Advertisement

Radial Hahn Moment Invariants for 2D and 3D Image Recognition

  • Mostafa El Mallahi
  • Amal Zouhri
  • Anass El Affar
  • Ahmed Tahiri
  • Hassan Qjidaa
Research Article

Abstract

Recently, orthogonal moments have become efficient tools for two-dimensional and three-dimensional (2D and 3D) image not only in pattern recognition, image vision, but also in image processing and applications engineering. Yet, there is still a major difficulty in 3D rotation invariants. In this paper, we propose new sets of invariants for 2D and 3D rotation, scaling and translation based on orthogonal radial Hahn moments. We also present theoretical mathematics to derive them. Thus, this paper introduces in the first case new 2D radial Hahn moments based on polar representation of an object by one-dimensional orthogonal discrete Hahn polynomials, and a circular function. In the second case, we present new 3D radial Hahn moments using a spherical representation of volumetric image by one-dimensional orthogonal discrete Hahn polynomials and a spherical function. Further 2D and 3D invariants are derived from the proposed 2D and 3D radial Hahn moments respectively, which appear as the third case. In order to test the proposed approach, we have resolved three issues: the image reconstruction, the invariance of rotation, scaling and translation, and the pattern recognition. The result of experiments show that the Hahn moments have done better than the Krawtchouk moments, with and without noise. Simultaneously, the mentioned reconstruction converges quickly to the original image using 2D and 3D radial Hahn moments, and the test images are clearly recognized from a set of images that are available in COIL-20 database for 2D image, and Princeton shape benchmark (PSB) database for 3D image.

Keywords

Orthogonal moments two-dimensional and three-dimensional (2D and 3D) radial Hahn moments Hahn polynomials image reconstruction 2D and 3D rotation invariants 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    F. A. Sadjadi, E. L. Hall. Three-dimensional moment invariants. IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. PAMI-2, no.2, pp. 127–136, 1980.CrossRefzbMATHGoogle Scholar
  2. [2]
    D. Cyganski, J. A. Orr. Applications of Tensor Theory to Object recognition and orientation determination. IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 7, no.6, pp. 662–673, 1985.CrossRefGoogle Scholar
  3. [3]
    C. H. Lo, and H. S. Don. 3D moment forms: Their construction and application to object identification and positioning. IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 11, no.10, pp. 1053–1064, 1989.CrossRefGoogle Scholar
  4. [4]
    X. Guo. Three-dimensional moment invariants under rigid transformation. In Proceedings of the 5th International Conference on Computer Analysis of Images and Patterns, Springer, London, UK, pp. 518–522, 1993.CrossRefGoogle Scholar
  5. [5]
    J. M. Galvez, M. Canton. Normalization and shape recognition of three-dimensional objects by 3D moments. Pattern Recognition, vol. 26, no.5, pp. 667–681, 1993.CrossRefGoogle Scholar
  6. [6]
    T. H. Reiss. Features invariant to linear transformations in 2D and 3D. In Proceedings of the 11th IAPR International Conference on Pattern Recognition, IEEE, The Hague, Netherlands, vol. 3, pp. 493–496, 1992.Google Scholar
  7. [7]
    N. Canterakis. Complete moment invariants and pose determination for orthogonal transformations of 3D objects. Mustererkennung, B. Jähne, P. Geisler, H. Hausecker, F. Hering, Eds., Berlin Heidelberg, Germany: Springer, pp. 339–350, 1996.Google Scholar
  8. [8]
    N. Canterakis. 3D Zernike moments and Zernike affine invariants for 3D image analysis and recognition. In Proceedings of the 11th Scandinavian Conference on Image Analysis, DSAGM, Kangerlussuaq, Denmark, pp. 85–93, 1999.Google Scholar
  9. [9]
    J. Flusser. On the independence of rotation moment invariants. Pattern Recognition, vol. 33, no.9, pp. 1405–1410, 2000.CrossRefGoogle Scholar
  10. [10]
    J. Flusser, J. Boldys, and B. Zitova. Moment forms invariant to rotation and blur in arbitrary number of dimensions. IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 25, no.2, pp. 234–246, 2003.CrossRefGoogle Scholar
  11. [11]
    A. Venkataramana, P. A. Raj. Image watermarking using Krawtchouk moments. In Proceedings of International Conference on Computing: Theory and Applications, IEEE, Kolkata, India, pp. 676–680, 2007.Google Scholar
  12. [12]
    M. Kazhdan. An approximate and efficient method for optimal rotation alignment of 3D models. IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 29, no.7, pp. 1221–1229, 2007.MathSciNetCrossRefGoogle Scholar
  13. [13]
    P. T. Yap, R. Paramesran, S. H. Ong. Image analysis using Hahn moments. IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 29, no.11, pp. 2057–2062, 2007.CrossRefGoogle Scholar
  14. [14]
    J. Fehr, H. Burkhardt. 3D rotation invariant local binary patterns. In Proceedings of the 19th International Conference on Pattern Recognition, IEEE Computer Society, Omnipress, Tampa, USA, pp. 1–4, 2008.Google Scholar
  15. [15]
    D. Xu, H. Li. Geometric moment invariants. Pattern Recognition, vol. 41, no.1, pp. 240–249, 2008.CrossRefzbMATHGoogle Scholar
  16. [16]
    M. Langbein, H. Hagen. A generalization of moment invariants on 2D vector fields to tensor fields of arbitrary order and dimension. In Proceedings of the 5th International Symposium, Las Vegas, USA, pp. 1151–1160, 2009.Google Scholar
  17. [17]
    R. Kakarala, D. S. Mao. A theory of phase-sensitive rotation invariance with spherical harmonic and moment-based representations. In Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, IEEE, San Francisco, USA, vol. 10, pp. 105–112, 2010.Google Scholar
  18. [18]
    J. Fehr. Local rotation invariant patch descriptors for 3D vector fields. In Proceedings of the 20th International Conference on Pattern Recognition, IEEE, New Jersey, USA, pp. 1381–1384, 2010.Google Scholar
  19. [19]
    T. Suk, J. Flusser. Tensor method for constructing 3D moment invariants. In Proceedings of the 14th International Conference on Computer Analysis of Images and Patterns, Springer, Seville, Spain, vol. 2, pp. 212–219, 2011.MathSciNetCrossRefGoogle Scholar
  20. [20]
    H. Skibbe, M. Reisert, H. Burkhardt. SHOG-spherical HOG descriptors for rotation invariant 3D object detection. In Proceedings of the 33rd DAGM Symposiam, Lecture Notes in Computer Science, Springer, vol. 6835, pp. 142–151, 2011.MathSciNetCrossRefGoogle Scholar
  21. [21]
    B. Xiao Bin, J. Fian-Feng Ma, and J. Tiang-Tao Cui. Radial Tchebichef moment invariants for image recognition. Journal of Visual Communication and Image Representation, vol. 23, no.2, pp. 381–386, 2012.CrossRefGoogle Scholar
  22. [22]
    B. Xiao Bin, and G. Yuo-yin Wang. Generic radial orthogonal moment invariants for invariant image recognition. Journal of Visual Communication and Image Representation, vol. 24, no.7, pp. 1002–1008, 2013.CrossRefGoogle Scholar
  23. [23]
    B. Xiao Bin, G. Yuo-yin Wang, and W. Sei-sheng Li. Radial shifted Legendre moments for image analysis and invariant image recognition. Image and Vision Computing, vol. 32, no.12, pp. 994–1006, 2014.CrossRefGoogle Scholar
  24. [24]
    B. Xiao, Y. H. Zhang, L. P. Li, W. S. Li, G. Y. Wang. Bin. Explicit Krawtchouk moment invariants for invariant image recognition. Journal of Electronic Imaging, vol. 25, no. 2, Article number 023002, 2016.Google Scholar
  25. [25]
    http://www.cs.columbia.edu/CAVE/software/softlib/coil-20.php.Google Scholar
  26. [26]
    Princeton, Princeton Shape Benchmark, PSB database, [Online], Available: http://www.cim.mcgill.ca/shape/ benchMark/.Google Scholar

Copyright information

© Institute of Automation, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Sidi Mohamed Ben Abdellah University, Faculty of Sciences Dhar el Mahraz, CED-ST Center of Doctoral Studies in Sciences and TechnologiesFezMorocco

Personalised recommendations