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A Merging Heuristic for the Rectangle Decomposition of Binary Matrices

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Experimental Algorithms (SEA 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9685))

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Abstract

In this paper we present a linear-time and linear-space algorithm for the decomposition of binary images into rectangles. Our contribution is a two-stage algorithm. In the first stage we compute a \({\textstyle \frac{1}{min(h,w)}}\)-approximation for the largest rectangle starting at each point of the matrix. In the second stage the algorithm walks through the matrix, alternatively stacking, merging or removing encountered rectangles. Through an experimental evaluation, we show that our algorithm outperforms state-of-the-art linear-time algorithms for small to medium-sized rectilinear polygons.

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Notes

  1. 1.

    https://olympiad.cs.uct.ac.za/old/camp1_2009/day2_camp1_2009_solutions.pdf.

  2. 2.

    http://www.github.com/jsubercaze/wsrm.

References

  1. Eppstein, D.: Graph-theoretic solutions to computational geometry problems. In: Paul, C., Habib, M. (eds.) WG 2009. LNCS, vol. 5911, pp. 1–16. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  2. Ferrari, L., Sankar, P.V., Sklansky, J.: Minimal rectangular partitions of digitized blobs. Comput. Graph. Image Process. 28(1), 58–71 (1984)

    Article  MATH  Google Scholar 

  3. Gao, D., Wang, Y.: Decomposing document images by heuristic search. In: Yuille, A.L., Zhu, S.-C., Cremers, D., Wang, Y. (eds.) EMMCVPR 2007. LNCS, vol. 4679, pp. 97–111. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  4. Gonzalez, T., Zheng, S.-Q.: Bounds for partitioning rectilinear polygons. In: 1st Symposium on Computational Geometry, pp. 281–287. ACM (1985)

    Google Scholar 

  5. Levcopoulos, C.: Improved bounds for covering general polygons with rectangles. In: Nori, K.V. (ed.) Foundations of Software Technology and Theoretical Computer Science. LNCS, vol. 287, pp. 95–102. Springer, Heidelberg (1987)

    Chapter  Google Scholar 

  6. Lingas, A., Pinter, R.Y., Rivest, R.L., Shamir, A.: Minimum edge length partitioning of rectilinear polygons. In: Proceeding of 20th Allerton Conference Communication Control and Computing, pp. 53–63 (1982)

    Google Scholar 

  7. Liou, W.T., Tan, J.J., Lee, R.C.: Minimum partitioning simple rectilinear polygons in o (n log log n)-time. In: Proceedings of the Fifth Annual Symposium on Computational Geometry, pp. 344–353. ACM (1989)

    Google Scholar 

  8. Lipski, W., Lodi, E., Luccio, F., Mugnai, C., Pagli, L.: On two dimensional data organization ii. Fundamenta Informaticae 2(3), 245–260 (1979)

    MathSciNet  MATH  Google Scholar 

  9. Nahar, S., Sahni, S.: Fast algorithm for polygon decomposition. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 7(4), 473–483 (1988)

    Article  Google Scholar 

  10. Ohtsuki, T.: Minimum dissection of rectilinear regions. In: Proceeding IEEE Symposium on Circuits and Systems, Rome, pp. 1210–1213 (1982)

    Google Scholar 

  11. Rocher, P.-O., Gravier, C., Subercaze, J., Preda, M.: Video stream transmodality. In: Cordeiro, J., Hammoudi, S., Maciaszek, L., Camp, O., Filipe, J. (eds.) ICEIS 2014. LNBIP, vol. 227, pp. 361–378. Springer, Heidelberg (2015)

    Chapter  Google Scholar 

  12. Soltan, V., Gorpinevich, A.: Minimum dissection of a rectilinear polygon with arbitrary holes into rectangles. Discrete Comput. Geom. 9(1), 57–79 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  13. Spiliotis, I.M., Mertzios, B.G.: Real-time computation of two-dimensional moments on binary images using image block representation. IEEE Trans. Image Process. 7(11), 1609–1615 (1998)

    Article  Google Scholar 

  14. Suk, T., Höschl IV, C., Flusser, J.: Decomposition of binary images a survey and comparison. Pattern Recogn. 45(12), 4279–4291 (2012)

    Article  Google Scholar 

  15. Tomás, A.P., Bajuelos, A.L.: Generating Random Orthogonal Polygons. In: Conejo, R., Urretavizcaya, M., Pérez-de-la-Cruz, J.-L. (eds.) CAEPIA/TTIA 2003. LNCS (LNAI), vol. 3040, pp. 364–373. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

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Authors and Affiliations

  1. Université de Lyon, UJM-Saint-Etienne CNRS, UMR5516, Laboratoire Hubert Curien, 42023, Saint-Etienne, France

    Julien Subercaze, Christophe Gravier & Pierre-Olivier Rocher

Authors
  1. Julien Subercaze
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  2. Christophe Gravier
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  3. Pierre-Olivier Rocher
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Corresponding author

Correspondence to Julien Subercaze .

Editor information

Editors and Affiliations

  1. Amazon.com, Inc., Palo Alto, California, USA

    Andrew V. Goldberg

  2. Russian Academy of Sciences, St. Petersburg, Russia

    Alexander S. Kulikov

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Subercaze, J., Gravier, C., Rocher, PO. (2016). A Merging Heuristic for the Rectangle Decomposition of Binary Matrices. In: Goldberg, A., Kulikov, A. (eds) Experimental Algorithms. SEA 2016. Lecture Notes in Computer Science(), vol 9685. Springer, Cham. https://doi.org/10.1007/978-3-319-38851-9_21

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  • DOI: https://doi.org/10.1007/978-3-319-38851-9_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-38850-2

  • Online ISBN: 978-3-319-38851-9

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