The polynomial Discrete Radon Transform

I. Elouedi , Richard A Fournier (1) , A. A. Nait-Ali (1) , A. Hamouda (2)

1 SYNAPSE
2 URPAH - Unité de Recherche en Programmation Algorithmique et Heuristique

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×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.

Mots clés: Polynomial curves; Discrete Radon transform; Exact inversion; Pattern recognition

Domaines: Robotique [cs.RO]; Automatique / Robotique; Imagerie médicale; Traitement du signal et de l'image [eess.SP]; Réseaux et télécommunications [cs.NI]; Vision par ordinateur et reconnaissance de formes [cs.CV]

I. Elouedi, Richard A Fournier, A. A. Nait-Ali, A. Hamouda. The polynomial Discrete Radon Transform. Signal, Image and Video Processing, 2015, 9 (1), pp.145-154. ⟨hal-01569670⟩