In spite of its success, the standard 2-D discrete wavelet transform (2D-DWT) 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 2-D non separable filtering. We present two oriented lifting-based 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.