R-PointHop

R-PointHop: Hierarchical 3D Point Cloud Registration via Local Reference Frames

R-PointHop performs 3D point cloud registration by constructing rotation- and translation-invariant features using a local reference frame (LRF) defined by nearest neighbors and establishing point correspondences in a hierarchical feature space to estimate rigid transformations.

Key Features:

• Local Reference Frame Construction: Computes an LRF for each point from nearest neighbors to encode local geometric structure with rotation and translation invariance.
• Hierarchical Feature Extraction: Applies point downsampling, neighborhood expansion with geometric attribute construction, and dimensionality reduction to generate compact multi-scale descriptors.
• Point Correspondence Building: Establishes inter-cloud correspondences using nearest neighbor search in the hierarchical feature space.
• Salient Point Selection and Transformation Estimation: Selects high-quality correspondences to estimate the 3D rigid transformation aligning point clouds.

Scientific Applications:

• 3D Data Registration: Aligns point clouds in computer vision, robotics, and medical imaging, including scenarios with large rotational differences.

Methodology:

R-PointHop computes local reference frames from nearest neighbors, performs hierarchical feature extraction through iterative downsampling, neighborhood expansion, geometric attribute construction, and dimensionality reduction, constructs correspondences via nearest neighbor matching in feature space, and estimates rigid 3D transformations from selected salient point pairs.