We present a Multi-Resolution Dual method based on an incremental octree-based refinement strategy. Our solution is able to generate multi-resolution surfaces from segmented volumetric data. It extends the Dual Marching Cubes algorithm over a generalized octree and guarantees that the produced surfaces are always manifold by introducing a new cell-based criterion for dual vertices generation. Moreover, we propose a top-bottom refinement algorithm that is able to locally adapt the mesh resolution according to a curvature parameter. Our algorithm is suitable to process volumetric data sets and we show on different volumes that the produced surfaces are manifold and approximate well the original object.