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A Fast Computation of Novel Set of Meixner Invariant Moments for Image Analysis

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Abstract

Recently, the discrete orthogonal moments have been introduced in image analysis and pattern recognition. They have better capacities than the continuous orthogonal moments but the use of these moments as feature descriptors is limited by their high computational cost. As a solution to this problem, we present in this paper an approach for fast computation of Meixner’s discrete orthogonal moments. By using the recurrence relation with respect to variable x instead of order n in computation of Meixner’s discrete orthogonal polynomials and the image block representation for binary images and intensity slice representation for gray-scale images. The acceleration of the computation time of Meixner moments is due to an innovative image representation where the image is described by a number of homogenous rectangular blocks instead of individual pixels. A novel set of invariant moments based on the Meixner discrete orthogonal moments is also proposed. These invariant moments are derived algebraically from the geometric invariant momenst and their computation is accelerated using image representation scheme. The presented algorithms are tested in several well-known computer vision datasets, regarding computational time, image reconstruction, invariability, and classification. The performances of Meixner invariant moments used as pattern features for a pattern classification application are compared with Hu, Tchebichef, dual-Hahn, and Krawtchouk invariant moments.

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Authors and Affiliations

  1. CED-ST, LESSI, Faculty of Sciences Dhar el mehraz, University Sidi Mohamed, Ben Abdellah, B.P., 1796, Fez-Atlas, Morocco

    Mhamed Sayyouri, Abdeslam Hmimid & Hassan Qjidaa

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  1. Mhamed Sayyouri
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  2. Abdeslam Hmimid
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  3. Hassan Qjidaa
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Correspondence to Abdeslam Hmimid.

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Sayyouri, M., Hmimid, A. & Qjidaa, H. A Fast Computation of Novel Set of Meixner Invariant Moments for Image Analysis. Circuits Syst Signal Process 34, 875–900 (2015). https://doi.org/10.1007/s00034-014-9881-7

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  • DOI: https://doi.org/10.1007/s00034-014-9881-7

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