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Reconstruction of Binary Images with Fixed Number of Strips

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Image Analysis and Recognition (ICIAR 2018)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10882))

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Abstract

We consider the problem of reconstructing a binary matrix from its row and column sums with the additional constraint that for each row and column the number of strips (consecutive 1 s of maximal length) is given. The problem is connected both to binary tomography and to nonogram puzzles, and is in general NP-hard. Here, we propose an integer programming framework and an approximation algorithm based on simulated annealing to solve this issue. The effectiveness of the two methods are compared on randomly generated binary matrices.

This research was supported by the NKFIH OTKA [grant number K112998] and by the project “Integrated program for training new generation of scientists in the fields of computer science”, no EFOP-3.6.3-VEKOP-16-2017-0002. The project has been supported by the European Union and co-funded by the European Social Fund.

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References

  1. Aert, S.V., Batenburg, K.J., Rossell, M.D., Erni, R., Tendeloo, G.V.: Three-dimensional atomic imaging of crystalline nanoparticles. Nature 470, 374–377 (2011)

    Article  Google Scholar 

  2. Balázs, P., Gara, M.: An evolutionary approach for object-based image reconstruction using learnt priors. In: Salberg, A.-B., Hardeberg, J.Y., Jenssen, R. (eds.) SCIA 2009. LNCS, vol. 5575, pp. 520–529. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-02230-2_53

    Chapter  Google Scholar 

  3. Batenburg, K.J., Bals, S., Sijbers, J., Kuebel, C., Midgley, P.A., Hernandez, J.C., Kaiser, U., Encina, E.R., Coronado, E.A., Tendeloo, G.V.: 3D imaging of nanomaterials by discrete tomography. Ultramicroscopy 109(6), 730–740 (2009)

    Article  Google Scholar 

  4. Batenburg, K.J., Kosters, W.A.: Solving Nonograms by combining relaxations. Pattern Recogn. 42(8), 1672–1683 (2009)

    Article  Google Scholar 

  5. Baumann, J., Kiss, Z., Krimmel, S., Kuba, A., Nagy, A., Rodek, L., Schillinger, B., Stephan, J.: Discrete tomography methods for nondestructive testing. In: [8], pp. 303–331 (2007)

    Google Scholar 

  6. Dahl, G., Flatberg, T.: Optimization and reconstruction of \(hv\)-convex \((0,1)\)-matrices. Disc. Appl. Math. 151, 93–105 (2005)

    Article  MathSciNet  Google Scholar 

  7. Di Gesù, V., Lo Bosco, G., Millonzi, F., Valenti, C.: A memetic algorithm for binary image reconstruction. In: Brimkov, V.E., Barneva, R.P., Hauptman, H.A. (eds.) IWCIA 2008. LNCS, vol. 4958, pp. 384–395. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78275-9_34

    Chapter  Google Scholar 

  8. Herman, G.T., Kuba, A. (eds.): Advances in Discrete Tomography and its Applications. Birkhäuser, Boston (2007)

    Google Scholar 

  9. Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220, 671–680 (1983)

    Article  MathSciNet  Google Scholar 

  10. Kiss, Z., Rodek, L., Nagy, A., Kuba, A., Balaskó, M.: Reconstruction of pixel-based and geometric objects by discrete tomography. Simulation and physical experiments. Electron. Notes Discret. Math. 20, 475–491 (2005)

    Article  MathSciNet  Google Scholar 

  11. Lukic, T., Lukity, A.: A spectral projected gradient optimization for binary tomography. In: Rudas, I.J., Fodor, J., Kacprzyk, J. (eds.) Computational Intelligence in Engineering. SCI, vol. 313, pp. 263–272. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15220-7_21

    Chapter  Google Scholar 

  12. Russell, S., Norvig, P.: Artificial Intelligence, A Modern Approach, 2nd edn. Prentice-Hall, Englewood Cliffs (2003)

    MATH  Google Scholar 

  13. Ryser, H.J.: Combinatorial properties of matrices of zeros and ones. Canad. J. Math. 9, 371–377 (1957)

    Article  MathSciNet  Google Scholar 

  14. Schüle, T., Schnörr, C., Weber, S., Hornegger, J.: Discrete tomography by convex concave regularization and DC programming. Disc. Appl. Math. 151(1), 229–243 (2005)

    Article  Google Scholar 

  15. Szűcs, J., Balázs, P.: Binary image reconstruction using local binary pattern priors. Int. J. Circuits Syst. Sig. Process. 11, 296–299 (2017)

    Google Scholar 

  16. Varga, L., Balázs, P., Nagy, A.: Discrete tomographic reconstruction via adaptive weighting of gradient descents. Comput. Methods Biomech. Biomed. Eng. Imaging Vis. 3(2), 100–109 (2015)

    Article  Google Scholar 

  17. Woeginger, G.W.: The reconstruction of polyominoes from their orthogonal projections. Inform. Process. Lett. 77, 225–229 (2001)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Image Processing and Computer Graphics, University of Szeged, Árpád tér 2, Szeged, 6720, Hungary

    Péter Balázs & Judit Szűcs

Authors
  1. Péter Balázs
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  2. Judit Szűcs
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Correspondence to Judit Szűcs .

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Editors and Affiliations

  1. University of Porto, Porto, Portugal

    Aurélio Campilho

  2. University of Waterloo, Waterloo, Ontario, Canada

    Fakhri Karray

  3. Biomedical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands

    Bart ter Haar Romeny

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Balázs, P., Szűcs, J. (2018). Reconstruction of Binary Images with Fixed Number of Strips. In: Campilho, A., Karray, F., ter Haar Romeny, B. (eds) Image Analysis and Recognition. ICIAR 2018. Lecture Notes in Computer Science(), vol 10882. Springer, Cham. https://doi.org/10.1007/978-3-319-93000-8_2

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  • DOI: https://doi.org/10.1007/978-3-319-93000-8_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-92999-6

  • Online ISBN: 978-3-319-93000-8

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