We present an approach to find dense point-to-point correspondences between two deformed surfaces corresponding to different postures of the same non-rigid object in a fully automatic way. The approach requires no prior knowledge about the shapes being registered or the initial alignment of the shapes. We consider surfaces that are represented by possibly incomplete triangular meshes. We model the deformations of an object as isometries. To solve the correspondence problem, our approach maps the intrinsic geometries of the surfaces into a low-dimensional Euclidean space via multi-dimensional scaling. This results in posture-invariant shapes that can be registered using rigid correspondence algorithms.