Global Optimality for Point Set Registration Using Semidefinite Programming
Paper in proceedings, 2020

In this paper we present a study of global optimality conditions for Point Set Registration (PSR) with missing data. PSR is the problem of aligning multiple point clouds with an unknown target point cloud. Since non-linear rotation constraints are present the problem is inherently non-convex and typically relaxed by computing the Lagrange dual, which is a Semidefinite Program (SDP). In this work we show that given a local minimizer the dual variables of the SDP can be computed in closed form. This opens up the possibility of verifying the optimally, using the SDP formulation without explicitly solving it. In addition it allows us to study under what conditions the relaxation is tight, through spectral analysis. We show that if the errors in the (unknown) optimal solution are bounded the SDP formulation will be able to recover it.

Author

José Pedro Lopes Iglesias

Chalmers, Electrical Engineering, Signal Processing and Biomedical Engineering, Imaging and Image Analysis

Carl Olsson

Chalmers, Electrical Engineering, Signal Processing and Biomedical Engineering, Imaging and Image Analysis

Fredrik Kahl

Chalmers, Electrical Engineering, Signal Processing and Biomedical Engineering, Imaging and Image Analysis

Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition

10636919 (ISSN)

Vol. 2020 8284-8292 9157383

2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2020
Virtual; online, USA,

Optimization Methods with Performance Guarantees for Subspace Learning

Swedish Research Council (VR), 2019-01-01 -- 2022-12-31.

Subject Categories

Computer Engineering

Computer Science

Computer Vision and Robotics (Autonomous Systems)

DOI

10.1109/CVPR42600.2020.00831

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1/7/2021 9