Journal
JOURNAL OF MATHEMATICAL IMAGING AND VISION
Volume 64, Issue 1, Pages 57-67Publisher
SPRINGER
DOI: 10.1007/s10851-021-01054-y
Keywords
SDP relaxations; Duality; Algebraic geometry; Almost minimal varieties; Sum-of-squares; Rotation estimation
Categories
Funding
- Chalmers University of Technology
- Wallenberg AI, Autonomous Systems and Software Program (WASP) - Knut and Alice Wallenberg Foundation
- Swedish Foundation for Strategic Research (Semantic Mapping and Visual Navigation for Smart Robots)
- Swedish Research Council [2018-05375]
- Swedish Research Council [2018-05375] Funding Source: Swedish Research Council
Ask authors/readers for more resources
Semidefinite relaxations have been highly successful in solving non-convex optimization problems involving rotations in computer vision and robotics. By studying empirical performance and introducing a general framework based on tools from algebraic geometry, further theoretical understanding of the power of semidefinite relaxations has been gained.
Why is it that semidefinite relaxations have been so successful in numerous applications in computer vision and robotics for solving non-convex optimization problems involving rotations? In studying the empirical performance, we note that there are few failure cases reported in the literature, in particular for estimation problems with a single rotation, motivating us to gain further theoretical understanding. 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, and rotation averaging. We characterize the extreme points and show that there exist failure cases for which the relaxation is not tight, even in the case of a single rotation. We also show that some problem classes are always tight given an appropriate parametrization. Our theoretical findings are accompanied with numerical simulations, providing further evidence and understanding of the results.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available