGMA/SDE2012.html.
This research was supported in parts by NSF grant CCF-0728929 |
uk_UA |
dc.language.iso |
en |
uk_UA |
dc.publisher |
Інститут математики НАН України |
uk_UA |
dc.relation.ispartof |
Symmetry, Integrability and Geometry: Methods and Applications |
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dc.title |
The Pascal Triangle of a Discrete Image: Definition, Properties and Application to Shape Analysis |
uk_UA |
dc.type |
Article |
uk_UA |
dc.status |
published earlier |
uk_UA |
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