A Generic Deformation Model for Dense Non-rigid Surface Registration: A Higher-Order MRF-Based Approach
We propose a novel approach for dense non-rigid 3D surface registration, which brings together Riemannian geometry and graphical models. To this end, we first introduce a generic deformation model, called Canonical Distortion Coefficients (CDCs), by characterizing the deformation of every point on a surface using the distortions along its two principle directions. This model subsumes the deformation groups commonly used in surface registration such as isometry and conformality, and is able to handle more complex deformations. We also derive its discrete counterpart which can be computed very efficiently in a closed form. Based on these, we introduce a higher-order Markov Random Field (MRF) model which seamlessly integrates our deformation model and a geometry/texture similarity metric. Then we jointly establish the optimal correspondences for all the points via maximum a posteriori (MAP) inference. Moreover, we develop a parallel optimization algorithm to efficiently perform the inference for the proposed higher-order MRF model. The resulting registration algorithm outperforms state-of-the-art methods in both dense non-rigid 3D surface registration and tracking.