Discrete tomography deals with the reconstruction of images from their projections where the images are assumed to contain only a small number of grey values. In particular, there is a strong focus on the reconstruction of binary images (binary tomography). A variety of binary tomography problems have been considered in the literature, each using different projection models or additional constr...

Discrete Tomography (DT) is concerned with the reconstruction of binary images from their horizontal and vertical projections. In this paper we consider an evolutionary algorithm for computing such reconstructions. We show that the famous Japanese puzzles are a special case of a more general DT problem and successfully apply our algorithm to such puzzles.

The problem of reconstructing finite subsets of the integer lattice from X-rays has been studied in discrete mathematics and applied in several fields like data security, electron microscopy, medical imaging. In this paper we focus on the stability of the reconstruction problem for some special lattice sets. First we prove that if the sets are additive, then a stability result holds for very sm...

There exists an elegant correspondence between the problem of reconstructing a 0-1 lattice image from two of its projections and the problem of finding a maximum flow in a certain graph. In this chapter we describe how network flow algorithms can be used to solve a variety of problems from discrete tomography. First, we describe the network flow approach for two projections and several of its g...

In this paper we study how the choice of projection angles affect the quality of the discrete tomographic reconstruction of an object. We supply four different strategies for selecting projection angle sets and compare them by conducting experiments on a set of software phantoms. We also discuss some consequences of our observations. Furthermore, we introduce a possible application of the propo...

One of the main problems in Discrete Tomography is the reconstruction of binary matrices from their projections in a small number of directions. In this thesis we consider a new algorithmic approach for reconstructing binary matrices from only two projections. This problem is usually underdetermined and the number of solutions can be very large. We present an evolutionary algorithm for finding ...

Computed tomography is a noninvasive technique for reconstructing an object from projection data. If the object consists of only a few materials, discrete tomography allows us to use prior knowledge of the gray values corresponding to these materials to improve the accuracy of the reconstruction. The Discrete Algebraic Reconstruction Technique (DART) is a reconstruction algorithm for discrete t...

Abstract In X-ray computed tomography, discrete tomography (DT) algorithms have been successful at reconstructing objects composed of only a few distinct materials. Many DT-based methods rely on divide-and-conquer procedure to reconstruct the volume in parts, which improves their run-time and reconstruction quality. However, this is based static rules, introduces redundant computation diminishe...

Key members: Péter Balázs [1] Mihály Gara [2] Tamás Sámuel Tasi [3] László G. Nyúl [4] Founded by: PhD Scholarship of the Doctoral School in Informatics of the University of Szeged [5] János Bolyai Research Scholarship of the Hungarian Academy of Sciences [6] TÁMOP-4.2.2/B-10/1-2010-0012 program of the Hungarian National Development Agency [7] OTKA PD100950 grant of the Hungarian Scientific Res...

A sequence π = (d1, . . . , dn) is graphic if there is a simple graph G with vertex set {v1, . . . , vn} such that the degree of vi is di. We say that graphic sequences π1 = (d (1) 1 , . . . , d (1) n ) and π2 = (d (2) 1 , . . . , d (2) n ) pack if there exist edge-disjoint n-vertex graphs G1 and G2 such that for j ∈ {1, 2}, dGj (vi) = d (j) i for all i ∈ {1, . . . , n}. Here, we prove several ...