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Fundamenta Informaticae is an international journal publishing original research results in all areas of theoretical computer science. Papers are encouraged contributing:
- solutions by mathematical methods of problems emerging in computer science
- solutions of mathematical problems inspired by computer science.
Topics of interest include (but are not restricted to): theory of computing, complexity theory, algorithms and data structures, computational aspects of combinatorics and graph theory, programming language theory, theoretical aspects of programming languages, computer-aided verification, computer science logic, database theory, logic programming, automated deduction, formal languages and automata theory, concurrency and distributed computing, cryptography and security, theoretical issues in artificial intelligence, machine learning, pattern recognition, algorithmic game theory, bioinformatics and computational biology, quantum computing, probabilistic methods, & algebraic and categorical methods.
Authors: Dulio, Paolo | Frosini, Andrea | Rozenberg, Grzegorz
Article Type: Other
DOI: 10.3233/FI-2017-1587
Citation: Fundamenta Informaticae, vol. 155, no. 4, pp. i-vii, 2017
Authors: Alpers, Andreas | Gritzmann, Peter
Article Type: Research Article
Abstract: The present paper deals with the discrete inverse problem of reconstructing binary matrices from their row and column sums under additional constraints on the number and pattern of entries in specified minors. While the classical consistency and reconstruction problems for two directions in discrete tomography can be solved in polynomial time, it turns out that these window constraints cause various unexpected complexity jumps back and forth from polynomialtime solvability to ℕℙ-hardness.
DOI: 10.3233/FI-2017-1588
Citation: Fundamenta Informaticae, vol. 155, no. 4, pp. 321-340, 2017
Authors: Arcadu, Filippo | Vogel, Jakob | Stampanoni, Marco | Marone, Federica
Article Type: Research Article
Abstract: This work introduces and characterizes a fast parameterless filter based on the Helgason-Ludwig consistency conditions, used to improve the accuracy of analytical reconstructions of tomographic undersampled datasets. The filter, acting in the Radon domain, extrapolates intermediate projections between those existing. The resulting sinogram, doubled in views, is then reconstructed by a standard analytical method. Experiments with simulated and real data prove that the peak-signal-to-noise ratio of the results computed by filtered backprojection is improved up to 5–6 dB, if the filter is used prior to reconstruction.
Keywords: Tomography, analytical reconstruction algorithms, consistency conditions
DOI: 10.3233/FI-2017-1589
Citation: Fundamenta Informaticae, vol. 155, no. 4, pp. 341-361, 2017
Authors: Brun, Emmanuel | Ferrero, Claudio | Vicente, Jerome
Article Type: Research Article
Abstract: The granulometry operator is a mathematical operator largely employed in the 3D analysis of porous media to estimate the sizes of the pores detected in pervious materials and tissues. Quantifying the total porosity volume in a material with only closed pores is a relatively easy task. A simple numerical analysis of connected void or fluid phase components enables one to obtain such a volume. Unfortunately, for materials and/or tissues with (partly) open porosity granulometry calculations might become excessively time and memory consuming. In this work we suggest a method by means of which the open porosity map can be rapidly …calculated on the basis of a pre-calculated distance map. Show more
Keywords: mathematical morphology, granulometry, 3D images
DOI: 10.3233/FI-2017-1590
Citation: Fundamenta Informaticae, vol. 155, no. 4, pp. 363-372, 2017
Authors: Chapdelaine, Camille | Mohammad-Djafari, Ali | Gac, Nicolas | Parra, Estelle
Article Type: Research Article
Abstract: Iterative reconstruction methods in Computed Tomography (CT) are known to provide better image quality than analytical methods but they are not still applied in many fields because of their computational cost. In the last years, Graphical Processor Units (GPU) have emerged as powerful devices in order to parallelize calculations, but the efficiency of their use is conditionned on applying algorithms that can be massively parallelizable. Moreover, in non-destructive testing (NDT) applications, a segmentation of the reconstructed volume is often needed in order to have an accurate diagnosis on the material health, but performing a segmentation after the reconstruction introduces uncertainties …in the diagnosis from both the reconstruction and the segmentation algorithms. In this paper, we propose an iterative reconstruction method for 3D CT that performs a joint reconstruction and segmentation of the controlled object in NDT for industrial applications. The method is based on a 3D Gauss-Markov-Potts prior model in Bayesian framework, which has shown its effective use in many image restoration and super-resolution problems. First, we briefly describe this model, before deriving the expression of the joint posterior distribution of all the unknowns. Next, an effective maximization of this distribution is presented. We use a ray-driven projector and a voxel-driven backprojector implemented on GPU. The algorithm is developed so it can be massively parallelized. Finally, we present our results on simulated and real phantoms. In addition, we investigate further reconstruction quality indicators in order to compare our results with other methods. Show more
Keywords: 3D Computed Tomography, Bayesian, Gauss-Markov-Potts, iterative CT reconstruction, X-ray
DOI: 10.3233/FI-2017-1591
Citation: Fundamenta Informaticae, vol. 155, no. 4, pp. 373-405, 2017
Authors: Dulio, Paolo | Pagani, Silvia M.C. | Frosini, Andrea
Article Type: Research Article
Abstract: In discrete tomographic image reconstruction, projections are taken along a finite set S of valid directions for a working grid 𝒜. In general, uniqueness cannot be achieved in the whole grid 𝒜. Usually, some information on the object to be reconstructed is introduced, that, sometimes, allows possible ambiguities to be removed. From a different perspective, one aims in finding subregions of 𝒜 where uniqueness can be guaranteed, and obtained in linear time, only from the knowledge of S . When S consists of two lattice directions, the shape of any such region of uniqueness, say ROU, …have been completely characterized in previous works by means of a double Euclidean division algorithm called DEDA. Results have been later extended to special triples of directions, under a suitable assumption on their entries. In this paper we remove the previous assumption, so providing a complete characterization of the shape of the ROU for such kind of triples. We also show that the employed strategy can be even applied to more general sets of three directions, where the corresponding ROU can be characterized as well. Independently of the combinatorial interest of the problem, the result can be exploited to define in advance, namely before using any kind of radiation, suitable sets of directions that allow regions of interest to be included in the corresponding ROU. Results have been proved in all details, and several experiments are considered, in order to support the theoretical steps and to clarify possible applications. Show more
Keywords: Discrete Tomography, Lattice grid, Projection, Uniqueness region
DOI: 10.3233/FI-2017-1592
Citation: Fundamenta Informaticae, vol. 155, no. 4, pp. 407-423, 2017
Authors: Hajdu, Lajos | Tijdeman, Rob
Article Type: Research Article
Abstract: For continuous tomography Helgason and Ludwig developed consistency conditions. They were used by others to overcome defects in the measurements. In this paper we introduce a consistency criterion for discrete tomography. We indicate how the consistency criterion can be used to overcome defects in measurements.
Keywords: Discrete tomography, linear dependencies, global dependencies
DOI: 10.3233/FI-2017-1593
Citation: Fundamenta Informaticae, vol. 155, no. 4, pp. 425-447, 2017
Authors: Wang, Li | Mohammad-Djafari, Ali | Gac, Nicolas
Article Type: Research Article
Abstract: X-ray Computed Tomography (CT) has become a hot topic in both medical and industrial applications in recent decades. Reconstruction by using a limited number of projections is a significant research domain. In this paper, we propose to solve the X-ray CT reconstruction problem by using the Bayesian approach with a hierarchical structured prior model basing on the multilevel Haar transformation. In the proposed model, the multilevel Haar transformation is used as the sparse representation of a piecewise continuous image, and a generalized Student-t distribution is used to enforce its sparsity. The simulation results compare the performance of the proposed method …with some state-of-the-art methods. Show more
Keywords: Computed Tomography (CT), Bayesian Approach, Hierarchical Model, Generalized Student-t distribution, Joint Maximum A Posterior (JMAP)
DOI: 10.3233/FI-2017-1594
Citation: Fundamenta Informaticae, vol. 155, no. 4, pp. 449-480, 2017
Article Type: Other
Citation: Fundamenta Informaticae, vol. 155, no. 4, pp. 481-482, 2017
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