[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

New set of non-separable 2D and 3D invariant moments for image representation and recognition

  • Published:
Multimedia Tools and Applications Aims and scope Submit manuscript

Abstract

The extraction of feature vectors of the images is the most important step in image recognition, because it allows a good description of the forms to be recognized. This step is an operation that makes it possible to convert an image into a vector of real or complex values that can serve as a signature for this image. For an accurate recognition system, the used feature vector must be invariant to the three image transformations (translation, rotation and scale), which means that, the descriptor vectors of the image and the transformed image by translation, rotation or scale must be equal. Given the importance of moments and their invariants in pattern recognition and imaging, based on Newton’s binomial and trinomial formulas and the normalized central moments, we construct in this paper four new series of moments for 2D and 3D image recognition, which are invariant to translation, scaling and rotation (TSR): the first is a set of non-orthogonal moment invariants for 2D images (2dMIs), the second is a set of orthogonal moment invariants for 2D images (2dOMIs), the third is a set of non-orthogonal moment invariants for 3D images (3dMIs) and the fourth is a set of orthogonal moment invariants for 3D images (3dOMIs). Using the proposed invariant moments (2dMIs), (2dOMIs), (3dMIs) and (3dOMIs), we construct two types of image descriptor vectors for 2D images and two types for 3D images, which are invariant to translation, rotation and scale. A series of experiments is performed to validate this new set of invariant moments and compare its performance with the existing invariants moments. The obtained results ensure the superiority of the proposed moments over all existing moments in image recognition. Experiments on processing time show that the proposed method is faster than the existing orthogonal invariant moments.

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
£29.99 /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 includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. Batiou I, Benouini R, Zenkouar K (2020) Image recognition using new set of separable three-dimensional discrete orthogonal moment invariants. Multimed Tools Appl 79:13217–13245. https://doi.org/10.1007/s11042-019-08083-1

    Article  Google Scholar 

  2. Batioua I, Benouini R, Zenkouar K, Zahi A, El Fadili H (2017) 3D image analysis by separable discrete orthogonal moments based on Krawtchouk and Tchebichef polynomials. Pattern Recogn 71:264–277. https://doi.org/10.1016/j.patcog.2017.06.013

    Article  Google Scholar 

  3. Cyganski D, Orr JA (1985) Applications of tensor theory to object recognition and orientation determination. IEEE Trans Pattern Anal Mach Intell PAMI-7(6):662–673

    Article  Google Scholar 

  4. Doha EH, Bhrawy AH, Baleanu D, Ezz-Eldien SS (2013) On shifted Jacobi spectral approximations for solving fractional differential equations. Appl Math Comput 219(15):8042–8056. https://doi.org/10.1016/j.amc.2013.01.051

    Article  MathSciNet  MATH  Google Scholar 

  5. EL Mallahi M, El-Mekkaoui J, Zouhri A, Amakdouf H, Qjidaa H (2018) Rotation scaling and translation invariants of 3D radial shifted Legendre moments. Int J Autom Comput 15:169–180. https://doi.org/10.1007/s11633-017-1105-8

    Article  Google Scholar 

  6. Flusser J, Boldyš J, Zitová B (2003) Moment forms invariant to rotation and blur in arbitrary number of dimensions. IEEE Trans Pattern Anal Mach Intell 25:234–246

    Article  Google Scholar 

  7. Flusser J, Suk T, Zitova B (2016) 2D and 3D image analysis by moments. John Wiley & Sons, Ltd, 2016. https://doi.org/10.1002/9781119039402

  8. Galvez JM, Canton M (1993) Normalization and shape recognition of three-dimensional objects by 3D moments. Pattern Recogn 26(5):667–681. https://doi.org/10.1016/0031-3203(93)90120-L

    Article  Google Scholar 

  9. Guo X (1993) Three-dimensional moment invariants under rigid transformation. In: Chetverikov D., Kropatsch W.G. (eds) Computer Analysis of Images and Patterns. CAIP 1993. Lecture Notes in Computer Science, vol. 719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57233-3_67

  10. Hjouji A, Jourhmane M, El-Mekkaoui J, Es-Sabry M (2018) Mixed finite element approximation for bivariate Perona-Malik model arising in 2D and 3D image Denoising. 3D Res 9:36. https://doi.org/10.1007/s13319-018-0187-6

    Article  Google Scholar 

  11. Hjouji A, Jourhmane M, El-Mekkaoui J, Qjidaa H, Bouikhalene B (2019) Image retrieval and classification using shifted Legendre invariant moments and radial basis functions neural networks. Procedia Comput Sci 148:154–163. https://doi.org/10.1016/j.procs.2019.01.019

    Article  Google Scholar 

  12. Hjouji A, El-Mekkaoui J, Jourhmane M (2019) Mixed finite element method for nonlinear diffusion equation in image processing. Pattern Recognit Image Anal 29:296–308. https://doi.org/10.1134/S1054661819020020

    Article  Google Scholar 

  13. Hjouji A, El-Mekkaoui J, Jourhmane M (2020) Rotation scaling and translation invariants by a remediation of Hu’s invariant moments. Multimed Tools Appl 79:14225–14263. https://doi.org/10.1007/s11042-020-08648-5

    Article  Google Scholar 

  14. Hjouji A, El-Mekkaoui J, Jourhmane M, Bouikhalene B (2020) New set of non-separable orthogonal invariant moments for image recognition. J Math Imaging Vis 62:606–624. https://doi.org/10.1007/s10851-020-00948-7

    Article  MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  16. Li H, He F, Liang Y, Quan Q (2020) A dividing-based many-objective evolutionary algorithm for large-scale feature selection. Soft Comput 24:6851–6870. https://doi.org/10.1007/s00500-019-04324-5

    Article  Google Scholar 

  17. Lo CH, Don HS (1989) 3-D moment forms: their construction and application to object identification and positioning. IEEE Trans Pattern Anal Mach Intell 11:1053–1064

    Article  Google Scholar 

  18. Sadjadi FA, Hall EL (1980) Three-dimensional moment invariants. IEEE Trans Pattern Anal Mach Intell PAMI-2(2):127–136

    Article  Google Scholar 

  19. Siddiqi K, Zhang J, Macrini D, Shokoufandeh A, Bouix S, Dickinson S (2008) Retrieving articulated 3D models using medial surfaces. Mach Vis Appl 19:261–275. https://doi.org/10.1007/s00138-007-0097-8

    Article  MATH  Google Scholar 

  20. Suk T, Flusser J (2011) Tensor method for constructing 3D moment invariants. In: Real P., Diaz-Pernil D., Molina-Abril H., Berciano A., Kropatsch W. (eds) Computer Analysis of Images and Patterns. CAIP 2011. Lecture Notes in Computer Science, vol 6855. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23678-5_24

  21. Suk T, Flusser J (2014) Recognition of symmetric 3D bodies. Symmetry. 6(3):722–757. https://doi.org/10.3390/sym6030722

    Article  MathSciNet  MATH  Google Scholar 

  22. Suk T, Flusser J, Boldyš J (2015) 3D rotation invariants by complex moments. Pattern Recogn 48(11):3516–3526. https://doi.org/10.1016/j.patcog.2015.05.007

    Article  MATH  Google Scholar 

  23. Xiao B, Wang G, Li W (2014) Radial shifted Legendre moments for image analysis and invariant image recognition. Image Vis Comput 32(12):994–1006. https://doi.org/10.1016/j.imavis.2014.09.002

    Article  Google Scholar 

  24. Xiao B, .Li L, Li Y, Li W, Wang G (2017) Image analysis by fractional-order orthogonal moments. Inf Sci, 382-383, pp.135–149. https://doi.org/10.1016/j.ins.2016.12.011

  25. Xu D, Li H (2006) 3-D affine moment invariants generated by geometric primitives. in Proceedings of the 18th International Conference on Pattern Recognition ICPR’06, IEEE, Print ISBN: 0-7695-2521-0. pages 544–547, 2006. https://doi.org/10.1109/ICPR.2006.21

  26. Xu D, Li H (2008) Geometric moment invariants. Pattern Recogn 41(1):240–249. https://doi.org/10.1016/j.patcog.2007.05.001

    Article  MATH  Google Scholar 

  27. Yang J, Zhang L, Tang YY (2019) Mellin polar coordinate moment and its affine invariance. Pattern Recogn 85:37–49. https://doi.org/10.1016/j.patcog.2018.07.036

    Article  Google Scholar 

  28. Yu H, He F, Pan Y (2020) A scalable region-based level set method using adaptive bilateral filter for noisy image segmentation. Multimed Tools Appl 79:5743–5765. https://doi.org/10.1007/s11042-019-08493-1

    Article  Google Scholar 

  29. Zhang S, He F (2019) DRCDN: learning deep residual convolutional dehazing networks. Vis Comput 36:1797–1808. https://doi.org/10.1007/s00371-019-01774-8

    Article  Google Scholar 

  30. Zhang J, He F, Chen Y (2020) A new haze removal approach for sky/river alike scenes based on external and internal clues. Multimed Tools Appl 79:2085–2107. https://doi.org/10.1007/s11042-019-08399-y

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. TIAD Laboratory, Sultan Moulay Slimane University, Beni Mellal, Morocco

    Amal Hjouji

  2. Sidi Mohamed Ben Abdellah University, Fez, Morocco

    Jaouad El-Mekkaoui & Hassan Qjidaa

  3. TIN Laboratory, Sidi Mohamed Ben Abdellah University, Fez, Morocco

    Jaouad El-Mekkaoui

  4. LESSI Laboratory, Sidi Mohamed Ben Abdellah University, Fez, Morocco

    Hassan Qjidaa

Authors
  1. Amal Hjouji
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jaouad El-Mekkaoui
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hassan Qjidaa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jaouad El-Mekkaoui.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

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

Hjouji, A., El-Mekkaoui, J. & Qjidaa, H. New set of non-separable 2D and 3D invariant moments for image representation and recognition. Multimed Tools Appl 80, 12309–12333 (2021). https://doi.org/10.1007/s11042-020-10356-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11042-020-10356-z

Keywords

Search

Navigation