Möbius Invariants of Shapes and Images
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Möbius Invariants of Shapes and Images
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| Creator |
Marsland, S.
McLachlan, R.I. |
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| Description |
Identifying when different images are of the same object despite changes caused by imaging technologies, or processes such as growth, has many applications in fields such as computer vision and biological image analysis. One approach to this problem is to identify the group of possible transformations of the object and to find invariants to the action of that group, meaning that the object has the same values of the invariants despite the action of the group. In this paper we study the invariants of planar shapes and images under the Möbius group PSL(2,C), which arises in the conformal camera model of vision and may also correspond to neurological aspects of vision, such as grouping of lines and circles. We survey properties of invariants that are important in applications, and the known Möbius invariants, and then develop an algorithm by which shapes can be recognised that is Möbius- and reparametrization-invariant, numerically stable, and robust to noise. We demonstrate the efficacy of this new invariant approach on sets of curves, and then develop a Möbius-invariant signature of grey-scale images.
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| Date |
2019-02-16T09:14:36Z
2019-02-16T09:14:36Z 2016 |
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| Type |
Article
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| Identifier |
Möbius Invariants of Shapes and Images / S. Marsland, R.I. McLachlan // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 43 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 68T45; 68U10 DOI:10.3842/SIGMA.2016.080 http://dspace.nbuv.gov.ua/handle/123456789/147846 |
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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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