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Analysis of moment invariants under general linear transformation

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Abstract

This paper presents the necessary and sufficient condition of moment invariants under general linear transformation. Based on this condition, arbitrary order and dimensional moment invariant sets can be constructed. Due to their linear independence, previous invariants are special cases of them.

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References

  1. Hu M K. Visual pattern recognition by moment invariants. IRE Trans Inf Theory, 1962, 8: 179–187

    Google Scholar 

  2. Li Y. Reforming the theory of invariant moments for pattern recognition. Patt Recog, 1992, 25: 723–730

    Article  Google Scholar 

  3. Wong W H, Siu W C, Lam K M. Generation of moment invariants and their uses for character recognition. Patt Recog Lett, 1995, 16: 115–123

    Article  Google Scholar 

  4. Psaltis Y S, Abu-Mostafa D. Recognitive aspects of moment invariants. IEEE Trans Patt Anal Mach Intell, 1984, 6: 698–706

    Article  Google Scholar 

  5. Flusser J, Zitova B. Combined invariants to linear filtering and rotation. Int J Patt Recog Artif Intell, 1999, 13: 1123–1136

    Article  Google Scholar 

  6. Suk T, Flusser J. Graph method for generating affine moment invariants. In: 17th International Conference on Pattern Recognition Proc, Cambridge, UK, 2004. 192–195

  7. Suk T, Flusser J. Projective moment invariants. IEEE Trans Patt Anal Mach Intell, 2004, 26: 1053–1064

    Google Scholar 

  8. Flusser J. On the independence of rotation moment invariants. Patt Recog, 2000, 33: 1405–1410

    Article  Google Scholar 

  9. Teh C H, Chin R T. On image analysis by the method of moments. IEEE Trans Patt Anal Mach Intell, 1988, 10: 496–513

    Article  MATH  Google Scholar 

  10. Sadjadi F A, Hall E L. Three dimensional moment invariants. IEEE Trans Patt Anal Mach Intell, 1980, 2: 127–136

    Article  MATH  Google Scholar 

  11. Lo C H, Don H S. 3-D moment forms: their construction and application to object identification and positioning. IEEE Trans Patt Anal Mach Intell, 1989, 11: 1053–1064

    Article  Google Scholar 

  12. Reiss T H. Features invariant to linear transformations in 2D and 3D. In: 11th Int’l Conf Pattern Recognition Proc, The Hague, The Netherlands, 1992. 493–496

  13. Taubin G, Cooper D B. Object recognition based on moment (or algebraic) invariants. In: Mundy J L, Zisserman A, eds. Geometric Invariance in Computer Vision, Cambridge, MA: MIT Press, 1992. 375–397

    Google Scholar 

  14. Mamistvalov A G. n-Dimensional moment invariants and conceptual mathematical theory of recognition n-dimensional solids. IEEE Trans Patt Anal Mach Intell, 1998, 20: 819–831

    Article  Google Scholar 

  15. Flusser J, Boldys J, Zitova B. Moment forms invariant to rotation and blur in arbitrary number of dimensions. IEEE Trans Patt Anal Mach Intell, 2003, 25: 234–246

    Article  Google Scholar 

  16. Xu D, Li H. Geometric moment invariants. Patt Recog, 2008, 41: 240–249

    Article  MATH  Google Scholar 

  17. Gao X S, Wang D K, Qiu Z Y, et al. Equation Solving and Mechanical Proving-Solving Problems Based on MMP (in Chinese). Beijing: Science Press, 2006

    Google Scholar 

  18. Sturmfels B. Algorithms in Invariant Theory. New York: Springer-Verlag, 1993

    MATH  Google Scholar 

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Authors and Affiliations

  1. College of Applied Sciences, Beijing University of Technology, Beijing, 100124, China

    LuHong Diao, Sen Zhang & Lei Liu

  2. National Center of Intelligent Computing, Institute of Computing Technology, Chinese Academy of Science, Beijing, 100080, China

    Hua Li

Authors
  1. LuHong Diao
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  2. Hua Li
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  3. Sen Zhang
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  4. Lei Liu
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Correspondence to LuHong Diao.

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Diao, L., Li, H., Zhang, S. et al. Analysis of moment invariants under general linear transformation. Sci. China Inf. Sci. 53, 1305–1311 (2010). https://doi.org/10.1007/s11432-010-4006-9

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  • DOI: https://doi.org/10.1007/s11432-010-4006-9

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