SYMMETRY AS A CONTINUOUS FEATURE

Symmetry is treated as a continuous feature and a Continuous Measure o f Distance from Symmetry in shapes is defined. The Symmetry Distance ( SD) of a shape is defined to be the minimum mean squared distance requ ired to move points of the original shape in order to obtain a symmetr ical shape. This general definition of a symmetry measure enables a co mparison of the ''amount'' of symmetry of different shapes and the ''a mount'' of different symmetries of a single shape. This measure is app licable to any type of symmetry in any dimension. The Symmetry Distanc e 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 Symm etry Distance to find the orientation of symmetric objects from their images, acid to find locally symmetric regions in images.