Fast point cloud simplification method based on optimized feature sampling and geometric continuity preservation

Abstract With the development of three-dimensional laser scanning technology, high-density point cloud data provides a reliable database, and there is also a large amount of redundant information, which increases the storage and calculation burden of data processing. A point cloud simplification method that maintains the integrity of the geometric structure while compressing data is urgently needed. In this paper, we propose a density-aware sampling strategy following the construction of a grid structure, and the number of local sampling points is dynamically adjusted according to local density variations to enhance the global consistency of the simplified point cloud. During the feature point sampling stage, the sampling starting point is optimized based on the farthest point sampling (FPS) algorithm, and curvature weights are incorporated into the iterative selection strategy. This approach allows more points along the sampling path to be chosen to represent geometric features, thereby ensuring that the simplified point cloud more accurately preserves the features of the original model. However, feature-based sampling tends to sparsely select points in flat regions of the point cloud surface. In this study, surface fitting is performed using the moving least squares method, and auxiliary feature points are subsequently selected via uniform sampling. This combination effectively improves the geometric uniformity of the simplified results. By integrating both sampling strategies, a balance is achieved that maintains high geometric fidelity while ensuring uniformity, thereby supporting subsequent point cloud processing tasks with higher accuracy. The experimental results show that compared with existing methods such as AIVS, GF-Sim, FPS, and curvature-based, the proposed method has better fidelity and robustness in terms of running time, information entropy, geometric error spacing and error, and reconstruction quality on multiple public point cloud data sets.