Abstract
In this paper, we propose a new set of 2D and 3D rotation invariants based on orthogonal radial Meixner moments. We also present a theoretical mathematics to derive them. Hence, this paper introduces in the first case a new 2D radial Meixner moments based on polar representation of an object by a one-dimensional orthogonal discrete Meixner polynomials and a circular function. In the second case, we present a new 3D radial Meixner moments using a spherical representation of volumetric image by a one-dimensional orthogonal discrete Meixner polynomials and a spherical function. Further 2D and 3D rotational invariants are derived from the proposed 2D and 3D radial Meixner moments respectively. In order to prove the proposed approach, three issues are resolved mainly image reconstruction, rotational invariance and pattern recognition. The result of experiments prove that the Meixner moments have done better than the Krawtchouk moments with and without nose. Simultaneously, the reconstructed volumetric image converges quickly to the original image using 2D and 3D radial Meixner moments and the test images are clearly recognized from a set of images that are available in a PSB database.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
J. Flusser, T. Suk, and B. Zitová, Moments and Moment Invariants in Pattern Recognition (Wiley, Chichester, 2009).
M. El Mallahi, A. Mesbah, H. El Fadili, K. Zenkouar, and H. Qjidaa, “Compact computation of Tchebichef moments for 3D object representation,” WSEAS Trans. Circuits Syst. 13, 368–380 (2014).
M. El Mallahi, A. Mesbah, H. Qjidaa, K. Zenkouar, and H. El Fadili, “Translation and scale invariants of three-dimensional Tchebichef moments,” in Proc. 2015 Intelligent Systems and Computer Vision (ISCV) (IEEE, 2015), pp. 1–5.
M. El Mallahi, A. Mesbah, H. Qjidaa, A. Berrahou, K. Zenkouar, and H. El Fadili, “Volumetric image reconstruction by 3D Hahn moments,” in Proc. 2015 IEEE/ACS 12th Int. Conf. on Computer Systems and Applications (AICCSA) (IEEE, 2015), pp. 1–8.
M. El Mallahi, A. Zouhri, A. Mesbah, and H. Qjidaa, “3D radial invariant of dual Hahn moments,” Neural Comput. Applic., pp. 1–12 (2016). doi: 10.1007/s00521-016-2782-x
A. Mesbah, M. El Mallahi, H. El Fadili, K. Zenkouar, A. Berrahou, and H. Qjidaa, “An algorithm for fast computation of 3D Krawtchouk moments for volumetric image reconstruction,” in Proceedings of the Mediterranean Conference on Information Communication Technologies 2015, MedCT 2015, Vol. 1, Ed. by A. El Oualkadi, F. Choubani, and A. El Moussati, Lecture Notes in Electrical Engineering (Springer, Cham, 2016), Vol. 380, pp. 267–276.
A. Mesbah, A. Berrahou, M. El Mallahi, and H. Qjidaa, “Fast algorithm for 3D local feature extraction using Hahn and Charlier moments,” in Advances in Ubiquitous Networking 2, Proc. of the Unet’16, Ed. by R.El-Azouzi et al., ecture Notes in Electrical Engineering (Springer, Singapore, 2016), Vol. 397, pp. 375–373.
A. Mesbah, A. Berrahou, M. El Mallahi, and H. Qjidaa, “Fast and efficient computation of threedimensional Hahn moments,” J. Electron. Imaging 25 (6), 061621, 12 pages (2016).
A. Mesbah, A. Zouhri, M. El Mallahi, K. Zenkouar, and H. Qjidaa, “Robust reconstruction and generalized dual Hahn moments invariants extraction for 3D images,” 3D Research 8 (1), Article 7, 20 pages (2017).
J. Flusser, T. Suk, and B. Zitová, Moments and Moment Invariants in Pattern Recognition (Wiley, Chichester, 2009).
M. El Mallahi, A. Zouhri, J EL-Mekkaoui, and H. Qjidaa, “Three dimensional radial Tchebichef moment invariants for volumetric image recognition,” Pattern Recogn. Image Anal. 27 (4), 810–824 (2017).
B. Xiao, Y. Zhang, L. Li, W. Li, and G. Wang, “Explicit Krawtchouk moment invariants for invariant image recognition,” J. Electron. Imaging 25 (2), 023002, 10 pages (2016).
M. El Mallahi, A. Zouhri, A. Mesbah, A. Berrahou, I. El Affar, and H. Qjidaa, “Radial invariant of 2D and 3D Racah moments,” Multimed. Tools Appl. 77 (6), 6583–6604 (2017).
H. S. Hsu and W. H. Tsai, “Moment-preserving edge detection and its application to image data compression,” Opt. Eng. 32 (7), 1596–1608 (1993).
X.-Y. Wang, P.-P. Niu, H.-Y. Yang, et al., “A new robust color image watermarking using local quaternion exponent moments,” Inform. Sci. 277, 731–754 (2014).
M. El Mallahi, A. Zouhri, A. El Affar, A. Tahiri, and H. Qjidaa, “Radial Hahn moment invariants for 2D and 3D image recognition,” Int. J. Autom. Comput., 1–13 (2017). doi: 10.1007/s11633-017-1071-1
M. Kazhdan, “An approximate and efficient method for optimal rotation alignment of 3D models,” IEEE Trans. Pattern Anal. Mach. Intell. 29 (7), 1221–1229 (2007).
J. Fehr, “Local rotation invariant patch descriptors for 3D vector fields,” in Proc. 2010 20th Int. Conf. on Pattern Recognition (ICPR’10) (IEEE Computer Society, 2010), pp. 1381–1384.
J. Fehr and H. Burkhardt, “3D rotation invariant local binary patterns,” in Proc. 2008 19th Int. Conf. on Pattern Recognition (ICPR’08) (IEEE Computer Society, 2008), pp. 1–4.
H. Skibbe, M. Reisert, and H. Burkhardt, “SHOG–Spherical HOG descriptors for rotation invariant 3D object detection,” in Pattern Recognition, DAGM 2011, Ed. by R. Mester and M. Felsberg, Lecture Notes in Computer Science (Springer, Berlin, 2011), Vol. 6835, pp. 142–151.
N. Canterakis, “3D Zernike moments and Zernike affine invariants for 3D image analysis and recognition,” in Proc. 11th Scandinavian Conf. on Image Analysis SCIA’99, Greenland, 1999, Ed. by B. K. Ersbøll and P. Johansen (DSAGM, 1999), Vol. 1, pp. 85–93.
H. Zhu, H. Shu, J. Zhou, L. Luo, and J. L. Coatrieux, “Image Analysis by discrete orthogonal dual Hahn moments,” Pattern Recogn. Lett. 28 (13), 1688–1704 (2007).
http://www.cs.columbia.edu/CAVE/software/softlib/coil-20.php
Princeton, Princeton Shape Benchmark, 2013. http://shape.cs.princeton.edu/benchmark/
Author information
Authors and Affiliations
Corresponding author
Additional information
The article is published in the original.
Mostafa El Mallhi received the B.Sc, M.Sc, and Ph. D. degrees in computer science from Faculty of Sciences, University Sidi Mohammed Ben Abdellah, Morocco in 2000, 2007, and 2017, respectively. His research interests include image processing, pattern classification, orthogonal systems, neural networks, big data, data mining, data science, deep learning, genetic algorithms, and special functions.
Amal Zouhri received the B.Sc, M.Sc, and Ph.D. degrees in electrical engineering from Faculty of Sciences, Sidi Mohammed Ben Abdellah University, Morocco in 2008, 2011, and 2016, respectively. Her research interests include embedded system, stability and stabilization of interconnected systems, decentralized systems, robust and H∞ control, linear matrix inequalities LMIs, singular systems, time delay systems, computer science.
Professor Hassan Qjidaa received his M.Sc and PhD in applied physics from Claud Bernard University of Lyon France in 1983 and 1987, respectively. He got the Pr. Degree in Electrical Engineering from sidi mohammed Ben Abdellah university, Fez, Morocco 1999. He is now an professor in the Dept. of physics in Sidi Mohammed Ben Aabdellah university, Fez, Morocco. His main research interest include image manuscripts recognition, cognitive science, image processing, computer graphics, pattern recognition, neural networks, human-machine interface, artificial intelligence and robotics.
Rights and permissions
About this article
Cite this article
El Mallahi, M., Zouhri, A. & Qjidaa, H. Radial Meixner Moment Invariants for 2D and 3D Image Recognition. Pattern Recognit. Image Anal. 28, 207–216 (2018). https://doi.org/10.1134/S1054661818020128
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1054661818020128