Отрывок: Fig. 3. Examples of Eisenstein rotations of a hexagonal image. Note that not all of these properties may be considered as rigorous mathematical statements and so some terms above have been put in quotes. Indeed, the first property immediately implies that all the fragments are composed by distinct pixels of the original image and so are entirely different as discrete objects. It means that only visual similarity of the fragments occur and so in general we may talk only about some ...
Название : Hexagonal images processing over finite Eisenstein fields
Авторы/Редакторы : Karkishchenko, A.
Mnukhin, V.
Ключевые слова : Hexagonal imag
Eisenstein number
finite field
Дата публикации : 2017
Издательство : Новая техника
Библиографическое описание : Karkishchenko A. Hexagonal images processing over finite Eisenstein fields / A. Karkishchenko, V. Mnukhin // Сборник трудов III международной конференции и молодежной школы «Информационные технологии и нанотехнологии» (ИТНТ-2017) - Самара: Новая техника, 2017. - С. 568-575.
Аннотация : This paper considers a new algebraic method for analysis and processing of hexagonally sampled images. The method is based on the interpretation of such images as functions on “Eisenstein fields”. These are finite fields GF(p2) of special characteristics p = 12k + 5, where k > 0 is an integer. Some properties of such fields are studied; in particular, it is shown that its elements may be considered as ”discrete Eisenstein numbers” and are in natural correspondence with hexagons in a (p × p)-diamondshaped fragment of a regular plane tiling. We show that in some cases multiplications in Eisenstein fields correspond to rotations combined with appropriate scalings, and use this fact for hexagonal images sharpening, smoothering and segmentation. The proposed algorithms have complexity O(p2) and can be used also for processing of square-sampled digital images over finite Gaussian fields.
URI (Унифицированный идентификатор ресурса) : http://repo.ssau.ru/handle/Informacionnye-tehnologii-i-nanotehnologii/Hexagonal-images-processing-over-finite-Eisenstein-fields-63740
Другие идентификаторы : Dspace\SGAU\20170512\63740
Располагается в коллекциях: Информационные технологии и нанотехнологии

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