Fundamenta Informaticae - Volume 135, issue 1-2

Authors: Dulio, Paolo | Frosini, Andrea | Rozenberg, Grzegorz

Article Type: Other

DOI: 10.3233/FI-2014-1108

Citation: Fundamenta Informaticae, vol. 135, no. 1-2, pp. v-xxi, 2014

Authors: Plantagie, Linda | Batenburg, K. Joost

Article Type: Research Article

Abstract: Filtered Backprojection is the most widely used reconstruction method in transmission tomography. The algorithm is computationally efficient, but requires a large number of low-noise projections acquired over the full angular range to produce accurate reconstructions. Algebraic reconstruction methods on the other hand are in general more robust with respect to noise and can incorporate the available angular range in the underlying projection model. A drawback of these methods is their higher computational cost. In a recent article, we demonstrated that for linear algebraic reconstruction methods, a filter can be computed such that applying Filtered Backprojection using this filter yields reconstructions …that approximate the algebraic method. In the present work, we explore a modification of this approach, where we use more than one algebraic filter in the reconstructions, each covering a different region of the reconstruction grid. We report the results of a series of experiments to determine the how well the reconstruction and approximation accuracy of this approach. Show more

Keywords: Tomographic Reconstruction, Filtered Backprojection, Algebraic Reconstruction

DOI: 10.3233/FI-2014-1109

Citation: Fundamenta Informaticae, vol. 135, no. 1-2, pp. 1-19, 2014

Authors: Bleichrodt, Folkert | De Beenhouwer, Jan | Sijbers, Jan | Batenburg, Kees Joost

Article Type: Research Article

Abstract: In tomography, slight differences between the geometry of the scanner hardware and the geometric model used in the reconstruction lead to alignment artifacts. To exploit high-resolution detectors used in many applications of tomography, alignment of the projection data is essential. Markerless alignment algorithms are the preferred choice over alignment with markers, in case a fully automatic tomography pipeline is required. Moreover, marker based alignment is often not feasible or even possible. At the same time, markerless alignment methods often fail in scenarios where only a small number of projections are available. In this case, the angular separation between projection images …is large and therefore the correlation between them is low. This is a property that most markerless algorithms rely on. The intermediate reconstruction problem of alignment by projection matching is highly underdetermined in the limited data case. Therefore, we propose a projection matching method that incorporates prior knowledge of the ground truth. We focus on reconstructing binary volumes. A discrete tomography algorithm is employed to generate intermediate reconstructions. This type of reconstruction algorithm does not rely heavily on correlated projection images. Our numerical results suggest that alignment using discrete tomography projection matching produces much better results in the limited angle case, when compared to a projection matching method that employs an algebraic reconstruction method. Show more

Keywords: alignment, automatic, binary tomography, prior knowledge

DOI: 10.3233/FI-2014-1110

Citation: Fundamenta Informaticae, vol. 135, no. 1-2, pp. 21-42, 2014

Authors: Brocchi, Stefano

Article Type: Research Article

Abstract: In this paper we tackle the problem of the reconstruction of object based images, specifically formed by a set of circles inside a ring. By analyzing the projections of the image, we are able to determine some coordinates corresponding to interest points that give significant information about features of the image of aid in the reconstruction. Our approach yields promising results in comparison to other methods in literature. Finally, we discuss how a similar approach could be extended to more complex problems deriving from tomographic applications, in order to develop an efficient method exploiting the prior knowledge assumed on an …image. Show more

DOI: 10.3233/FI-2014-1111

Citation: Fundamenta Informaticae, vol. 135, no. 1-2, pp. 43-57, 2014

Authors: Brlek, Srečko | Lafreniére, Nadia

Article Type: Research Article

Abstract: We consider words on a finite alphabet Σ and study the structure of its σ-palindromes, i.e. words w satisfying w = σ($\tilde{w}$) for some involution σ on the alphabet. We provide algorithms for the computation of σ-lacunas in w, that is the positions where the longest σ-palindromic suffix is not uni-occurrent. The σ-palindromic defect is explicitly computed for Sturmian words and the Thue-Morse word. Finally, the problem of reconstructing words from a given fixed set of σ-palindromes is decidable.

Keywords: Generalized palindromes, complexity, σ-palindromic lacunas, σ-palindromic defect

DOI: 10.3233/FI-2014-1112

Citation: Fundamenta Informaticae, vol. 135, no. 1-2, pp. 59-72, 2014

Authors: Deniţiu, Andreea | Petra, Stefania | Schnörr, Claudius | Schnörr, Christoph

Article Type: Research Article

Abstract: We study unique recovery of cosparse signals from limited-view tomographic measurements of two- and three-dimensional domains. Admissible signals belong to the union of subspaces defined by all cosupports of maximal cardinality ℓ with respect to the discrete gradient operator. We relate ℓ both to the number of measurements and to a nullspace condition with respect to the measurement matrix, so as to achieve unique recovery by linear programming. These results are supported by comprehensive numerical experiments that show a high correlation of performance in practice and theoretical predictions. Despite poor properties of the measurement matrix from the viewpoint of compressed …sensing, the class of uniquely recoverable signals basically seems large enough to cover practical applications, like contactless quality inspection of compound solid bodies composed of few materials. Show more

Keywords: compressed sensing, underdetermined systems of linear equations, cosparsity, total variation, discrete and limited-view tomography

DOI: 10.3233/FI-2014-1113

Citation: Fundamenta Informaticae, vol. 135, no. 1-2, pp. 73-102, 2014

Authors: Hantos, Norbert | Balázs, Péter

Article Type: Research Article

Abstract: We provide a quadratic-time algorithm for generating hv-convex polyominoes according to a given horizontal projection. The method can be used to generate hv-convex polyominoes with the prescribed projection and with a fixed or arbitrary horizontal dimension, from a uniform random distribution.

Keywords: hv-convex polyomino, horizontal projection, random generation, binary tomography

DOI: 10.3233/FI-2014-1114

Citation: Fundamenta Informaticae, vol. 135, no. 1-2, pp. 103-115, 2014

Authors: Goupy, Alexandre | Pagani, Silvia M.C.

Article Type: Research Article

Abstract: In this paper the well-known problem of reconstructing hv-convex polyominoes is considered from a set of noisy data. Differently from the usual approach of Binary Tomography, this leads to a probabilistic evaluation in the reconstruction algorithm, where different pixels assume different probabilities to be part of the reconstructed image. An iterative algorithm is then applied, which, starting from a random choice, leads to an explicit reconstruction matching the noisy data.

Keywords: hv-convex polyomino, noisy data, polyomino, reconstruction algorithm

DOI: 10.3233/FI-2014-1115

Citation: Fundamenta Informaticae, vol. 135, no. 1-2, pp. 117-134, 2014

Authors: Fiorini, Rodolfo A.

Article Type: Research Article

Abstract: Discrete Tomography (DT), differently from GT and CT, focuses on the case where only few specimen projections are known and the images contain a small number of different colours (e.g. black-and-white). A concise review on main contemporary physical and mathematical CT system problems is offered. Stochastic vs. Combinatorially Optimized Noise generation is compared and presented by two visual examples to emphasise a major double-bind problem at the core of contemporary most advanced instrumentation systems. Automatic tailoring denoising procedures to real dynamic system characteristics and performance can get closer to ideal self-registering and self-linearizing system to generate virtual uniform and robust …probing field during its whole designed service life-cycle. The first attempt to develop basic principles for system background low-level noise source automatic characterization, profiling and identification by CICT, from discrete system parameter, is presented. As a matter of fact, CICT can supply us with cyclic numeric sequences perfectly tuned to their low-level multiplicative source generators, related to experimental high-level overall perturbation (according to high-level classic perturbation computational model under either additive or multiplicative perturbation hypothesis). Numeric examples are presented. Furthermore, a practical NTT example is given. Specifically, advanced CT system, HRO and Mission Critical Project (MCP) for very low Technological Risk (TR) and Crisis Management (CM) system will be highly benefitted mostly by CICT infocentric worldview. The presented framework, concepts and techniques can be used to boost the development of next generation algorithms and advanced applications quite conveniently. Show more

Keywords: Discrete Tomography, Computerized Tomography, Computational Information Conservation Theory, Denoising, Modular Arithmetic, Number Theoretic Transform, Biomedical Cybernetics, Biomedical Engineering, HRO, Public Health, Digital Healthcare

DOI: 10.3233/FI-2014-1116

Citation: Fundamenta Informaticae, vol. 135, no. 1-2, pp. 135-170, 2014

Authors: Fedele, Roberto | Ciani, Antonia | Fiori, Fabrizio

Article Type: Research Article

Abstract: In this review paper the synergistic combination of X-ray microtomography, in situ mechanical tests on material samples and full-field kinematic measurements by 3D-Volume Digital Image Correlation is discussed. First, basic features are outlined, concerning X-ray microtomography by either laboratory sources or synchrotron radiation. The main equations for 3D-Volume Digital Image Correlation are then presented, and different provisions regularizing the ill-posed problem of motion estimation are outlined. Thereafter, a survey of the state of the art is provided, with reference to a variety of biological and engineering materials. Limitations and perspectives of the proposed methodology in diverse applications are highlighted. The …rapid growth of this research topic is emphasized, due to the truly multi-disciplinary vocation, the synergy between algorithmic and technological solutions, a fusion of experiments and numerical methods. Show more

Keywords: X-ray microtomography, 3D-Volume Digital Image Correlation, Regularization, Heterogeneous materials, Material characterization, Mechanical tests

DOI: 10.3233/FI-2014-1117

Citation: Fundamenta Informaticae, vol. 135, no. 1-2, pp. 171-197, 2014

Authors: Compagnoni, Marco | Notari, Roberto

Article Type: Research Article

Abstract: In this paper, we complete the study of the geometry of the TDOA map that encodes the noiseless model for the localization of a source from the range differences between three receivers in a plane, by computing the Cartesian equation of the bifurcation curve in terms of the positions of the receivers. From that equation, we can compute its real asymptotic lines. The present manuscript completes the analysis of [12]. Our result is useful to check if a source belongs or is closed to the bifurcation curve, where the localization in a noisy scenario is ambiguous.

DOI: 10.3233/FI-2014-1118

Citation: Fundamenta Informaticae, vol. 135, no. 1-2, pp. 199-210, 2014