The edge driven oriented wavelet transform : An anisotropic multidirectional representation with oriented lifting scheme In spite of its success, the standard 2D discrete wavelet transform (2DDWT) is not completely adapted to represent image entities like edges or oriented textures. Indeed the DWT is limited by the spatial isotropy of its basis functions that can not take advantage of edges regularity and moreover, direction edge that is neither vertical or horizontal is represented using many of these wavelet basis functions which does mean that DWT does not provide a sparse representation for such discontinuities. Several representations have been proposed to overcome this lack. Some of them deal with more orientations while introducing redundancy (e.g. ridgelets, curvelets, contourlets) and their implementations are not trivial or require 2D non separable filtering. We present two oriented liftingbased schemes using separable filtering, lead by edge extraction, and inspired from bandelets and curved wavelets. An image is decomposed into a quadtree according to the edge elements orientation. For each leaf, a wavelet transform is performed along the most regular orientation, and then along its orthogonal direction. Different adapted filters may be used for these two directions in order to achieve anisotropic filtering. Our method permits also a perfect reconstruction and a critical sampling.

Video coding with fully separable wavelet and wavelet packet transforms Threedimensional (t2D) wavelet coding schemes have been demonstrated to be efficient techniques for video compression applications. However, the separable wavelet transform used for removing the spatial redundancy allows a limited representation of the 2D texture because of spatial isotropy of the wavelet basis functions. In this case, anisotropic transforms, such as fully separable wavelet transforms (FSWT), can represent a solution for spatial decorrelation. FSWT inherits the separability, the computational simplicity and the filter bank characteristics of the standard 2D wavelet transform, but it improves the representation of directional textures, as the ones which can be found in temporal detail frames of t  2D decompositions. The extension of both classical wavelet and waveletpacket transforms to fully separable decompositions preserve at the same time the lowcomplexity and bestbases selection algorithms of these ones. We apply these transforms in t  2D video coding schemes and compare them with classical decompositions.