Reconstruction of Discrete Sets from Three or More X-Rays

Abstract

The problem of reconstructing a discrete set from its X-rays in a finite number of prescribed directions is NP-complete when the number of prescribed directions is greater than two. In this paper, we consider an interesting subclass of discrete sets having some connectivity and convexity properties and we provide a polynomial-time algorithm for reconstructing a discrete set of this class from its X-rays in directions (1, 0), (0, 1) and (1, 1). This algorithm can be easily extended to contexts having more than three X-rays