Fundamenta Informaticae - Volume 155, issue 4

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