Non-iterative rigid 2D/3D point-set registration using semidefinite programming

TL;DR

This paper introduces a non-iterative, convex semidefinite programming framework for 2D/3D point-set registration with unknown correspondences, capable of joint pose and correspondence estimation, and robust to noise.

Contribution

It presents the first convex relaxations for joint 2D/3D registration with unknown correspondences, enabling efficient and exact solutions under noiseless conditions.

Findings

Exact recovery in noiseless scenarios

Robustness to noise demonstrated

Efficient convex optimization approach

Abstract

We describe a convex programming framework for pose estimation in 2D/3D point-set registration with unknown point correspondences. We give two mixed-integer nonlinear program (MINP) formulations of the 2D/3D registration problem when there are multiple 2D images, and propose convex relaxations for both of the MINPs to semidefinite programs (SDP) that can be solved efficiently by interior point methods. Our approach to the 2D/3D registration problem is non-iterative in nature as we jointly solve for pose and correspondence. Furthermore, these convex programs can readily incorporate feature descriptors of points to enhance registration results. We prove that the convex programs exactly recover the solution to the original nonconvex 2D/3D registration problem under noiseless condition. We apply these formulations to the registration of 3D models of coronary vessels to their 2D projections obtained from multiple intra-operative fluoroscopic images. For this application, we experimentally corroborate the exact recovery property in the absence of noise and further demonstrate robustness of the convex programs in the presence of noise.