Skip to main content
SpringerLink
Log in

Lloyd’s Algorithm on GPU

  • Conference paper
Advances in Visual Computing (ISVC 2008)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 5358))

Included in the following conference series:

Abstract

The Centroidal Voronoi Diagram (CVD) is a very versatile structure, well studied in Computational Geometry. It is used as the basis for a number of applications. This paper presents a deterministic algorithm, entirely computed using graphics hardware resources, based on Lloyd’s Method for computing CVDs. While the computation of the ordinary Voronoi diagram on GPU is a well explored topic, its extension to CVDs presents some challenges that the present study intends to overcome.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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.

Similar content being viewed by others

References

  1. Du, Q., Faber, V., Gunzburger, M.: Centroidal voronoi tessellations: Applications and algorithms. SIAM Rev. 41, 637–676 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  2. Har-Peled, S., Sadri, B.: How fast is the k-means method? In: SODA 2005: Proceedings of the 16th ACM-SIAM Symp. on Discrete algorithms, pp. 877–885 (2005)

    Google Scholar 

  3. Du, Q., Emelianenko, M.: Acceleration schemes for computing centroidal voronoi tessellations. Numerical Linear Algebra with Applications 13, 173–192 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  4. Hausner, A.: Simulating decorative mosaics. In: SIGGRAPH 2001: Papers, pp. 573–580. ACM, New York (2001)

    Google Scholar 

  5. Du, Q., Gunzburger, M., Ju, L., Wang, X.: Centroidal voronoi tessellation algorithms for image compression, segmentation, and multichannel restoration. J. Math. Imaging Vis. 24, 177–194 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  6. Kenneth, E., Hoff III, Culver, T., Keyser, J., Lin, M., Manocha, D.: Fast computation of generalized voronoi diagrams using graphics hardware. In: SCG 2000: Proceedings of the 16th Annual Symp. on Computational geometry, pp. 375–376. ACM, New York (2000)

    Google Scholar 

  7. Denny, M.: Solving geometric optimization problems using graphics hardware. In: EUROGRAPHICS 2003. Computer Graphics Forum, vol. 22, pp. 441–451 (2003)

    Google Scholar 

  8. Rong, G., Tan, T.S.: Jump flooding in gpu with applications to voronoi diagram and distance transform. In: I3D 2006: Proceedings of the Symp. on Interactive 3D graphics and games, pp. 109–116. ACM, New York (2006)

    Chapter  Google Scholar 

  9. Rong, G., Tan, T.S.: Variants of jump flooding algorithm for computing discrete voronoi diagrams. In: ISVD 2007: Proceedings of the 4th Int. Symp. on Voronoi Diagrams in Science and Engineering, pp. 176–181. IEEE Computer Society, Los Alamitos (2007)

    Google Scholar 

  10. Rong, G., Tan, T.S., Cao, T.T., Stephanus: Computing two-dimensional delaunay triangulation using graphics hardware. In: SI3D 2008: Proceedings of the 2008 Symp. on Interactive 3D graphics and games, pp. 89–97. ACM, New York (2008)

    Chapter  Google Scholar 

  11. Jesse, D., Hall, J.C.H.: Gpu acceleration of iterative clustering. In: Manuscript accompanying poster at GP2: The ACM Workshop on General Purpose Computing on Graphics Processors, and SIGGRAPH 2004 poster. ACM, New York (2004)

    Google Scholar 

  12. Owens, J., Luebke, D., Govindaraju, N., Harris, M., Krüger, J., Lefohn, A.E., Purcell, T.: A survey of general-purpose computation on graphics hardware. Computer Graphics Forum 26, 80–113 (2007)

    Article  Google Scholar 

  13. Owens, J.: Data-parallel algorithms and data structures. In: SIGGRAPH 2007: Courses, p. 3. ACM, New York (2007)

    Chapter  Google Scholar 

  14. Roger, D., Assarsson, U., Holzschuch, N.: Efficient stream reduction on the gpu. In: Workshop on General Purpose Processing on Graphics Processing Units (2007)

    Google Scholar 

  15. Krüger, J., Westermann, R.: Linear algebra operators for gpu implementation of numerical algorithms. In: SIGGRAPH 2003: Papers, pp. 908–916. ACM, New York (2003)

    Chapter  Google Scholar 

  16. Fluck, O., Aharon, S., Cremers, D., Rousson, M.: Gpu histogram computation. In: SIGGRAPH 2006: Research Posters, p. 53. ACM, New York (2006)

    Chapter  Google Scholar 

  17. Vasconcelos, C., Sá, A., Teixeira, L., Carvalho, P.C., Gattass, M.: Real-time video processing for multi-object chromatic tracking. In: BMVC 2008, pp. 113–123 (2008)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Depto. de Informática, Pontifícia Universidade Católica (PUC-Rio), Brasil

    Cristina N. Vasconcelos & Marcelo Gattass

  2. Tecgraf - (PUC-Rio), Brasil

    Asla Sá & Marcelo Gattass

  3. Instituto de Matemática Pura e Aplicada (IMPA), Brasil

    Paulo Cezar Carvalho

Authors
  1. Cristina N. Vasconcelos
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Asla Sá
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Paulo Cezar Carvalho
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Marcelo Gattass
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, University of Nevada, Reno, USA

    George Bebis

  2. NASA Ames Research Center, Moffett Field, CA, USA

    Richard Boyle

  3. Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    Bahram Parvin

  4. Desert Research Institute, Reno, NV, USA

    Darko Koracin

  5. Digital Image Research Center, Kingston University, London, UK

    Paolo Remagnino

  6. Mitsubishi Electric Research Laboratories, P.O. Box 02139, Cambridge, MA, USA

    Fatih Porikli

  7. Computer and Information Science and Engineering, University of Florida, P.O. Box, FL 32611-6120, Gainsville, USA

    Jörg Peters

  8. IBM T.J. Watson Research Center, 19 Skyline Drive, NY 10532, Hawthorne, USA

    James Klosowski

  9. 128 Memorial Mall, Stewart B001, IN 47907, West Lafayette, USA

    Laura Arns

  10. Denver Museum of Nature and Space, 2001 Colorade Blvd. Denver,, CO 80205, USA

    Yu Ka Chun

  11. Departmen of Computer Science,, NC State University, Campus Box 8206, NC 27695-8206, Raleigh, USA

    Theresa-Marie Rhyne

  12. Los Alamos National Labs, P.O. Box 1663, NM 87545, Los Alamos, USA

    Laura Monroe

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Vasconcelos, C.N., Sá, A., Carvalho, P.C., Gattass, M. (2008). Lloyd’s Algorithm on GPU. In: Bebis, G., et al. Advances in Visual Computing. ISVC 2008. Lecture Notes in Computer Science, vol 5358. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89639-5_91

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-89639-5_91

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-89638-8

  • Online ISBN: 978-3-540-89639-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation