Skip to main content
SpringerLink
Log in

On Maximum Weight Objects Decomposable into Based Rectilinear Convex Objects

  • Conference paper
Book cover Algorithms and Data Structures (WADS 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8037))

Included in the following conference series:

Abstract

Our main concern is the following variant of the image segmentation problem: given a weighted grid graph and a set of vertical and/or horizontal base lines crossing through the grid, compute a maximum-weight object which can be decomposed into based rectilinear convex objects with respect to the base lines. Our polynomial-time algorithm reduces the problem to solving a polynomial number of instances of the maximum flow problem.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Anzai, S., Chun, J., Kasai, R., Korman, M., Tokuyama, T.: Effect of corner information in simultaneous placement of k rectangles and tableaux. Discrete Mathematics, Algorithms and Applications 2(4), 527–537 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  2. Asano, T., Chen, D.Z., Katoh, N., Tokuyama, T.: Efficient algorithms for optimization-based image segmentation. Int. J. Comput. Geometry Appl. 11(2), 145–166 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  3. Chan, T.F., Zhu, W.: Level set based shape prior segmentation. In: CVPR (2), pp. 1164–1170 (2005)

    Google Scholar 

  4. Chen, D.Z., Chun, J., Katoh, N., Tokuyama, T.: Efficient algorithms for approximating a multi-dimensional voxel terrain by a unimodal terrain. In: Chwa, K.-Y., Munro, J.I. (eds.) COCOON 2004. LNCS, vol. 3106, pp. 238–248. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  5. Chen, D.Z., Hu, X.S., Luan, S., Wu, X., Yu, C.X.: Optimal terrain construction problems and applications in intensity-modulated radiation therapy. In: Möhring, R.H., Raman, R. (eds.) ESA 2002. LNCS, vol. 2461, pp. 270–283. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  6. Chun, J., Horiyama, T., Ito, T., Kaothanthong, N., Ono, H., Otachi, Y., Tokuyama, T., Uehara, R., Uno, T.: Base location problems for base-monotone regions. In: Ghosh, S.K., Tokuyama, T. (eds.) WALCOM 2013. LNCS, vol. 7748, pp. 53–64. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  7. Chun, J., Kasai, R., Korman, M., Tokuyama, T.: Algorithms for computing the maximum weight region decomposable into elementary shapes. In: Dong, Y., Du, D.-Z., Ibarra, O. (eds.) ISAAC 2009. LNCS, vol. 5878, pp. 1166–1174. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  8. Chun, J., Korman, M., Nöllenburg, M., Tokuyama, T.: Consistent digital rays. Discrete & Computational Geometry 42(3), 359–378 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. Chun, J., Sadakane, K., Tokuyama, T.: Efficient algorithms for constructing a pyramid from a terrain. IEICE Transactions 89-D(2), 783–788 (2006)

    MathSciNet  Google Scholar 

  10. Das, P., Veksler, O., Zavadsky, V., Boykov, Y.: Semiautomatic segmentation with compact shape prior. Image Vision Comput. 27(1-2), 206–219 (2009)

    Article  Google Scholar 

  11. Freedman, D., Zhang, T.: Interactive graph cut based segmentation with shape priors. In: CVPR (1), pp. 755–762 (2005)

    Google Scholar 

  12. Fukuda, T., Morimoto, Y., Morishita, S., Tokuyama, T.: Data mining using two-dimensional optimized accociation rules: Scheme, algorithms, and visualization. In: Jagadish, H.V., Mumick, I.S. (eds.) SIGMOD Conference, pp. 13–23. ACM Press (1996)

    Google Scholar 

  13. Fukuda, T., Morimoto, Y., Morishita, S., Tokuyama, T.: Data mining with optimized two-dimensional association rules. ACM Trans. Database Syst. 26(2), 179–213 (2001)

    Article  MATH  Google Scholar 

  14. Gibson, M., Han, D., Sonka, M., Wu, X.: Maximum weight digital regions decomposable into digital star-shaped regions. In: Asano, T., Nakano, S.-I., Okamoto, Y., Watanabe, O. (eds.) ISAAC 2011. LNCS, vol. 7074, pp. 724–733. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  15. Gibson, M., Varadarajan, K., Wu, X.: On a planar segmentation problem (2012)

    Google Scholar 

  16. Hochbaum, D.S.: A new - old algorithm for minimum-cut and maximum-flow in closure graphs. Networks 37(4), 171–193 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  17. Picard, J.-C.: Maximal closure of a graph and applications to combinatorial problems. Management Science 22(11), 1268–1272 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  18. Thiruvenkadam, S.R., Chan, T.F., Hong, B.-W.: Segmentation under occlusions using selective shape prior. SIAM J. Imaging Sciences 1(1), 115–142 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  19. Veksler, O.: Star shape prior for graph-cut image segmentation. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008, Part III. LNCS, vol. 5304, pp. 454–467. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Texas at San Antonio, San Antonio, TX, USA

    Mahmuda Ahmed, Iffat Chowdhury, Matt Gibson, Mohammad Shahedul Islam & Jessica Sherrette

Authors
  1. Mahmuda Ahmed
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Iffat Chowdhury
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Matt Gibson
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mohammad Shahedul Islam
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jessica Sherrette
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. School of Computer Science, Parallel Computing and Bioinformatics Laboratory, Carleton University, VISM Building, Room 6210, 1125 Colonel By Drive, K1S 5B6, Ottawa, ON, Canada

    Frank Dehne

  2. Department of Computer Science, The University of Western Ontario, N6A 5B7, London, ON, Canada

    Roberto Solis-Oba

  3. School of Computer Science, Carleton University, K1S 5B6, Ottawa, ON, Canada

    Jörg-Rüdiger Sack

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ahmed, M., Chowdhury, I., Gibson, M., Islam, M.S., Sherrette, J. (2013). On Maximum Weight Objects Decomposable into Based Rectilinear Convex Objects. In: Dehne, F., Solis-Oba, R., Sack, JR. (eds) Algorithms and Data Structures. WADS 2013. Lecture Notes in Computer Science, vol 8037. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40104-6_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-40104-6_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40103-9

  • Online ISBN: 978-3-642-40104-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation