Abstract
The problem of reconstruction of a binary image in the field of discrete tomography is a classic instance of seeking solution applying mathematical techniques. Here two such binary image reconstruction problems are considered given some numerical information on the image. Algorithms are developed for solving these problems and correctness of the algorithms are discussed.
Similar content being viewed by others
References
Balázs, P. Discrete tomographic reconstruction of binary images with disjoint components using shape information. Int. J. Shape Modeling, 14: 189–207 (2008)
Batenburg, K.J. Analysis and optimization of an algorithm for discrete tomography. Elect. Notes Disc. Math., 12: 35–46 (2003)
Brocchi, S., Frosini, A., Picouleau, C. Reconstruction of binary matrices under fixed size neighborhood constraints. Theor. Comp. Sci., 406: 43–54 (2008)
Brualdi, R.A. Algorithms for constructing (0, 1)-matrices with prescribed row and column sum vectors. Discrete Math., 306: 3054–3062 (2006)
Brunetti, S., Frosini, A., Picouleau, C. Reconstructing a binary matrix under timetabling constraints. Electronic Notes in Discrete Mathematics, 20: 99–112 (2005)
Brunetti, S., Del Lungo, A., Gritzmann, P., de Vries, S. On the reconstruction of binary and permutation matrices under (binary) tomographic constraints. Theor. Comp. Sci., 406: 63–71 (2008)
Costa, M.-C., Jarray, F., Picouleau, C. Reconstruction of binary matrices under adjacency constraints. Electronic Notes in Discrete Math., 20: 281–297 (2005)
Dahl, G., Brualdi, R.A. Matrices of zeros and ones with given line sums and a zero block. Electronic Notes in Discrete Math., 20: 83–97 (2005)
Frosini, A., Nivat, M. Binary matrices under the microscope: a tomographical problem. Theor. Comp. Sci., 370: 201–217 (2007)
Gale, D. A theorem on flow in net works. Pacific J. Math., 7: 1073–1083 (1957)
Herman, G.T., Kuba, A. (eds.) Discrete Tomography: Foundations, Algorithms and Applications, Birkhuser, 1999
Herman, G.T., Kuba, A. (eds.) Advances in Discrete Tomography and Its Applications, Birkhuston, 2007
Kuba, A. Reconstruction of unique binary matrices with prescribed elements. Acta Cybernetica, 12: 57–70 (1995)
Ozsvár, Z., Balázs, P. An empirical study of reconstructing hv-convex binary matrices from horizontal and vertical projections. Acta Cybernetica, 21: 149–163 (2013)
Masilamani, V., Krithivasan, K., Subramanian, K.G., Miin Huey, A. Efficient Algorithms for Reconstruction of 2D-Arrays from Extended Parikh Images. Lect. Notes in Comp. Sci., 5359: 1137–1146 (2008)
Masilamani, V., Krithivasan, K. Bi-level image reconstruction from its two orthogonal projections with periodicity and a subimage constraint. Int. J. Imaging Sci. and Engineering, 2: 170–173 (2008)
Mateescu, A., Salomaa, A. Matrix indicators for subword occurrences and ambiguity. Int. J. Found. Comput. Sci., 15: 277–292 (2004)
Mateescu, A., Salomaa, A., Salomaa, K., Yu, S. A Sharpening of the Parikh Mapping. Theoret. Informatics Appl., 35: 551–564 (2001)
Parikh, R.J. On context-free languages. J. Assoc. Comput. Mach., 13: 570–581 (1966)
Ryser, H.J. Combinatorial propertiers of matrices of zeros and ones. Pacific J. Math., 9: 371–377 (1957)
Salomaa, A. Formal Languages, Academic Press, London, 1973
Salomaa, A. On the injectivity of Parikh matrix mappings. Fundam. Inf., 64: 391–404 (2005)
Subramanian, K.G., Huey, A.M., Nagar, A.K. On Parikh matrices. Int. J. Found. Comp. Sci., 20: 211–219 (2009)
Tawbe, K. Two Subclasses of 2-convex Polyominoes: Properties For Reconstruction. Appl. Anal. Discrete Math., 4: 136–155 (2010)
Yasar, O., Diner, C., Dogan, A., Weber, G.W., Ozbudak, F., Tiefenbach, A. On the applied mathematics of discrete tomography. J. Computational Technologies, 9(5): 14–32 (2004)
Author information
Authors and Affiliations
Corresponding author
Additional information
The first author K.G. Subramanian and the fourth author Ibrahim Venkat gratefully acknowledge support for this research respectively from a FRGS grant No. 203/PKOMP/6711267 and an ERGS Grant No. 203/PKOMP/6730075 of the Ministry of Higher Education (MoHE), Malaysia. The second author Pradeep Isawasan would like to thank MoHE for the award of MyPhD under which this research was jointly carried out by him.
Rights and permissions
About this article
Cite this article
Subramanian, K.G., Isawasan, P., Budiarto, R. et al. Binary image reconstruction based on prescribed numerical information. Acta Math. Appl. Sin. Engl. Ser. 31, 519–528 (2015). https://doi.org/10.1007/s10255-015-0482-4
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10255-015-0482-4