On the difference between solutions of discrete tomography problems.

We consider the problem of reconstructing binary images from their horizontal and vertical projections. It is well-known that the reconstruction may not be uniquely determined, and that it is in fact possible to have two disjoint reconstructions from the same set of projections. We will present a condition that the projections must necessarily satisfy in order for this to happen. More general, we can derive from given projections an upper bound on the symmetric difference between two reconstructions. We will also consider reconstructions from two different sets of projections, which gives us new stability results for the case of two directions.