Discrete tomography differs from standard computerized tomography since it deals with the reconstruction of objects made of just one homogeneous material. In this case we usually assume their shapes through a priori knowledge and reduce the number of projections to no more than four. Several issues arise due to this dearth of input data. For example, the consistency problem coincides with the ability to state whether there exists any object compatible with a given set of projections; the uniqueness problem derives from the fact that different objects can lead to the same projections; the stability problem concerns how the shape of an object changes while perturbing its projections. We have developed a simple genetic algorithm to reconstruct convex planar sets, giving a quantitative estimate for both the probability of finding solutions and of introducing errors at a given rate of instrumental noise in the projections. This method is fast and we have verified it on real images coming from biomedical tests. Further possible applications include non-destructive reverse engineering, industrial quality control, electron microscopy, X-rays crystallography, data coding and compression.

Genetic discrete reconstruction.