Abstract
This paper proposes a new set of 3D rotation scaling and translation invariants of 3D radially shifted Legendre moments. We aim to develop two kinds of transformed shifted Legendre moments: a 3D substituted radial shifted Legendre moments (3DSRSLMs) and a 3D weighted radial one (3DWRSLMs). Both are centered on two types of polynomials. In the first case, a new 3D radial complex moment is proposed. In the second case, new 3D substituted/weighted radial shifted Legendre moments (3DSRSLMs/3DWRSLMs) are introduced using a spherical representation of volumetric image. 3D invariants as derived from the suggested 3D radial shifted Legendre moments will appear in the third case. To confirm the proposed approach, we have resolved three issues. To confirm the proposed approach, we have resolved three issues: rotation, scaling and translation invariants. The result of experiments shows that the 3DSRSLMs and 3DWRSLMs have done better than the 3D radial complex moments with and without noise. Simultaneously, the reconstruction converges rapidly to the original image using 3D radial 3DSRSLMs and 3DWRSLMs, and the test of 3D images are clearly recognized from a set of images that are available in Princeton shape benchmark (PSB) database for 3D image.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
[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. DOI: 10.1109/TPAMI.1980.4766990.
[2]M. R. Teague. Image analysis via the general theory of moments. Journal of the Optical Society of America, vol. 70, no. 8, pp. 920–930, 1980. DOI: 10.1364/JOSA.70. 000920.
C. W. Chong, P. Raveendran, R. Mukundan. Translation and scale invariants of Legendre moments. Pattern Recognition, vol. 37, no. 1, pp. 119–129, 2004. DOI: 10.1016/j. patcog.2003.06.003.
A. Khotanzad, Y. H. Hong. Invariant image recognition by Zernike moments. IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 12, no. 5, pp. 489–497, 1990. DOI: 10.1109/34.55109.
J. Shen. Orthogonal Gaussian–hermite moments for image characterization. In Proceedings of SPIE 3208, Intelligent Robots and Computer Vision XVI: Algorithms, Techniques, Active Vision, and Materials Handling, SPIE, Pittsburgh, USA, vol. 3280, pp. 224–233, 1997.
C. H. Teh, R. T. Chin. On image analysis by the methods of moments. IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 10, no. 4, pp. 496–513, 1983.
A. Mesbah, A. Zouhri, M. El Mallahi, K. Zenkouar, H. Qjidaa. Robust reconstruction and generalized dual Hahn moments invariants extraction for 3D images. 3D Research, vol. 8, article number 7, 2017. DOI: 10.1007/ s13319-016-0113-8.
M. El Mallahi, A. Mesbah, H. El Fadili, K. Zenkouar, H. Qjidaa. Compact computation of tchebichef moments for 3D object representation. WSEAS Transactions on Circuits and Systems, vol. 13, pp. 368–380, 2014.
M. El Mallahi, A. Zouhri, A. Mesbah, H. Qjidaa. 3D radial invariant of dual Hahn moments. Neural Computing and Applications, Online First. DOI: 10.1007/s00521-016-2782-x.
M. El Mallahi, A. Zouhri, A. Mesbah, A. Berrahou, I. El Affar, H. Qjidaa. Radial invariant of 2D and 3D racah moments. Multimedia Tools and Application, Online First. DOI: 10.1007/s11042-017-4573-5.
M. El Mallahi, A. Zouhri, A. El Affar, A. Tahiri, H. Qjidaa. Radial Hahn moment invariants for 2D and 3D image recognition. International Journal of Automation and Computing, Online First. DOI: 10.1007/s11633-017-1071-1.
M. El Mallahi, A. Mesbah, H. Karmouni, A. El Affar, A. Tahiri, H. Qjidaa. Radial Charlier moment invariants for 2D object/image recognition. In proceedings of the 5th International Conference on Multimedia Computing and Systems, IEEE, Marrakech, Morocco, pp. 41–45, 2016.
M. El Mallahi, A. Zouhri, J. El-Mekkaoui, H. Qjidaa. Radial meixner moments for rotational invariant pattern recognition. Intelligent Systems and Computer Vision, 2017. DOI: 10.1109/ISACV.2017.8054943.
B. Xiao, J. F. Ma, X. Wang. Image analysis by Bessel-Fourier moments. Pattern Recognition, vol. 43, no. 8, pp. 2620–2629, 2010. DOI: 10.1016/j.patcog.2010.03.013.
H. Z. Shu, L. M. Luo, W. X. Yu, Y. Fu. A new fast method for computing Legendre moments. Pattern Recognition, vol. 33, no. 2, pp. 341–348, 2000. DOI: 10.1016/ S0031-3203(99)00044-8.
P. T. Yap, R. Paramesran. An efficient method for the computation of Legendre moments. IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 27, no. 12, pp. 1996–2002, 2005. DOI: 10.1109/TPAMI.2005. 232.
G. Y. Yang, H. Z. Shu, C. Toumoulin, G. N. Han, L. M. Luo. Efficient Legendre moment computation for grey level images. Pattern Recognition, vol. 39, no. 1, pp. 74–80, 2006. DOI: 10.1016/j.patcog.2005.08.008.
C. W. Chong, P. Raveendran, R. Mukundan. Translation and scale invariants of Legendre moments. Pattern Recognition, vol. 37, no. 1, pp. 119–129, 2004. DOI: 10.1016/j. patcog.2003.06.003.
H. Zhang, H. Z. Shu, G. N. Han, G. Coatrieux, L. M. Luo, J. L. Coatrieux. Blurred image recognition by Legendre moment invariants. IEEE Transactions on Image Processing, vol. 19, no. 3, pp. 596–611, 2010. DOI: 10.1109/ TIP.2009.2036702.
H. Z. Shu, L. M. Luo, W. X. Yu, Y. Fu. A new fast method for computing Legendre moments. Pattern Recognition, vol. 33, no. 2, pp. 341–348, 2000. DOI: 10.1016/ S0031-3203(99)00044-8.
B. Xiao, L. P. Li, Y. Li, W. S. Li, G. Y. Wang. Image analysis by fractional-order orthogonal moments. Information Sciences, vol. 382-383, pp. 135–149, 2017. DOI: 10.1016/j. ins.2016.12.011.
B. Xiao, Y. H. Zhang, L. P. Li, W. S. Li, G. Y. Wang. Explicit Krawtchouk moment invariants for invariant image recognition. Journal of Electronic Imaging, vol. 25, no. 2, Article number 023002, 2016.
B. Xiao, J. F. Ma, J. T. Cui. Radial tchebichef moment invariants for image recognition. Journal of Visual Communication and Image Representation, vol. 23, no. 2, pp. 381–386, 2012. DOI: 10.1016/j.jvcir.2011.11.008.
B. Xiao, J. T. Cui, H. X. Qin, W. S. Li, G. Y. Wang. Moments and moment invariants in the Radon space. Pattern Recognition, vol. 48, no. 9, pp. 2772–2784, 2015. DOI: 10.1016/j.patcog.2015.04.007.
C. W. Chong, P. Raveendran, R. Mukundan. Translation and scale invariants of Legendre moments. Pattern Recognition, vol. 37, no. 1, pp. 119–129, 2004. DOI: 10.1016/j. patcog.2003.06.003.
B. Xiao, G. Y. Wang, W. S. Li. Radial shifted Legendre moments for image analysis and invariant image recognition. Image and Vision Computing, vol. 32, no. 12, pp. 994–1006, 2014. DOI: 10.1016/j.imavis.2014.09.002.
F. Retter, C. Plant, B. Burgeth, G. Botella, T. Schlossbauer, A. Meyer-Bäse. Computer-aided diagnosis for diagnostically challenging breast lesions in DCE-MRI based on image registration and integration of morphologic and dynamic characteristics. EURASIP Journal on Advances in Signal Processing, vol. 157, pp. 1–9, 2013. DOI: 10.1186/1687-6180-2013-157.
Shape Analysis Group. McGill 3D Shape Benchmark,[Online], Available: http://www.cim.mcgill.ca/~%20shape/ benchMark/.
Author information
Authors and Affiliations
Corresponding author
Additional information
Recommended by Guest Editor Zhi-Jie Xu
Mostafa El Mallahi 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.
Jaouad El Mekkaoui received the B. Sc., M. Sc. and Ph. D. degrees in mathematics from Faculty of Sciences, Sidi Mohammed Ben Abdellah University, Morocco in 1999, 2002 and 2014, respectively. He is now a professor in Department of Mathematics and Computer Science, Polydisciplinaire Faculty, Morocco.
His research interests include mathematics, numerical analysis, classification, image processing, pattern recognition, orthogonal systems, neural networks, deep learning and data science, big data, genetic algorithms and special functions, image manuscripts recognition, cognitive science, human-machine interface, artificial intelligence and robotics.
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 2017, respectively.
Her research interests include embedded system, stability and stabilization of interconnected systems, decentralized systems, robust and H∞ control, linear matrix inequalities, singular systems, time delay systems, computer science, image processing, pattern classification, orthogonal systems, neural networks, deep learning, genetic algorithms and special functions.
Hicham Amakdouf received the B. Sc., M. Sc. degrees in computer sciences from Faculty of Sciences, Sidi Mohammed Ben Abdellah University, Morocco in 2003 and 2007, respectively. He is presently a Ph. D. degree candidate in computer science at the Faculty of Sciences, Sidi Mohammed Ben Abdellah University, Morocco.
His research interests include image processing, computer graphics, artificial intelligence, geographic information systems.
Hassan Qjidaa received the M. Sc. and Ph. D. degrees in physics from Claud Bernard University of Lyon, France in 1983 and 1987, respectively. He is a full profossor of electrical engineering at the Faculty of Sciences, Sidi Mohammed Ben Abdellah University, Morocco 1999. He is now a professor in Sidi Mohammed Ben Abdellah University, Morocco.
His research interests include classification, image processing, pattern recognition, orthogonal systems, neural networks, deep learning and data science, big data, genetic algorithms and special functions.
Rights and permissions
About this article
Cite this article
El Mallahi, M., El Mekkaoui, J., Zouhri, A. et al. Rotation Scaling and Translation Invariants of 3D Radial Shifted Legendre Moments. Int. J. Autom. Comput. 15, 169–180 (2018). https://doi.org/10.1007/s11633-017-1105-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11633-017-1105-8