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Symmetries of 2-D Images: Cases without Periodic Translations

Griffin, LD; (2009) Symmetries of 2-D Images: Cases without Periodic Translations. J MATH IMAGING VIS , 34 (3) 259 - 269. 10.1007/s10851-009-0148-z.

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Abstract

The different ways in which images, defined as scalar functions of the Euclidean plane, can be symmetrical is considered. The symmetries analyzed are relative to the class of image isometries, each of which is a combined spatial and intensity isometry. All symmetry types, apart from those with discrete periodic translations, are derived. Fifteen such types are found, including one that has not previously been reported. The novel type occurs when an image has a continuous line of centres of symmetry each like the one found in the Taiji (Yin-Yang) symbol.

Type:Article
Title:Symmetries of 2-D Images: Cases without Periodic Translations
DOI:10.1007/s10851-009-0148-z
Keywords:Image structure, Isomorphism, Group theory, LOCAL SYMMETRY, PERCEPTION, MODEL
UCL classification:UCL > School of BEAMS > Faculty of Engineering Science > Computer Science

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