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

arXiv: https://arxiv.org/abs/1501.00630 · HTML: https://mlsanity.com/paper/1501.00630/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jan 2015.

## Built on by (most cited first, 4 of 4)

- [Advances in Global Solvers for 3D Vision](https://mlsanity.com/paper/2602.14662/) (2026)
- [Towards Understanding The Semidefinite Relaxations of Truncated Least-Squares in Robust Rotation Search](https://mlsanity.com/paper/2207.08350/) (2022)
- [Generalized Orthogonal Procrustes Problem under Arbitrary Adversaries](https://mlsanity.com/paper/2106.15493/) (2021)
- [SANDRO: a Robust Solver with a Splitting Strategy for Point Cloud Registration](https://mlsanity.com/paper/2503.07743/) (2025)

## Abstract (arXiv)

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.