Deformation transfer of 3D human shapes and poses on manifolds

In this paper, we introduce a novel method to transfer the deformation of a human body to another directly on a manifold. There exists a rich literature on transferring deformations based on Euclidean representations. However, a 3D human shape and pose live on a manifold and have a Riemannian structure. The proposed method uses the Lie Bodies manifold representation of 3D triangulated bodies. Its benefits are preserved, namely, minimum required degrees of freedom for any triangle deformation and no heuristics to constrain excessive ones. We give a closed form solution for deformation transfer directly on the Lie Bodies. The deformations have strictly positive determinants ensuring that non-physical deformations are removed. We show examples on three datasets, and highlight differences with the Euclidean deformation transfer.