Nothing Special   »   [go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

Necessary Condition of Affine Moment Invariants

  • Published:
Journal of Mathematical Imaging and Vision Aims and scope Submit manuscript

Abstract

In this paper, a method is presented for generating affine moment invariants of arbitrary dimension and order. It is proved that all the affine moment invariants can be generated by using determinants. Therefore, the necessary condition of the general affine moment invariants is given in this paper.

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

Access this article

Log in via an institution

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

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

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

    MATH  Google Scholar 

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

    Article  Google Scholar 

  3. Liu, J., Li, D., Tao, W., Yan, L.: An automatic method for generating affine moment invariants. Pattern Recogn. Lett. 28(27), 2295–2304 (2007)

    Article  Google Scholar 

  4. Suk, T., Flusser, J.: Affine moment invariants generated by graph method. Pattern Recogn. 44, 2047–2056 (2011)

    Article  Google Scholar 

  5. Xu, D., Li, H.: 3-D Affine moment invariants generated by geometric primitives. In: The 18th International Conference on Pattern Recognition, pp. 544–547 (2006)

  6. Reiss, T.H.: The revised fundamental theorem of moment invariants. IEEE Trans. Pattern Anal. Mach. Intell. 13, 830–834 (1991)

    Article  Google Scholar 

  7. Jan, Flusser, Tomáš, Suk, Barbara, Zitová: 2D and 3D image analysis by moments. Wiley, Hoboken (2016)

    Google Scholar 

  8. Suk, T., Flusser, J.: Affine moment invariants generated by automated solution of the equations. In: The 18th International Conference on Pattern Recognition, pp. 1–4 (2006)

  9. Hickman, Mark S.: Geometric moments and their invariants. J. Math. Imaging Vis. 44, 223–235 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  10. Diao, Luhong, Peng, Juan, Dong, Junliang, Kong, Fanyu: Moment invariants under similarity transformation. Pattern Recogn. 48, 3641–3651 (2015)

    Article  MATH  Google Scholar 

  11. Luhong, Diao, Hua, Li, Sen, Zhang, Lei, Liu: Analysis of moment invariants under general linear transformation. Sci. China Inf. Sci. 53, 1305–1311 (2010)

    Article  MathSciNet  Google Scholar 

  12. Gurevich, G.B.: Foundations of the Theory of Algebraic Invariants. Nordhoff, Groningen (1964)

    MATH  Google Scholar 

Download references

Acknowledgements

Research supported by National Natural Science Foundation of China (Grants 61100129 and 61379106), Open Program of Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Sciences (Grants IIP2014-7) and Collaborative Innovation Center on Beijing Society-building and Social Governance.

Author information

Authors and Affiliations

  1. Beijing Institute for Scientific and Engineering Computing, Beijing University of Technology, Beijing, China

    Luhong Diao

  2. College of Applied Sciences, Beijing University of Technology, Beijing, China

    Luhong Diao, Zhenmeng Zhang & Dong Nan

  3. Key Lab of Intelligent Information Processing, Chinese Academy of Sciences, Beijing, China

    Luhong Diao & Zhenmeng Zhang

  4. College of Computer and Communication Engineering, China University of Petroleum, Qingdao, Shandong, China

    Yujie Liu

Authors
  1. Luhong Diao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhenmeng Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yujie Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Dong Nan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dong Nan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Diao, L., Zhang, Z., Liu, Y. et al. Necessary Condition of Affine Moment Invariants. J Math Imaging Vis 61, 602–606 (2019). https://doi.org/10.1007/s10851-018-0864-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10851-018-0864-3

Keywords

Search

Navigation