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

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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.

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Authors and Affiliations

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

    Mostafa El Mallahi, Amal Zouhri, Anass El Affar, Ahmed Tahiri & Hassan Qjidaa

Authors
  1. Mostafa El Mallahi
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  2. Amal Zouhri
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  3. Anass El Affar
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  4. Ahmed Tahiri
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  5. Hassan Qjidaa
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Correspondence to Mostafa El Mallahi.

Additional information

Recommended by Associate Editor Hong Qiao

Mostafa El Mallahi received the M.Eng. degrees in computer engineering from Faculty of Sciences, the University Sidi Mohammed Ben Abdellah, Morocco in 2005 and 2007, respectively. He is currently the Ph. D. degree candidate in sciences and technologies at CED-ST Center of Doctoral Studies, Faculty of sciences Dhar el Mahraz, Sidi Mohammed Ben Abdellah University, Morocco.

His research interests includes image processing, pattern classification, orthogonal systems, neural networks, deep learning, genetic algorithms and special functions.

Amal Zouhri received the M. Sc. degree in information science and systems from University of Sidi Mohammed Ben Abdellah, Morocco in 2011.

Her research interests include stability and stabilization of large-scale systems, multivariable nonlinear systems, robust and H∞ control, linear matrix inequalities (LMIs), singular systems, time delay systems and computer science.

Anass El Affar received the M. Sc. degree in engineering signals systems informatics from Departmnt of Physics, Sidi Mohammed Ben Abdellah University, Morocco in 2003. He successfully completed his undergraduate project on image processing under the supervision of Professor Hassan Qjidaa in 2007.

His research interests include image processing, pattern recognition, and Big data.

Ahmed Tahiri received the M. Sc. degree in ESSI from Department of Physics, Sidi Mohammed Ben Abdellah University, Morocco in 2003, received the Ph.D. degree in physics and environment from the University Sidi Mohamed Ben Abdellah, Faculty of Science, Morocco in 2005. He completed his doctoral studies in didactics of science in the University of Sherbrooke in Canada in 2009. He is now a professor in Ecole Normal Sup´erieur (ENS), Morocco.

His research interests include image processing, didactics of scientific disciplines and environmental education.

Hassan Qjidaa received the M. Sc. and Ph.D. degrees in applied physics from Claud Bernard university of Lyon, France in 1983 and 1987, respectively. He was a professor in electrical engineering at in the Faculty of Sciences, Sidi Mohammed Ben Abdellah university, Morocco in 1999. He is now a professor in the Department of physics, SidiMohammed Ben Abdellah university, Morocco.

His research interests include image manuscripts recognition, cognitive science, image processing, computer graphics, pattern recognition, neural networks, human-machine interface, artificial intelligence and robotics.

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El Mallahi, M., Zouhri, A., El Affar, A. et al. Radial Hahn Moment Invariants for 2D and 3D Image Recognition. Int. J. Autom. Comput. 15, 277–289 (2018). https://doi.org/10.1007/s11633-017-1071-1

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  • DOI: https://doi.org/10.1007/s11633-017-1071-1

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