Issue No. 12 - December (1995 vol. 17)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/34.476508
<p><it>Abstract</it>—Symmetry is treated as a continuous feature and a Continuous Measure of Distance from Symmetry in shapes is defined. The Symmetry Distance (SD) of a shape is defined to be the minimum mean squared distance required to move points of the original shape in order to obtain a symmetrical shape. This general definition of a symmetry measure enables a comparison of the “amount” of symmetry of different shapes and the “amount” of different symmetries of a single shape. This measure is applicable to any type of symmetry in any dimension. The Symmetry Distance gives rise to a method of reconstructing symmetry of occluded shapes. We extend the method to deal with symmetries of noisy and fuzzy data. Finally, we consider grayscale images as 3D shapes, and use the Symmetry Distance to find the orientation of symmetric objects from their images, and to find locally symmetric regions in images.</p>
Symmetry, local symmetry, symmetry distance, similarity measure, occlusion, fuzzy shapes, face orientation.
Hagit Zabrodsky, David Avnir, Shmuel Peleg, "Symmetry as a Continuous Feature", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 17, no. , pp. 1154-1166, December 1995, doi:10.1109/34.476508