A Fast Algorithm for Reconstructing hv-Convex Binary Images from Their Horizontal Projection
08 Dec 2014-pp 789-798
TL;DR: This paper provides a fast polynomial-time algorithm for reconstructing canonical hv-convex images with given number of 4-connected components and with minimal number of columns satisfying a prescribed horizontal projection and shows that the method gives a solution that is always 8-connected.
Abstract: The reconstruction of certain types of binary images from their projections is a frequently studied problem in combinatorial image processing. hv-convex images with fixed projections play an important role in discrete tomography. In this paper, we provide a fast polynomial-time algorithm for reconstructing canonical hv-convex images with given number of 4-connected components and with minimal number of columns satisfying a prescribed horizontal projection. We show that the method gives a solution that is always 8-connected. We also explain how the algorithm can be modified to obtain solutions with any given number of columns, and also with non-connected components.
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11 Mar 2016
TL;DR: A tomografia celja egy haromdimenzios objektum ketdimenzosios szeleteit abrazolo kepeinek előallitasa a vetuletek ismereteben.
Abstract: A tomografia celja egy haromdimenzios objektum ketdimenzios szeleteit abrazolo kepeinek előallitasa a vetuletek ismereteben. A tomografia elsősorban orvostudomanyi problema, de előfordul fizikai, kemiai, biologiai, ipari alkalmazasokban is. Egy fontos alterulete a tomografianak a binaris tomografia, ahol a cel homogen alakzatok binaris rekonstrukcioja. A legtobb esetben csak keves vetulet all rendelkezesre, mivel a vetuletkepzes koltseges, illetve roncsolhatja a vizsgalt objektumot. Ezen felul a kepalkoto berendezesek fizikai korlatai miatt a valos alkalmazasokban nem lehetseges tetszőlegesen sok vetuletet kepezni; marpedig keves vetulet eseten a rekonstrukcio bizonytalan, a lehetseges megoldasok szama nagy lehet. A lehetseges megoldasok szamanak csokkentese erdekeben gyakran felteteleznek a rekonstrualando kepről bizonyos geometriai tulajdonsagokat. Jelen ertekezes a Szerző binaris tomografiaban elert, binaris matrixokat erintő eredmenyeit tartalmazza. Az ertekezes elsősorban a ket vetuletből tortenő rekonstrukciora terjed ki, ha a rekonstrukcio soran bizonyos megszoritasokat teszunk az eredmenykepre. Tovabbi eredmenyeket tartalmaz a kapcsolo komponensekről, a rekonstrukcios problema bonyolultsagelmeleteről, a lehetseges megoldasok szamarol, es uj algoritmusokat mutat be binaris kepek alosztalyainak rekonstrukciojahoz.
2 citations
Cites background from "A Fast Algorithm for Reconstructing..."
...The findings of this reasearch have been published in two conference proceedings [15, 20], and one journal paper [19]....
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...[15] [16] [17] [18] [19] [20] [21] [22] [23] I/1....
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...The results were published in two conference proceedings [15, 20], and one journal paper [19]....
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01 Aug 2016
TL;DR: The proposed model, which has been proposed with the genetic programming and robust dual-stage post-processing module, can be considered the clear winner in comparison with the subsisted model based upon the metallurgy temperature flattening algorithm in the subsisting model.
Abstract: The binary matrix or binary image reconstruction plays vital role in the reconstruction of the binary image matrix from the projection data. The several types of projection data can be taken from the binary matrices. The horizontal and vertical projections are the simplest form of the projections, whereas the diagonal and anti-diagonal projections can also be utilized for the purpose of image reconstruction from the projection data. The variance or covariance based projections also plays the important role in the case of binary image reconstruction. The binary image reconstruction may require a number of computations over the input projection data. The initial solution is essentially required because of the certain requirement for the initial stage matrix for the later stage processing, which has been proposed with the genetic programming and robust dual-stage post-processing module in this case. The results of the proposed model have been collected in the time and accuracy based parameters. The proposed model can be considered the clear winner in comparison with the subsisting model based upon the metallurgy temperature flattening algorithm in the subsisting model.
References
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TL;DR: The number of comparisons required to select the i-th smallest of n numbers is shown to be at most a linear function of n by analysis of a new selection algorithm-PICK.
1,384 citations
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
TL;DR: The basic principles of DART are described and it is shown that it can be applied successfully to three different types of samples, consisting of embedded ErSi(2) nanocrystals, a carbon nanotube grown from a catalyst particle and a single gold nanoparticle, respectively.
286 citations
01 Jan 2007
TL;DR: A. Kuba and G.T. Herman Discrete point X-ray (DPT) reconstruction as discussed by the authors is a well-known technique in the field of discrete tomography.
Abstract: ANHA Series Preface Preface List of Contributors Introduction / A. Kuba and G.T. Herman Part I. Foundations of Discrete Tomography An Introduction to Discrete Point X-Rays / P. Dulio, R.J. Gardner, and C. Peri Reconstruction of Q-Convex Lattice Sets / S. Brunetti and A. Daurat Algebraic Discrete Tomography / L. Hajdu and R. Tijdeman Uniqueness and Additivity for n-Dimensional Binary Matrices with Respect to Their 1-Marginals / E. Vallejo Constructing (0, 1)-Matrices with Given Line Sums and Certain Fixed Zeros / R.A. Brualdi and G. Dahl Reconstruction of Binary Matrices under Adjacency Constraints / S. Brunetti, M.C. Costa, A. Frosini, F. Jarray, and C. Picouleau Part II. Discrete Tomography Reconstruction Algorithms Decomposition Algorithms for Reconstructing Discrete Sets with Disjoint Components / P. Balazs Network Flow Algorithms for Discrete Tomography / K.J. Batenburg A Convex Programming Algorithm for Noisy Discrete Tomography / T.D. Capricelli and P.L. Combettes Variational Reconstruction with DC-Programming / C. Schnoerr, T. Schule, and S. Weber Part III. Applications of Discrete Tomography Direct Image Reconstruction-Segmentation, as Motivated by Electron Microscopy / Hstau Y. Liao and Gabor T. Herman Discrete Tomography for Generating Grain Maps of Polycrystals / A. Alpers, L. Rodek, H.F. Poulsen, E. Knudsen, G.T. Herman Discrete Tomography Methods for Nondestructive Testing / J. Baumann, Z. Kiss, S. Krimmel, A. Kuba, A. Nagy, L. Rodek, B. Schillinger, and J. Stephan Emission Discrete Tomography / E. Barcucci, A. Frosini, A. Kuba, A. Nagy, S. Rinaldi, M. Samal, and S. Zopf Application of a Discrete Tomography Approach to Computerized Tomography / Y. Gerard and F. Feschet Index
256 citations
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