Skip to main content
SpringerLink
Log in

Ridgelet moment invariants for robust pattern recognition

  • Short Paper
  • Published:
Pattern Analysis and Applications Aims and scope Submit manuscript

Abstract

Moment invariants are an especially important research topic in pattern recognition. There are many kinds of moment invariants published in the literature already. However, there is a need to further improve them, especially under the noisy environments. In this article, we develop a new set of moment invariants by means of ridgelet function. The ridgelet function is capable of capturing line features in an image, which is a particularly important property in pattern recognition. It is well-known that every curve can be approximated by short line segments, so ridgelet moment invariants should be good at robust pattern recognition. We can prove that this set of moments is invariant to the rotation of 2D images. Experiments show that our proposed ridgelet moment invariants are better than the Gaussian–Hermite moments, the Fourier–wavelet descriptor, and Zernike’s moment invariants for one Chinese character database and one 2D shape database. Furthermore, our proposed ridgelet moment invariants can do an excellent job for noise-robust pattern recognition.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

References

  1. Prokop RJ, Reeves AP (1992) A survey of moments-based techniques for unoccluded object representation and recognition. CVGIP Graph Models Image Process 54:438–460

    Article  Google Scholar 

  2. Hu MK (1962) Visual pattern recognition by moment invariants. IRE Trans Inf Theory 8:179–187

    MATH  Google Scholar 

  3. Dudani S, Breeding K, McGhee R (1977) Aircraft identification by moment invariants. IEEE Trans Comput C–26:39–45

    Article  Google Scholar 

  4. Abu-Mostafa YS, Psaltis D (1984) Recognitive aspects of moment invariants. IEEE Trans Pattern Anal Mach Intell 6:698–706

    Article  Google Scholar 

  5. Resis TH (1991) The revised fundamental theorem of moment invariants. IEEE Trans Pattern Anal Mach Intell 13:830–834

    Article  Google Scholar 

  6. Li Y (1992) Reforming the theory of invariant moments for pattern recognition. Pattern Recognit 25:723–730

    Article  Google Scholar 

  7. Teague M (1980) Image analysis via the general theory of moments. J Opt Soc Am 70:920–930

    Article  MathSciNet  Google Scholar 

  8. The CH, Chin RT (1988) On image analysis by the method of moments. IEEE Trans Pattern Anal Mach Intell 10:496–513

    Article  Google Scholar 

  9. Khotanzad A, Hong YH (1990) Rotation invariant image recognition using features selected via a systematic method. Pattern Recognit 23:1089–1101

    Article  Google Scholar 

  10. Khotanzad A, Hong YH (1990) Invariant image recognition by Zernike moments. IEEE Trans Pattern Anal Mach Intell 12:489–497

    Article  Google Scholar 

  11. Shen D, Ip HHS (1999) Discriminative wavelet shape descriptors for recognition of 2-D patterns. Pattern Recognit 32:151–165

    Article  Google Scholar 

  12. Flusser J, Suk T, Zitova B (2009) Moments and moment invariants for pattern recognition. Wiley, New York

    Book  Google Scholar 

  13. Sommer I, Muller O, Dominiques FS, Sander O, Weickert J, Lengauer T (2007) Moment invariants as shape recognition technique for comparing protein binding sites. Bioinformatics 23:3139–3146

    Article  Google Scholar 

  14. Sheng Y, Shen L (1994) Orthogonal Fourier–Mellin moments for invariant pattern recognition. J Opt Soc Am 6:1748–1757

    Article  Google Scholar 

  15. Zhang H, Shu H, Haigron P, Li BS, Luo L (2010) Construction of a complete set of orthogonal Fourier–Mellin moment invariants for pattern recognition applications. Image Vis Comput 28:38–44

    Article  Google Scholar 

  16. Xia T, Zhu H, Shu H, Haigron P, Luo L (2007) Image description with generalized pseudo-Zernike moments. J Opt Soc Am 24:50–59

    Article  Google Scholar 

  17. Flusser J, Suk T (2006) Rotation moment invariants for recognition of symmetric objects. IEEE Trans Image Process 15:3784–3790

    Article  MathSciNet  Google Scholar 

  18. Yang B, Kostkova J, Flusser J, Suk T (2017) Scale invariants from Gaussian–Hermite moments. Signal Process 132:77–84

    Article  Google Scholar 

  19. Yang B, Flusser J, Suk T (2015) Design of high-order rotation invariants from Gaussian–Hermite moments. Signal Process 113:61–67

    Article  Google Scholar 

  20. Farokhi S, Sheikh U, Flusser J, Yang B (2015) Near infrared face recognition using Zernike moments and hermite kernels. Inf Sci 316:234–245

    Article  Google Scholar 

  21. Flusser J, Suk T, Zitova B (2016) 2D and 3D image analysis by moments. Wiley, Chichester

    Book  Google Scholar 

  22. Guo L, Dai M, Zhu M (2014) Quaternion moment and its invariants for color object classification. Inf Sci 273:132–143

    Article  MathSciNet  Google Scholar 

  23. Chen GY, Bui TD, Krzyzak A (2009) Invariant pattern recognition using radon, dual-tree complex wavelet and Fourier transforms. Pattern Recognit 42:2013–2019

    Article  Google Scholar 

  24. Chen GY, Bhattacharya P (2009) Invariant pattern recognition using ridgelet packets and the Fourier transform. Int J Wavelets Multiresolut Inf Process 7:215–228

    Article  MathSciNet  Google Scholar 

  25. Chen GY, Bui TD, Krzyzak A (2006) Rotation invariant feature extraction using ridgelet and Fourier transforms. Pattern Anal Appl 9:83–93

    Article  MathSciNet  Google Scholar 

  26. Chen GY, Bui TD, Krzyzak A (2005) Rotation invariant pattern recognition using ridgelet, wavelet cycle-spinning, and Fourier features. Pattern Recognit 38:2314–2322

    Article  Google Scholar 

  27. Donoho DL, Flesia AG (2001) Digital ridgelet transform based on true ridge functions. In: Stoecker J, Welland GV (eds) Beyond wavelets. Academic Press, Cambridge

    Google Scholar 

  28. Candes EJ (2001) Ridgelets and the representation of mutilated Sobolev functions. SIAM J Math Anal 33:347–368

    Article  MathSciNet  Google Scholar 

  29. Candes EJ, Donoho DL (1999) Ridgelets: a key to higher-dimensional intermittency? Philos Trans R Soc Lond Ser A 357:2495–2509

    Article  MathSciNet  Google Scholar 

  30. Candes EJ (1998) Ridgelets: theory and applications. Ph.D. Thesis, technical report, Department of Statistics, Stanford University

  31. Chen GY, Bui TD (1999) Invariant Fourier–wavelet descriptor for pattern recognition. Pattern Recognit 32:1083–1088

    Article  Google Scholar 

  32. Chen GY, Gleason S (2012) Ridgelet moment invariants for pattern recognition. In: Proceedings of IEEE Canadian conference on electrical and computer engineering. IEEE, Montreal, Quebec, Canada

  33. Sebastian TB, Klein PN, Kimia BB (2004) Recognition of shapes by editing their shock graphs. IEEE Trans Pattern Anal Mach Intell 26:550–571

    Article  Google Scholar 

  34. Bruntha PM, Dhanasekar S, Sagayam KM, Immanuel S, Pandian A (2019) A modified approach for face recognition using PSO and ABC optimization. Int J Innov Technol Explor Eng 8(7):1571–1577

    Google Scholar 

  35. Sagayam KM, Ponraj DN, Winston J, Yaspy JC, Jeba ED, Clara A (2019) Authentication of biometric system using fingerprint recognition with Euclidean distance and neural network classifier. Int J Technol Explor Eng 8(4):766–771

    Google Scholar 

  36. Sagayam KM, Hemanth DJ (2019) A probabilistic model for state sequence analysis in hidden Markov model for hand gesture recognition. Comput Intell 35(1):51–81

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors thank the Associate Editor and the anonymous reviewer for their valuable comments and suggestions. The authors would also like to thank Dr. Bo Yang for providing his MATLAB code of the Gaussian–Hermite moments.

Author information

Authors and Affiliations

  1. Department of Computer Science and Software Engineering, Concordia University, Montreal, QC, H3G 1M8, Canada

    Guang Yi Chen

  2. School of Computer and Software Engineering, University of Science and Technology Liaoning, Anshan, 114051, China

    Changjun Li

Authors
  1. Guang Yi Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Changjun Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Guang Yi Chen.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chen, G.Y., Li, C. Ridgelet moment invariants for robust pattern recognition. Pattern Anal Applic 24, 1367–1376 (2021). https://doi.org/10.1007/s10044-021-00996-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10044-021-00996-8

Keywords

Search

Navigation