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Adapted Jacobi Orthogonal Invariant Moments for Image Representation and Recognition

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Abstract

Images recognition and classification require an extraction technique of feature vectors of these images. These vectors must be invariant to the three geometric transformations: rotation, translation and scaling. Several authors used the theory of orthogonal moments to extract the feature vectors of images. Jacobi moments are orthogonal moments, which have been widely applied in imaging and pattern recognition. However, the invariance to rotation of Cartesian Jacobi moments is very difficult to obtain. In this paper, we obtain at first a set of transformed orthogonal Jacobi polynomials, called “Adapted Jacobi polynomials”. Based on these polynomials, a set of orthogonal moments is presented, named adapted Jacobi moments (AJMs). These moments are orthogonal on the rectangle \(\left[ {0, N\left] { \times } \right[0, M} \right],\) where \(N \times M\) is the size of the described image. We also provide a new series of feature vectors of images based on adapted Jacobi orthogonal invariants moments, which are a linear combination of geometric moment invariants, where the latest ones are invariant under rotation, translation and scaling of the described image. Based on k-NN algorithm, we apply a new 2D image classification system. We introduce a set of experimental tests in pattern recognition. The obtained results express the efficiency of our method. The performance of these feature vectors is compared with someones extracted from Hu, Legendre and Tchebichef invariant moments using three different 2D image databases: MPEG7-CE shape database, Columbia Object Image Library (COIL-20) database and ORL database. The results of the comparative study show the performance and superiority of our orthogonal invariant moments.

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Data Availability

The data used to support the findings of this study are available in [3, 13, 15].

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Acknowledgements

The essay’s authors express their deepest gratitude to the Editor-in-Chief and other reviewers and acknowledge their valuable comments and contributions.

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Authors and Affiliations

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

    Amal Hjouji & Rachid Chakid

  2. Transmission and Information Processing Laboratory, EST, Sidi Mohamed Ben Abdellah University, Fez, Morocco

    Jaouad El-Mekkaoui

  3. CED-ST, LESSI, Sidi Mohamed Ben Abdellah University, Fez, Morocco

    Hassan Qjidaa

Authors
  1. Amal Hjouji
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  2. Rachid Chakid
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  3. Jaouad El-Mekkaoui
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  4. Hassan Qjidaa
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Correspondence to Amal Hjouji.

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Hjouji, A., Chakid, R., El-Mekkaoui, J. et al. Adapted Jacobi Orthogonal Invariant Moments for Image Representation and Recognition. Circuits Syst Signal Process 40, 2855–2882 (2021). https://doi.org/10.1007/s00034-020-01600-w

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