A genus oblivious approach to cross parameterization

In this paper we present a robust approach to construct a map between two triangulated meshes, M and M′ of arbitrary and possibly unequal genus. We introduce a novel initial alignment scheme that allows the user to identify “landmark tunnels” and/or a “constrained silhouette” in addition to the standard landmark vertices. To describe the evolution of non-landmark tunnels we automatically derive a continuous deformation from M to M′ using a variational implicit approach. Overall, we achieve a cross parameterization scheme that is provably robust in the sense that it can map M to M′ without constraints on their relative genus. We provide a number of examples to demonstrate the practical effectiveness of our scheme between meshes of different genus and shape.