GraphCPD: Coherent Point Drift for Point Cloud Registration via Graph Signal Processing

Probabilistic point cloud registration has attracted increasing attention due to its robustness to noise, outliers and occlusions. However, existing methods often suffer from high computational cost and neglect the role of informative priors. In this paper, we propose a new probabilistic registration method based on graph signal processing (GSP), called graph coherent point drift (GraphCPD). Specifically, we design a high-pass graph filter to extract high-frequency components, which are theoretically proven to be invariant under rigid transformations. These components are combined with point coordinates and normals to form a high-dimensional graph signal. We construct a local graph based on the graph signal and use the graph Laplacian model for registration. Compared with the classical Gaussian mixture models (GMMs), graph Laplacian models provide more discriminative geometric representations and enhance the model’s ability to capture graph structure. Furthermore, we exploit the invariance of high-frequency components to define prior probabilities, significantly reducing the corresponding search space and improving the speed of registration. Experimental results demonstrate that our method improves runtime efficiency over most existing probabilistic methods, while maintaining competitive registration accuracy, especially on large-scale point clouds. The source code is available at https://github.com/YCLai1997/GraphCPD.