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Symmetry and Asymmetry from Local Phase

Symmetry is an important mechanism by which we identify the structure of objects. Man-made objects, plants and animals are usually highly recognizable from the symmetry, or partial symmetries that they often exhibit. Two difficulties found in most symmetry detection algorithms are firstly, that they usually require objects to be segmented prior to any symmetry analysis, and secondly, that they do not provide any absolute measure of the degree of symmetry at any point in an image. This paper presents a new measure of symmetry that is based on the analysis of local frequency information. It is shown that points of symmetry and asymmetry give rise to easily recognized patterns of local phase. This phase information can be used to construct a contrast invariant measure of symmetry that does not require any prior recognition or segmentation of objects.