In this paper, we are concerned with a discrete tomography problem. We seek to reconstruct a binary image from its orthogonal projections, i.e, its horizontal and vertical line sums without interior black holes. We provide a tabu search approach to minimize the number of holes while satisfying the projections. We test our approach on some random binary images. Computational results show that th...

The binary steering process is a heuristic designed to intervene between consecutive steps of a nonbinary iterative image reconstruction algorithm in order to gradually steer the iterates towards a binary solution. We present computational results which show that a strongly overrelaxed simultaneous nonbinary iterative algorithm performs in our experiments better than a strongly underrelaxed seq...

In this paper we investigate for two well-known machine learning methods, decision trees and neural networks, how they classify discrete images from their projections. As an example, we present classification results when the task is to guess the number of intensity values of the discrete image. Machine learning can be used in Discrete Tomography as a preprocessing step in order to choose the p...

A new deconvolution algorithm for binary images based on the theory of discrete tomography is proposed. The proposed algorithm is inherently binary as opposed to traditional filtering techniques such as Wiener filtering which require thresholding to produce binary images. Time and space complexity of the proposed algorithm are polynomial in the image size whereas the two-dimensional Viterbi met...

Twenty five patients with manifestations of cerebrovascular ischemic disease were evaluated with high resolution computed tomography of the neck, following intravenous infusion of a contrast agent. Computed tomography images of extracranial carotid arteries revealed atherosclerotic plaque formations and their complications: stenosis, occlusion, ulceration, calcification and mural lucent defects...

We study the determination of finite subsets of the integer lattice Zn, n ≥ 2, by X-rays. In this context, an X-ray of a set in a direction u gives the number of points in the set on each line parallel to u. For practical reasons, only X-rays in lattice directions, that is, directions parallel to a nonzero vector in the lattice, are permitted. By combining methods from algebraic number theory a...

While X-ray radiography is commonly used for inline inspection of food, it is insufficient if 3D information is needed from the scanned object. Computed Tomography (CT) on the other hand, does provide 3D information, but is known to be expensive and relatively slow. This work proposes a low-cost X-ray scanning system based on a static X-ray source with a wide cone, along with a large detector w...

Soft computing is a term indicating a coalition of methodologies, and its basic dogma is that, in general, better results can be obtained through the use of constituent methodologies in combination, rather than in a stand alone mode. Evolutionary computing belongs to this coalition, and thus memetic algorithms. Here, we present a combination of several instances of a recently proposed memetic a...

Discrete tomography deals with image reconstruction of an object with finitely many gray levels (such as two). Different approaches are used to model the raw detector reading. The most popular models are line projection with a lattice of points and strip projection with a lattice of pixels/cells. The line-based projection model fits some applications but involves a major approximation since the...

Starting from the basic problem of reconstructing a 2-dimensional image given by its projections on two axes, one associates a model of edge coloring in a complete bipartite graph. The complexity of the case with k = 3 colors is open. Variations and special cases are considered for the case k = 3 colors where the graph corresponding to the union of some color classes (for instance colors 1 and ...