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Image segmentation by using the localized subspace iteration algorithm

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Abstract

An image segmentation algorithm called “segmentation based on the localized subspace iterations” (SLSI) is proposed in this paper. The basic idea is to combine the strategies in Ncut algorithm by Shi and Malik in 2000 and the LSI by E, Li and Lu in 2007. The LSI is applied to solve an eigenvalue problem associated with the affinity matrix of an image, which makes the overall algorithm linearly scaled. The choices of the partition number, the supports and weight functions in SLSI are discussed. Numerical experiments for real images show the applicability of the algorithm.

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References

  1. Perona P, Freeman W T. A factorization approach to grouping. In Burkardt H, eds. Proc ECCV. Berlin-Heidelberg: Springer, 1998, 655–670

    Google Scholar 

  2. Scott G L, Longuet-Higgins H C. Feature grouping by relocalisation of eigenvectors of the proxmity matrix. In: Proc British Machine Vision Conference, Oxford, 1990, 103–108

  3. Shi J, Malik J. Normalized cuts and image segmentation. IEEE Trans Pattern Anal Mach Intel, 22: 888–905 (2000)

    Article  Google Scholar 

  4. Saul L K, Weinberger K Q, Sha F, et al. Spectral methods for dimensionality reduction, semisupervised learning. Massachusetts: MIT Press, 2006

    Google Scholar 

  5. E W, Li T, Lu J. Localized basis of eigen-subspaces and operator compression. Submitted to Proc Nat Acad Sci, 2007

  6. Chung F R K. Spectral Graph Theory. Providence, RI: Amer Math Soc, 1997

    MATH  Google Scholar 

  7. Meila M, Shi J. A random walks view of spectral segmentation. In: Proceedings of the Eighth International Workshop on Artifical Intelligence and Statistics. San Francisco: Morgan Kaufmann, 2001, 92–97

    Google Scholar 

  8. Golub G H, Van Loan C F. Matrix Computations, 3rd ed. Baltimore-London: The Johns Hopkins University Press, 1996

    MATH  Google Scholar 

  9. Saad Y. Numerical Methods for Large Eigenvalue Problems. Manchester: Manchester University Press, 1992

    MATH  Google Scholar 

  10. Weiss Y. Segmentation using eigenvectors: a unifying view. In: International Conference on Computer Vision. Alamitos: IEEE Computer Society Press, 1999, 975–982

    Chapter  Google Scholar 

  11. Hastie T, Tibshirani R, Friedman J. The Elements of Statistical Learning. New York-Berlin-Heidelberg: Springer-Verlag, 2001

    MATH  Google Scholar 

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Authors and Affiliations

  1. LMAM and School of Mathematical Sciences, Peking University, Beijing, 100871, China

    JinLong Wu & TieJun Li

Authors
  1. JinLong Wu
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  2. TieJun Li
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Corresponding author

Correspondence to TieJun Li.

Additional information

This work was partially supported by the National Basic Research Program of China (Grant No. 2005CB321704).

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Wu, J., Li, T. Image segmentation by using the localized subspace iteration algorithm. Sci. China Ser. A-Math. 51, 1495–1509 (2008). https://doi.org/10.1007/s11425-008-0114-z

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  • DOI: https://doi.org/10.1007/s11425-008-0114-z

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