Genus Oblivious Cross Parameterization: Robust Topological Management of Inter-Surface Maps

摘要

In this paper we present the first robust approach to build a map between two meshes of arbitrary unequal genus. We also provide a simplified method for setting the initial alignment between M and M, reducing reliance on landmarks and allowing the user to select landmark tunnels in addition to the standard landmark vertices. After computing the map, we automatically derive a continuous deformation from M to M using a variational implicit approach to describe the evolution of non-landmark tunnels. Overall, we achieve a cross parameterization scheme that is provably robust in the sense that it can mapM toM without constraints on their relative genus or on the density of the triangulation with respect to the number of tunnels. To demonstrate the practical effectiveness of our scheme we provide a number of examples of inter-surface parameterizations between meshes of different genus and shape.