Discrete tomography deals with the reconstruction of binary images from their projections in a small number of directions. In this paper we consider possible neural network approaches to this tomographic reconstruction problem. In particular we are interested in methods that can compute reconstructions in real-time and make efficient use of prior knowledge about the images, even when this knowl...

Discrete tomography (DT) is an imaging technique for reconstructing discrete images from their projections using the knowledge that the object to be reconstructed contains only a few homogeneous materials characterized by known discrete absorption values. One of the main reasons for applying DT is that we will hopefully require relatively few projections. Using discreteness and some a priori in...

We consider the problem of recognizing arbitrary finite subsets of Z2 by X-rays corresponding to a small set of directions S. We show that if we fix any rectangle A in Z2 then there exists a so called valid set S of four directions (at least when A is not too ”small”) depending only on the size of A such that any two subsets of A can be distinguished, using these directions only. By our approac...

Particle tracking velocimetry in 3D is becoming an increasingly important imaging tool in the study of fluid dynamics and combustion as well as plasmas. We introduce a dynamic discrete tomography algorithm for reconstructing particle trajectories from projections. The algorithm is efficient for data from two projection directions and exact in the sense that it finds a solution consistent with t...

The affinely regular polygons in certain planar sets are characterized. It is also shown that the obtained results apply to cyclotomic model sets and, additionally, have consequences in the discrete tomography of these sets.

Discrete tomography DT is used for reconstructing special objects consisting of a few types of known homogeneous materials. For example, if we know that the object is made of wood, then the space contains only two materials: wood and air. Such objects can be represented with two-valued functions. The knowledge of the discrete range of the function to be reconstructed can also reduce the number ...

It has already been shown that the choice of projection angles can significantly influence the quality of reconstructions in discrete tomography. In this contribution we summarize and extend the previous results by explaining and demonstrating the effects of projection selection dependency, in a set of experimental software tests. We perform reconstructions of software phantoms, by using differ...

We consider the stability problem of reconstructing lattice sets from their noisy X-rays (i.e. line sums) taken along two directions. Stability is of major importance in discrete tomography because, in practice, these X-rays are affected by errors due to the nature of measurements. It has been shown that the reconstruction from noisy X-rays taken along more than two directions can lead to drama...

Discrete tomography is a powerful approach for reconstructing images that contain only a few grey levels from their projections. Most theory and reconstruction algorithms for discrete tomography assume that the values of these grey levels are known in advance. In many practical applications, however, the grey levels are unknown and difficult to estimate. In this paper, we propose a semiautomati...