Skip to main content

A Sharp Concentration-Based Adaptive Segmentation Algorithm

  • Conference paper
Advances in Visual Computing (ISVC 2010)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 6454))

Included in the following conference series:

  • 2364 Accesses

Abstract

We propose an adaptive procedure for segmenting images by merging of homogeneous regions. The algorithm is based on sharp concentration inequalities and is tailored to avoid over- and under-merging by controlling simultaneously the type I and II errors in the associated statistical testing problem.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

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. Pavlidis, T.: Segmentation of pictures and maps through functional approximation. Computer Graphics and Image Process 1, 360–372 (1972)

    Article  MathSciNet  Google Scholar 

  2. Zucker, S.W.: Survey: Region growing: Childhood and adolescence. Computer Vision, Graphics, and Image Processing 5, 382–399 (1976)

    Article  Google Scholar 

  3. Forsyth, D.A., Ponce, J.: Computer Vision: A Modern Approach. Prentice-Hall, Englewood Cliffs (2003)

    Google Scholar 

  4. Monga, O.: An optimal region growing algorithm for image segmentation. International Journal of Pattern Recognition and Artificial Intelligence 1, 351–375 (1987)

    Article  Google Scholar 

  5. Nock, R.: Fast and reliable color region merging inspired by decision tree pruning. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR 2001), vol. 1, pp. I–271–I–276 (2001)

    Google Scholar 

  6. Fiorio, C., Nock, R.: Image segmentation using a generic, fast and non-parametric approach. In: 10th IEEE International Conference on Tools with Artificial Intelligence, Taipe, Taiwan, R.O.C, pp. 450–458. IEEE Computer Society, Los Alamitos (1998)

    Google Scholar 

  7. Fiorio, C., Nock, R.: A concentration-based adaptive approach to region merging of optimal time and space complexities. In: British Machine Vision Conference, Bristol, England, vol. 2, pp. 775–784 (2000)

    Google Scholar 

  8. Nock, R., Nielsen, F.: Statistical region merging. IEEE Trans. Pattern Anal. Mach. Intell. 26, 1452–1458 (2004)

    Article  Google Scholar 

  9. Lehmann, E.L.: Testing statistical hypotheses, 2nd edn. Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics. John Wiley & Sons, New York (1986)

    Book  MATH  Google Scholar 

  10. Nock, R., Nielsen, F.: Semi-supervised statistical region refinement for color image segmentation. Pattern Recognition: Image Understanding for Photographs 38, 835–846 (2005)

    Article  MATH  Google Scholar 

  11. Demaine, E.D., Emanuel, D., Fiat, A., Immorlica, N.: Correlation clustering in general weighted graphs; approximation and online algorithms. Theoretical Computer Science 361, 172–187 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  12. Fiorio, C., Nock, R.: Sorted region merging to maximize test reliability. In: International Conference on Image Processing, Vancouver, Canada, vol. 01, pp. 808–811. IEEE, Los Alamitos (2000)

    Google Scholar 

  13. Mc Diarmid, C.: Concentration for independent permutations. Comb. Probab. Comput. 11, 163–178 (2002)

    MathSciNet  Google Scholar 

  14. Hoeffding, W.: Probability inequalitites for sums of bounded random variables. Journal of American Statistical Association 58, 13–30 (1963)

    Article  MathSciNet  MATH  Google Scholar 

  15. Bennett, G.: Probability inequalities for the sum of independent random variables. Journal of American Statistical Association 57, 33–45 (1962)

    Article  MATH  Google Scholar 

  16. Bernstein, S.: On a modification of chebyshev’s inequality and of the error formula of laplace. Ann. Sci. Inst. Sav. Ukraine, Sect. Math. 1 (1924)

    Google Scholar 

  17. Ledoux, M., Talagrand, M.: Probability in banach spaces. isoperimetry and processes. Ergebnisse der Mathematik und ihrer Grenzgebiete 3, xii+480 (1991)

    MATH  Google Scholar 

  18. Mc Diarmid, C.: Concentration. In: Habib, D.M., Ramirez-Alfonsin, R. (eds.) Probabilistic Methods for Algorithmic Discrete Mathematics, New-York, pp. 195–248. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  19. Fiorio, C., Gustedt, J.: Two linear time Union-Find strategies for image processing. Theoretical Computer Science 154, 165–181 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  20. Tarjan, R.E.: Efficiency of a good but not linear set union algorithm. J. of the Association for Computing Machinery 22, 215–225 (1975)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Fiorio, C., Mas, A. (2010). A Sharp Concentration-Based Adaptive Segmentation Algorithm. In: Bebis, G., et al. Advances in Visual Computing. ISVC 2010. Lecture Notes in Computer Science, vol 6454. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17274-8_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-17274-8_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17273-1

  • Online ISBN: 978-3-642-17274-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics