Vector extension of monogenic wavelets for geometric representation of color images

Raphaël Soulard (1) , Philippe Carré (1) , Christine Fernandez-Maloigne (2)

1 XLIM-SIC - SIC
2 XLIM - XLIM

Monogenic wavelets offer a geometric representation of grayscale images through an AM/FM model allowing invariance of coefficients to translations and rotations. The underlying concept of local phase includes a fine contour analysis into a coherent unified framework. Starting from a link with structure tensors, we propose a non-trivial extension of the monogenic framework to vector-valued signals to carry out a non marginal color monogenic wavelet transform. We also give a practical study of this new wavelet transform in the contexts of sparse representations and invariant analysis, which helps to understand the physical interpretation of coefficients and validates the interest of our theoretical construction.

Mots clés: wavelet transform; color; analytic signal; monogenic signal; monogenic wavelets

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Raphaël Soulard, Philippe Carré, Christine Fernandez-Maloigne. Vector extension of monogenic wavelets for geometric representation of color images. IEEE Transactions on Image Processing, 2013, 22 (3), pp.1070-1083. ⟨10.1109/TIP.2012.2226902⟩. ⟨hal-00794409⟩