Symmetry

Motivation

In nature as in day-to-day life, symmetry is a manifold and widespread feature. Many of the artifacts that we use show a symmetric structure by some means or another. Animals and human beings take advantage of symmetry as a landmark for visual exploration of objects and scenes. Until today, symmetry has been investigated in multiple diverse domains, e.g. in biology, where animals take preferences for pairing by symmetry [KirkpatrickR'94, EnquistA'94] or pigeons have been successfully trained to discriminate between symmetric and asymmetric shapes [DeliusN'82]. Aspects of symmetry were also explored in the fields of psychology and psychophysics [PalmerH'78, LocherN'89], mathematics and computer vision. Many of the aspects related to nature and mathematics can be found in the book "Fearful Symmetry: Is God a Geometer?" by Stewart and Golubitsky [StewartG'92]. In computer vision, symmetry describes a regional feature, whose significance grows along with the considered image region - in contrast to more familiar approaches like edge detection. The hereby caused disadvantage of many symmetry approaches is the high effort in calculation time, because of the necessarily wider operators for symmetry detection.

References

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