An Algorithm for Reconstructing a Convex Polygon from its Covariogram

Abstract

The covariogram of a compact convex set $K \subset \mathbb R^n$ is the function that at each point $x \in \mathbb R^n$ associates the volume of $K \cap (K + x)$. The covariogram determines, among all convex bodies, any planar convex polygon. In this paper we present an algorithm for reconstructing an arbitrary convex polygon from its covariogram.