Point Cloud Registration Using Virtual Interest Points from Macaulay’s Resultant of Quadric Surfaces

A novel formulation called Virtual Interest Point is presented and used to register point clouds. An implicit quadric surface representation is first used to model the point cloud segments. Macaulay’s resultant then provides the intersection of three such quadrics, which forms a virtual interest point (VIP). A unique feature descriptor for each VIP is computed, and correspondences in descriptor space are established to compute the rigid transformation to register two point clouds. Each step in the process is designed to consider robustness to noise and data density variations, as well as computational efficiency. Experiments were performed on 12 data sets, collected with a variety of range sensors, to characterize robustness to noise, data density variation, and computational efficiency. The data sets were extracted from both natural scenes, including plants and rocks, and indoor architectural scenes, such as cluttered offices and laboratories. Similarly, several 3D models were tested for registration to demonstrate the generality of the technique. The proposed method significantly outperformed a variety of alternative state-of-the-art approaches, such as 2.5D SIFT-based RANSAC method, Super 4-Point Congruent Sets and Super Generalized 4PCS, and the Go-ICP method in registering overlapping point clouds with both a higher success rate and reduced computational cost.