Rotation Averaging with the Chordal Distance: Global Minimizers and Strong Duality
Journal article, 2021

In this paper we explore the role of duality principles within the problem of rotation averaging, a fundamental task in a wide range of applications. In its conventional form, rotation averaging is stated as a minimization over multiple rotation constraints. As these constraints are non-convex, this problem is generally considered challenging to solve globally. We show how to circumvent this difficulty through the use of Lagrangian duality. While such an approach is well-known it is normally not guaranteed to provide a tight relaxation. Based on spectral graph theory, we analytically prove that in many cases there is no duality gap unless the noise levels are severe. This allows us to obtain certifiably global solutions to a class of important non-convex problems in polynomial time. We also propose an efficient, scalable algorithm that outperforms general purpose numerical solvers by a large margin and compares favourably to current state-of-the-art. Further, our approach is able to handle the large problem instances commonly occurring in structure from motion settings and it is trivially parallelizable. Experiments are presented for a number of different instances of both synthetic and real-world data.

structure from motion

rotation averaging

chordal distance

graph laplacian

lagrangian duality

Author

Anders Eriksson

University of Queensland

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

Tat-Jun Chin

University of Adelaide

IEEE Transactions on Pattern Analysis and Machine Intelligence

0162-8828 (ISSN)

Vol. 43 1 256-268 8770111

Optimization Methods with Performance Guarantees for Subspace Learning

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

Subject Categories

Computational Mathematics

Signal Processing

Discrete Mathematics

DOI

10.1109/TPAMI.2019.2930051

PubMed

31352332

More information

Latest update

3/12/2021