On the Tightness of Semidefinite Relaxations for Rotation Estimation
Preprint, 2021
A general framework based on tools from algebraic geometry is introduced for analyzing the power of semidefinite relaxations of problems with quadratic objective functions and rotational constraints. Applications include registration, hand-eye calibration, camera resectioning and rotation averaging. We characterize the extreme points, and show that there are plenty of failure cases for which the relaxation is not tight, even in the case of a single rotation. We also show that for some problem classes, an appropriate rotation parametrization guarantees tight relaxations. Our theoretical findings are accompanied with numerical simulations, providing further evidence and understanding of the results.
Sum-of-Squares
Duality
Algebraic Geometry
Almost Minimal Varieties
SDP Relaxations
Rotation Estimation
Författare
Lucas Brynte
Chalmers, Elektroteknik, Signalbehandling och medicinsk teknik, Digitala bildsystem och bildanalys
Viktor Larsson
Eidgenössische Technische Hochschule Zürich (ETH)
José Pedro Lopes Iglesias
Chalmers, Elektroteknik, Signalbehandling och medicinsk teknik, Digitala bildsystem och bildanalys
Carl Olsson
Chalmers, Elektroteknik, Signalbehandling och medicinsk teknik, Digitala bildsystem och bildanalys
Fredrik Kahl
Chalmers, Elektroteknik, Signalbehandling och medicinsk teknik, Digitala bildsystem och bildanalys
Styrkeområden
Informations- och kommunikationsteknik
Ämneskategorier
Beräkningsmatematik
Annan matematik
Robotteknik och automation