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The polynomial discrete Radon transform

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Abstract

This paper presents a new approach called polynomial discrete Radon transform (PDRT), regarded as a generalization of the classical finite discrete Radon transform. Specifically, the PDRT transforms an image into Radon space by summing the pixels according to polynomial curves. The PDRT can be applied on square \(p \times p\) images where \(p\) is assumed to be a prime number. It is based on a simple arithmetic operations and requires no data interpolation. An interesting property of the PDRT is its exact inversion. This means that an image can be transformed and then perfectly reconstructed. Through this study, we show that the new approach can be applied for some pattern recognition applications.

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Authors and Affiliations

  1. Laboratoire d’Informatique, Programmation Algorithmique et Heuristiques (LIPAH), Computer Technology Department, Faculté des Sciences de Tunis, Tunis, Tunisia

    Ines ELouedi & Atef Hamouda

  2. Laboratoire d’Images, Signaux et Systèmes Intelligents (LISSI), Université Paris Est-Creteil, Paris, France

    Régis Fournier & Amine Naït-Ali

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  1. Ines ELouedi
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  2. Régis Fournier
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  3. Amine Naït-Ali
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  4. Atef Hamouda
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Correspondence to Ines ELouedi.

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ELouedi, I., Fournier, R., Naït-Ali, A. et al. The polynomial discrete Radon transform. SIViP 9 (Suppl 1), 145–154 (2015). https://doi.org/10.1007/s11760-014-0727-3

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  • DOI: https://doi.org/10.1007/s11760-014-0727-3

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