Registering partial point clouds is crucial in numerous applications in the field of robotics, vision, and graphics. For arbitrary configurations, the registration problem requires an initial global alignment, which is computationally expensive and often still requires refinement. In this paper, we propose a pair-wise global registration method that combines the fast convergence made possible by global hierarchical surface descriptors with the arbitrarily fine sampling enabled by continuous surface representations. Registration is performed by matching descriptors of increasing resolution – which the continuous surfaces allow us to choose arbitrarily high – while restricting the search space according to the hierarchy. We evaluated our method on a large set of pair-wise registration problems, demonstrating very competitive registration accuracy that often makes subsequent refinement with a local method unnecessary.