Reflection symmetry measure for convex sets

We investigate the properties of Blaschke symmetrization of compact sets (binary images) and introduce a convex set reflection symmetry measure via this symmetrization. A lower bound for the reflection symmetry measure is obtained. For the case of two and three dimensions we consider also a derivative reflection symmetry measure. In the two dimensional case a perimetric measure representation of convex sets is applied for the convex sets symmetrization as well as for the reflection symmetry measure calculation. In the case of discrete sets we suggest to use fast Fourier transformation for the fast implementation of the symmetrization transformation. >