The Pascal Triangle of a Discrete Image: Definition, Properties and Application to Shape Analysis
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 t...
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| Дата: | 2013 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2013
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/149235 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-149235 |
|---|---|
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dspace |
| spelling |
irk-123456789-1492352019-02-20T01:24:05Z The Pascal Triangle of a Discrete Image: Definition, Properties and Application to Shape Analysis Boutin, M. Huang, S. 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. 2013 Article 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 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Boutin, M. Huang, S. |
| spellingShingle |
Boutin, M. Huang, S. The Pascal Triangle of a Discrete Image: Definition, Properties and Application to Shape Analysis Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Boutin, M. Huang, S. |
| author_sort |
Boutin, M. |
| title |
The Pascal Triangle of a Discrete Image: Definition, Properties and Application to Shape Analysis |
| title_short |
The Pascal Triangle of a Discrete Image: Definition, Properties and Application to Shape Analysis |
| title_full |
The Pascal Triangle of a Discrete Image: Definition, Properties and Application to Shape Analysis |
| title_fullStr |
The Pascal Triangle of a Discrete Image: Definition, Properties and Application to Shape Analysis |
| title_full_unstemmed |
The Pascal Triangle of a Discrete Image: Definition, Properties and Application to Shape Analysis |
| title_sort |
pascal triangle of a discrete image: definition, properties and application to shape analysis |
| publisher |
Інститут математики НАН України |
| publishDate |
2013 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149235 |
| citation_txt |
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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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