A straightforward method to establish correspondence between two surfaces is to correspond points distributed on the surfaces directory. In mesh-to-mesh strategy, each of the boundaries is first represented using a mesh (or a set of points), and then the meshes are registered together for the correspondence generation. For example, a standard rigid matching algorithm such as the iterative closest point (ICP) algorithm  or the softassign Procrustes  would be applicable. Given two surfaces, one of the surfaces is transformed to match the other. Once the two surfaces are matched, it is easy to generate a set of pairs of corresponding points. Both methods accept different numbers of initial points distributed on the surfaces, and the optimal similarity transformation from one surface to the other surface is defined. Nonrigid registration of shapes can also be utilized (see, e.g., [10, 11]).
In this strategy, one surface of an organ in one training image is represented by a mesh, and it is registered not to a surface in other training image but to a labeled organ region in other training image [12-15], where the voxel values are equal to one (1) in the target regions and are equal to zero outside of the regions. The key issue in this strategy is robustness of the deformable template algorithm. Techniques to ensure this robustness include the multi-resolution approach , gradient vector flow , and regularization of internal energies [12, 14, 15]. Dam et al. proposed a bootstrap approach to segment learning data and to iteratively refine correspondences . For all these approaches to mesh-to-volume registration, homeomorphic mapping between the input shapes is guaranteed unless the template does not fold itself in the adaptation process.