Journal of Mathematical Imaging and Vision

, Volume 34, Issue 3, pp 259–269 | Cite as

Symmetries of 2-D Images: Cases without Periodic Translations



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.


Image structure Isomorphism Group theory 


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Computer ScienceUniversity College LondonLondonUK

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