The Pascal Triangle of a Discrete Image: Definition, Properties and Application to Shape Analysis
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
The Pascal Triangle of a Discrete Image: Definition, Properties and Application to Shape Analysis
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| Creator |
Boutin, M.
Huang, S. |
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| Description |
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.
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| Date |
2019-02-19T19:04:43Z
2019-02-19T19:04:43Z 2013 |
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| Type |
Article
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| Identifier |
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.
1815-0659 2010 Mathematics Subject Classification: 30E05; 57S25; 68T10 DOI: http://dx.doi.org/10.3842/SIGMA.2013.031 http://dspace.nbuv.gov.ua/handle/123456789/149235 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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