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. INDEX TERMSIterative closest point algorithm, computer aided manufacturing, differential equations, HHD.

No abstract

No abstract

No abstract

In recent years, we have seen more and more interest in the field of medical images and shape comparison motivated by the latest advances in microcomputed tomography (μCT) acquisition, modelling, and visualization technologies. Usually, biologists need to evaluate the effect of different root canal preparation systems. Current root canal preparation evaluation methods are based on the volume difference, area difference, and transportation of two root canals before and after treatment. The purpose of root canal preparation is to minimize the volume difference and ensure the complete removal of the smear layer. Previous methods can reflect some general geometric differences, but they are not enough to evaluate the quality of root canal shape. To solve this problem, we proposed a novel root canal evaluation method based on spectrum and eigenfunctions of Steklov operators, which can be served as a better alternative to current methods in root canal preparation evaluation. Firstly, the ideal root canal model was simulated according to the root canal model before and after preparation. Secondly, the Steklov spectrum of the two models was calculated. Thirdly, based on the spectrum and the histogram of the Gaussian curvature on the surface, the weight of each eigenvalue was computed. Therefore, the Steklov spectrum distance (SSD), which measures shape difference between the root canals, was defined. Finally, the calculation method that quantifies the root canal preparation effect of root canals was obtained. Through experiments, our method manifested high robustness and accuracy compared with existing state-of-the-art approaches. It also demonstrates the significance of our algorithm's advantages on a variety of challenging root canals through result comparison with counterpart methods.