Use the discrete geometry to discretize the ridgelet transform

David Helbert (1) , Philippe Carré (1)

1 SIC - SIGNAL-IMAGE-COMMUNICATION

The Ridgelet transform allows to represent effectively rectilinear discontinuities in an image, essential information for image analysis. In this paper, we present our nD implementation, the Discrete Analytical Ridgelet Transform (DART). The innovative step is the definition of a discrete transform with the discrete analytical geometry theory by the construction of discrete analytical lines in the Fourier domain. The DART uses the Fourier strategy for the computation of the associated discrete Radon transform [2, 3]. It has a very simple forward/inverse algorithm that provides an exact reconstruction without any iterative method. In order to illustrate the potentiality of this discrete transform, we compare 3D DART denoising of colour video with reference methods.

Domaines: Traitement des images [eess.IV]

David Helbert, Philippe Carré. Use the discrete geometry to discretize the ridgelet transform. WavE: Wavelets and Applications 2006, Jul 2006, EPFL, Lausanne, Switzerland. http://wavelet.epfl.ch/. ⟨hal-00331498⟩