Progressive curvature encoding for 3d representation learning

Abstract

Understanding unordered 3D point sets is crucial for identifying and differentiating complex geometric patterns, and curvature features play a pivotal role in this process. Despite their significance, many point cloud encoders predominantly rely on Euclidean coordinate features for shape information extraction. While some prior works have proposed incorporating curvature information into point features, they often lack a comprehensive consideration of coarse-grained curvature from a broader perspective, focusing solely on local curvature based on nearest points. This limitation becomes more evident in real-world point clouds with high irregularities and local noise. Moreover, existing methods often overlook curvature along different directions, despite the fact that the contour of 3D objects can vary based on their orientation. To address these challenges, this thesis introduces an effective curvature encoding strategy named Progressive Curvature Scanning (PCS). This approach models direction-dependent curvature features at multiple levels of granularity, estimating local curvature within the frame of a sphere by analyzing differences in normal vectors belonging to specific spherical sections. Additionally, global contour features are encoded with the assistance of multi-view 2D depth maps obtained through the projection of point clouds.