Convex set symmetry measurement using Blaschke addition

In this paper we state a new way for measuring symmetry of convex sets. The measures introduced are based on the Blaschke sum. This operation has some important properties, and is a natural way for combining convex objects when represented by their extended gaussian image. Different kinds of symmetry are considered and their properties outlined. To form the Blaschke sum, it is necessary to solve the Minkowski reconstruction problem. We study the method of reconstruction and give some improvements to make the scheme more efficient.