Symmetry is treated as a continuous feature and a Continuous Measure of Distance from Symmetry in shapes is de ned. The Symmetry Distance SD of a shape is de ned to be the minimum mean squared distance required to move points of the original shape in order to obtain a symmetrical shape. This general de nition of a symmetry measure enables a comparison of the amount" of symmetry of di erent shapes and the amount" of di erent symmetries of a single shape. This measure is applicable to any t ype 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, w e consider grayscale images as 3D shapes, and use the Symmetry Distance to nd the orientation of symmetric objects from their images, and to nd locally symmetric regions in images.
REF define a measure of symmetry for nonperfect models, defined as the minimum amount of work required to transform a shape into a symmetric shape.
Symmetry as a Continuous Feature
IEEE Transactions on Pattern Analysis and Machine Intelligence
Mathematics Computer Science