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Эта публикация цитируется в 4 научных статьях (всего в 4 статьях)
Möbius Invariants of Shapes and Images
Stephen Marsland, Robert I. McLachlan Massey University, Palmerston North, New Zealand
Аннотация:
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 $\mathrm{PSL}(2,\mathbb{C})$, 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.
Ключевые слова:
invariant; invariant signature; Möbius group; shape; image.
Поступила: 1 апреля 2016 г.; в окончательном варианте 8 августа 2016 г.; опубликована 11 августа 2016 г.
Образец цитирования:
Stephen Marsland, Robert I. McLachlan, “Möbius Invariants of Shapes and Images”, SIGMA, 12 (2016), 080, 29 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma1162 https://www.mathnet.ru/rus/sigma/v12/p80
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