On the difference between solutions of discrete tomography problems II

Details On the difference between solutions of discrete tomography problems II On the difference between solutions of discrete tomography problems II

2009-06-26

arxiv.org/abs/0906.4907v1

Mathematics

Combinatorics

Scientific paper

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.

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