On the difference between solutions of discrete tomography problems II
Combinatorics
2009-06-29 v1
Abstract
We consider the problem of reconstructing binary images from their horizontal and vertical projections. It is known that the projections do not necessarily determine the image uniquely. In a previous paper it was shown that the symmetric difference between two solutions (binary images that satisfy the projections) is at most 4A times the square root of 2N. Here N is the sum of the projections in one direction (i.e. the size of the image) and A is a parameter depending on the projections. In this paper we give a lower bound: for each set of projections that has at least two solutions, we construct two solutions that have a symmetric difference of at least 2A+2. We also show that this is the best possible.
Keywords
Cite
@article{arxiv.0906.4907,
title = {On the difference between solutions of discrete tomography problems II},
author = {Birgit van Dalen},
journal= {arXiv preprint arXiv:0906.4907},
year = {2009}
}