results show that our algorithm significantly outperforms previous algorithms when the number of correspondences is small. Besides, when the global minimizer is the solution, our algorithm achieves the same accuracy as previous algorithms that have guaranteed global optimality, but our algorithm is applicable to real-time applications.'
author:
- |
    Lipu Zhou$^1$, Shengze Wang$^1$, Jiamin Ye$^2$, Michael Kaess$^1$\
    $^1$Carnegie Mellon University, $^2$Chinese Academy of Sciences\
    [$^1$zhoulipu@outlook.com, $^1${shengzew,kaess}@andrew.cmu.edu, $^2$yejiamin@iet.cn]{}
bibliography:
- 'plp\_registration\_arxiv.bib'
title: 'Do not Omit Local Minimizer: a Complete Solution for Pose Estimation from 3D Correspondences '
---

Introduction
============

Estimating the pose from 3D correspondences, point-to-point, point-to-line and point-to-plane correspondences, is known as the 3D registration problem in the literature [@olsson2006registration; @olsson2008solving; @olsson2009branch; @wientapper2016unifying; @briales2017convex; @wientapper2018universal]. It is one of the fundamental problems in computer vision with a wide range of applications, such as simultaneous localization and mapping (SLAM) [@zhang2015visual; @zhang2014loam; @newcombe2011kinectfusion; @proencca2018probabilistic; @taguchi2013point], extrinsic calibration [@zhang2004extrinsic; @unnikrishnan2005fast; @naroditsky2011automatic; @gomez2015extrinsic; @zhou2018automatic] and iterative closes point (ICP) framework [@besl1992method]. Besides, some camera pose estimation problems, such as the perspective-n-point (PnP) problem [@hesch2011direct; @kneip2014upnp] and the perspective-n-line (PnL) problem [@xu2017pose; @pvribyl2017absolute], can be transformed to a 3D registration problem [@wientapper2018universal]. However, the research on this problem is not as thorough as other 