Efficient Registration for Human Surfaces via Isometric Regularization on Embedded Deformation

3D registration is a fundamental step to obtain the correspondences between surfaces. Traditional mesh alignment methods tackle this problem through non-rigid deformation, mostly accomplished by applying ICP-based (Iterative Closest Point) optimization. The embedded deformation method is proposed for the purpose of acceleration, which enables various real-time applications. However, it regularizes on an underlying simplified structure, which could be problematic for intricate cases when the simplified graph doesn't fully represent the surface attributes. Moreover, without elaborate parameter-tuning, deformation usually performs suboptimally, leading to slow convergence or a local minimum if all regions on the surface are assumed to share the same rigidity during the optimization. In this article, we propose a novel solution that decouples regularization from the underlying deformation model by explicitly managing the rigidity of vertex clusters. We further design an efficient two-step solution that alternates between isometric deformation and embedded deformation with cluster-based regularization. Our method can easily support region-adaptive regularization with cluster refinement and execute efficiently. Extensive experiments demonstrate the effectiveness of our approach for mesh alignment tasks even under large-scale deformation and imperfect data. Our method outperforms state-of-the-art methods both numerically and visually.