Approximating hv-convex binary matrices and images from discrete projections
16 Apr 2008-pp 413-422
TL;DR: Since the problem of reconstructing hv-convex binary matrices from few projections is NP-complete, an iterative approximation based on a longest path and a min-cost/max-flow model is provided.
Abstract: We study the problem of reconstructing hv-convex binary matrices from few projections. We solve a polynomial time case and we determine some properties of the hv-convex matrices. Since the problem is NP-complete, we provide an iterative approximation based on a longest path and a min-cost/max-flow model. The experimental results show that the reconstruction algorithm performs quite well.
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24 Mar 2010
TL;DR: This variant of the NP-hard problem of reconstructing hv-convex binary matrices from two projections is reformulated as an integer programming problem and approximated by simulated annealing approach.
Abstract: We consider a variant of the NP-hard problem of reconstructing hv-convex binary matrices from two projections. This variant is reformulated as an integer programming problem and approximated by simulated annealing approach.
17 citations
Cites background from "Approximating hv-convex binary matr..."
...For certain constraints a polynomial time reconstruction algorithm exists....
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TL;DR: In this article, a variant of the NP-hard problem of reconstructing hv-convex binary matrices from two projections is reformulated as an integer programming problem and approximated by simulated annealing approach.
13 citations
TL;DR: A new hybrid optimisation algorithm combining the techniques of genetic algorithms and tabu search methods is proposed to find an optimal or an approximate solution for RCBIH, V problem, and its performance is evaluated and compared with other optimisation techniques.
Abstract: In this paper, we consider a variant of the NP-complete problem of reconstructing HV-convex binary images from two orthogonal projections, noted by RCBIH, V This variant is reformulated as a new integer programming problem Since this problem is NP-complete, a new hybrid optimisation algorithm combining the techniques of genetic algorithms and tabu search methods, noted by GATS is proposed to find an optimal or an approximate solution for RCBIH, V problem GATS starts from a set of solutions called 'population' initialised by using an extension of the network flow model, incorporating a cost function Two operators, namely crossover and mutation are used to explore the search space, then the quality of each individual in the population is improved by using another local search method named tabu search operator In this paper we describe the proposed algorithm, then we evaluate and compare its performance with other optimisation techniques The analysis of the experimental results shows the advantages of our GATS approach in terms of reconstruction quality and computational time
5 citations
TL;DR: This work reformulate the problem of reconstructing two-dimensional convex binary matrices from their row and column sums with adjacent ones by using integer programming and develops approximate solutions based on linearization and convexification techniques.
Abstract: We consider the problem of reconstructing two-dimensional convex binary matrices from their row and column sums with adjacent ones. Instead of requiring the ones to occur consecutively in each row and column, we maximize the number of adjacent ones. We reformulate the problem by using integer programming and we develop approximate solutions based on linearization and convexification techniques.
5 citations
Cites methods from "Approximating hv-convex binary matr..."
...[19] provide an approximate solution based on a longest path and network flow algorithms....
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23 May 2013
TL;DR: This paper considers the discret tomography problem (DTP), namely reconstruction convex binary matrices from their row and column sums respectively H and V, RBM(H,V), reformulated as an integer programming problem.
Abstract: In this paper, we consider the discret tomography problem (DTP), namely reconstruction convex binary matrices from their row and column sums respectively H and V, RBM(H,V). This is reformulated as an integer programming problem. Since the problem is NP-complete, a new hybrid genetic algorithm with simulated annealing algorithm is proposed to find an approximate solution.
3 citations
References
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TL;DR: In this paper, a matrix A of m rows and n columns, all of whose entries are 0's and 1's, is considered, and the sum of row i of A is denoted by r i (i = 1,..., m) and sum of column n of A are denoted as s i (1, n, n).
Abstract: This paper is concerned with a matrix A of m rows and n columns, all of whose entries are 0’s and 1’s. Let the sum of row i of A be denoted by r i (i = 1, ... , m) and let the sum of column i of A be denoted by S i (i = 1, ... ,n).
563 citations
"Approximating hv-convex binary matr..." refers background in this paper
...Ryser [12] gives necessary and sufficient conditions for the existence of a solution....
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...The problem of reconstructing a m × n binary matrix from its orthogonal projections H and V is the following [12]: givenH = (h1, ....
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Book•
01 Jan 1999
TL;DR: In this paper, Kuba, Gabor T. Herman, Eilat Vardi, and Cun-Hui Zhang present an algebraic solution for Discrete Tomography.
Abstract: Preface Contributors Part I. Foundations Discrete Tomography: A Historical Overview \ Attila Kuba, Gabor T. Herman Sets of Uniqueness and Additivity in Integer Lattices \ Peter C. Fishburn, Lawrence A. Shepp Tomopgraphic Equivalence and Switching Operations \ T. Yung Kong, Gabor T. Herman Uniqueness and Complexity in Discrete Tomography \ Richard J. Gardner, Peter Gritzmann Reconstruction of Plane Figures from Two Projections \ Akira Kaneko, Lei Huang Reconstruction of Two-Valued Functions and Matrices \ Attila Kuba Reconstruction of Connected Sets from Two Projections \ Alberto Del Lungo, Maurice Nivat Part II. Algorithms Binary Tomography Using Gibbs Priors \ Samuel Matej, Avi Vardi, Gabor T. Herman, Eilat Vardi Probabilistic Modeling of Discrete Images \ Michael T. Chan, Gabor T. Herman, Emanuel Levitan Multiscale Bayesian Methods for Discrete Tomography \ Thomas Frese, Charles A. Bouman, Ken Sauer An Algebraic Solution for Discrete Tomography \ Andrew E. Yagle Binary Steering of Nonbinary Iterative Algorithms \ Yair Censor, Samuel Matej Reconstruction of Binary Images via the EM Algorithm \ Yehuda Vardi, Cun-Hui Zhang Part III. Applications CT-Assisted Engineering and Manufacturing \ Jolyon A. Browne, Mathew Koshy 3D Reconstruction from Sparse Radiographic Data \ James Sachs, Jr., Ken Sauer Heart Chamber Reconstruction from Biplane Angiography \ Dietrich G.W. Onnasch, Guido P.M. Prause Discrete Tomography in Electron Microscopy \ J.M. Carazo, C.O. Sorzano, E. Rietzel, R. Schroeder, R. Marabini Tomopgraphy on the 3D-Torus and Crystals \ Pablo M. Salzberg, Raul Figueroa A Recursive Algorithm for Diffuse Planar Tomography \ Sarah K. Patch From Orthogonal Projections to Symbolic Projections \ Shi-KuoChang Index
480 citations
"Approximating hv-convex binary matr..." refers background in this paper
...The reader is referred to the book of Herman and Kuba [9] for an overview on discrete tomography....
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TL;DR: This work studies practical implementations of the scaling push-relabel method and develops heuristics which improve real-life performance of the method and may apply to other network algorithms.
362 citations
"Approximating hv-convex binary matr..." refers methods in this paper
...The min-cost/max-flowmodels used by the heuristic are solved by the CS2 network flow library developed by Andrew Goldberg [8]....
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TL;DR: Some operations for recontructing convex polyominoes by means of vectors H's and V's partial sums allows a new algorithm to be defined whose complexity is less than O(n2m2).
201 citations
TL;DR: In this paper, the combinational properties of all m × n matrices of 0's and 1's having r i 1's in row i and s i 1s in column j were studied.
191 citations