Triangular Model Registration Algorithm Through Differential Topological Singularity Points by Helmholtz-Hodge Decomposition

Iterative closest point algorithms suffer from non-convergence and local minima when dealing with cloud points with a different sampling density. Alternative global or semi-global registration algorithms may suffer from efficiency problem. This paper proposes a new registration algorithm through the differential topological singularity points (DTSP) based on the Helmholtz-Hodge decomposition (HHD), which is called DTSP-ICP method. The DTSP-ICP method contains two algorithms. First, the curvature gradient fields on surfaces are decomposed by the HHD into three orthogonal parts: divergence-free vector field, curl-free vector field, and a harmonic vector field, and then the DTSP algorithm is used to extract the differential topological singularity points in the curl-free vector field. Second, the ICP algorithm is utilized to register the singularity points into one aligned model. The singularity points represent the feature of the whole model, and the DTSP algorithm is designed to capture the nature of the differential topological structure of a mesh model. Through the singularity alignment, the DTSP-ICP method, therefore, possesses better performance in triangular model registration. The experimental results show that independent of sampling schemes, the proposed DTSP-ICP method can maintain convergence and robustness in cases where other alignment algorithms including the ICP alone are unstable. Moreover, this DTSP-ICP method can avoid the local errors of model registration based on Euclidean distance and overcome the computation insufficiencies observed in other global or semi-global registration publications. Finally, we demonstrate the significance of the DTSP-ICP algorithm's advantages on a variety of challenging models through result comparison with that of two other typical methods.