Survey on differential estimators for 3d point clouds

Abstract Recent advancements in 3D scanning technologies, including LiDAR and photogrammetry, have enabled the precise digital replication of real‐world objects. These methods are widely used in fields such as GIS, robotics, and cultural heritage. However, the point clouds generated by such scans are often noisy and unstructured, posing challenges for traditional geometry processing tasks. Accurately estimating differential properties like surface curvatures and normals is crucial for tasks such as shape matching and classification, but remains complex due to these inherent challenges. This paper reviews state‐of‐the‐art methods for estimating differential properties from 3D point clouds, with a focus on approaches that offer strong mathematical foundations and theoretical guarantees. We also benchmark these methods using various datasets, evaluating their performance in terms of accuracy, robustness, and efficiency. Our contributions include the release of datasets, tools, and code to promote reproducibility and support future research in this area.