Low‐rank path‐following algorithm for 3D similarity registration

Abstract

To address the 3D point matching problem where the pose difference between two point sets is unknown, the authors propose a path following (PF)–based algorithm. This method works by reducing the objective function of robust point matching (RPM) algorithm to a function of point correspondence variable and then using PF for optimisation. By using the 3D similarity transformation which has few parameters, authors’ method needs no regularisation on transformation and, therefore, can handle the case when the pose difference between two point sets is unknown. The authors also propose a novel convex term for use in the PF algorithm which is based on the low‐rank nature of authors’ objective function and leads to a PF algorithm which converges quickly. Experimental results demonstrated better robustness of the proposed method over state‐of‐the‐art methods and authors’ method is also efficient.