Abstract
This paper considered that two projections along the left and right horizontal directions uniquely determine a binary matrix when the absorbed coefficient is special. For the weakness of computational complexity of projection difference, an improved algorithm is proposed to reconstruct binary matrices along the diagonal projections based on determining conditions of sequence consistency. Furthermore, comparing with the existing algorithm, it’s more efficient to search solutions.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Herman, G., Kuba, A.: Discrete tomography: foundations, algorithms and applications. Birkhäuser, Boston (1999)
Frosini, S., Rinaldi, A., Kuba: An efficient algorithm for reconstructing binary matrices from horizontal and vertical absorbed projections. Electronic Notes in Discrete Mathematics 20, 347–363 (2005)
Kuba, Nivat, M.: A sufficient condition for non-uniqueness in binary tomography with absorption. Theoretical Computer Science 346, 335–357 (2005)
Kuba, Nagy, A., Balogh, E.: Reconstruction of hv-convex binary matrices from their absorbed projections. Discrete Applied Mathematics 139, 137–148 (2004)
Barcucci, E., Frosini, A., Rinaldi, S.: An algorithm for the reconstruction of discrete sets from two projections in presence of absorption. Discrete Applied Mathematics 151, 21–35 (2005)
Woeginger, G.W.: The reconstruction of polynomial from their orthogonal projections. Inform. Process. Lett. 77, 225–232 (2001)
Kuba, A., Nivat, M.: Reconstruction of Discrete Sets with Absorption. In: Nyström, I., Sanniti di Baja, G., Borgefors, G. (eds.) DGCI 2000. LNCS, vol. 1953, pp. 137–148. Springer, Heidelberg (2000)
Miklos, P., Tech, S.: Discrete tomographic reconstruction of binary matrices using tabu search and classic ryser algorithm. In: 9th International Symposium on Intelligent Systems and Informatics (SISY 2011), pp. 387–390 (2011)
Miklos, P., Csongor, G.: Discrete tomographic reconstruction of binary matrices using branch and bound method. In: 7th Intellithent Systems and Informatics (SISY 2009), pp. 85–88 (2009)
Jarray, F., Tlig, C.: A simulated annealing for reconstructing hv-convex binary matrices. Electronic Notes in Discrete Mathematics 36, 447–454 (2010)
Balazs, P.: A benchmark set for the reconstruction of hv-convex discrete sets. Discrete Applied Mathematics, 3447–3456 (2009)
Varga, L., Balazs, P., Nagy, A.: Direction-dependency of binary tomographic reconstruction algorithms. Graphical Models, 365–375 (2011)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Junyu, C., Aili, G., Chuanlin, Z. (2012). An Efficient Algorithm for Reconstruction of Discrete Sets from Horizontal Projections with Absorption. In: Liu, C., Wang, L., Yang, A. (eds) Information Computing and Applications. ICICA 2012. Communications in Computer and Information Science, vol 307. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34038-3_105
Download citation
DOI: https://doi.org/10.1007/978-3-642-34038-3_105
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-34037-6
Online ISBN: 978-3-642-34038-3
eBook Packages: Computer ScienceComputer Science (R0)