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

Abstract

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.

Point cloud registration method for indoor depth sensor acquisition system based on dual graph computation with irregular shape factors

“…Kamencay et al [15] proposed a method that reduces the amount of iterative computation by combining the 3D invariant feature transform (SIFT) with K-nearest neighbour (KNN) algorithm and estimated transformation with the fast point feature histograms (FPFH) descriptor. Wu et al [16] decomposed the point cloud surfaces into three orthogonal parts and designed the differential topological singularity points algorithm to extract key points from the curl-free vector component. Wu et al [37] designed a registration method combined with FPFH and ICP.…”

“…The DIRGMR performs supervised learning with correspondence labels recorded in the dataset to constrain the training direction, which is focused on the feature descriptor similarity calculation stage. Referred to DeepGMR [14], the cross entropy can measure the proximity between the computed correspondence C and labeled correspondence C g , which is used as a loss function and presented in Equation (16).…”

“…Wu et al. [16] decomposed the point cloud surfaces into three orthogonal parts and designed the differential topological singularity points algorithm to extract key points from the curl‐free vector component. Wu et al.…”

“…Although PDA is robust to noise and outliers, it is unsuitable for complex data scenes, as the same with ICP, due to large computation consumption. Many feature-based methods divide the registration process into two stages: to search key points and local feature descriptors instead of considering all points; the ICP was applied to these representative points [15][16][17]. The registration accuracy depends on the identification of points, which often fails in the data with obscure features.…”

A Coarse-to-Fine Registration Approach for Point Cloud Data with Bipartite Graph Structure

“…Lu et al [35] proposed a point cloud registration algorithm combined with improved K4PCS and ICP to improve the speed and accuracy. Wu et al [36] presented a triangular model registration algorithm based on differential topological singularity points (DTSP)-ICP. This algorithm is able to obtain the mesh model nature of differential topological structure and avoid local errors based on Euclidean distance.…”