SGPCR: Spherical Gaussian Point Cloud Representation and its Application to Object Registration and Retrieval

Retrieving and aligning CAD models from databases with scanned real-world point clouds remains an important topic for 3D reconstruction. Due to zero point-to-point correspondences between the sampled CAD model and the scanned real-world object, an information-rich representation of point clouds is needed. We propose SGPCR, a novel method for representing 3D point clouds by Spherical Gaussians for efficient, stable, and rotation-equivariant representation. We also propose a rotation-invariant convolution to improve the representation quality through a trainable optimization process. In addition, we demonstrate the strengths of SGPCR-based point cloud representation using the fundamental challenge of shape retrieval and point cloud registration on point clouds with zero point-to-point correspondences. Under these conditions, our approach improves registration quality by reducing chamfer distance by up to 90% and rotation root mean square error by up to 86% compared to the state of the art. Furthermore, the proposed SGCPR is used for one-shot shape retrieval and registration and improves retrieval precision by up to 58% over comparable methods.