This paper presents a novel algorithm for medial surfaces extraction that is based on the density-corrected Hamiltonian analysis of Torsello and Hancock [1]. In order to cope with the exponential growth of the number of voxels, we compute a first coarse discretization of the mesh which is iteratively refined until a desired resolution is achieved. The refinement criterion relies on the analysis of the momentum field, where only the voxels with a suitable value of the divergence are exploded to a lower level of the hierarchy. In order to compensate for the discretization errors incurred at the coarser levels, a dilation procedure is added at the end of each iteration. Finally we design a simple alignment procedure to correct the displacement of the extracted skeleton with respect to the true underlying medial surface. We evaluate the proposed approach with an extensive series of qualitative and quantitative experiments. 
Coarse-to-fine skeleton extraction for high resolution 3D meshes