On the Tightness of Semidefinite Relaxations for Rotation Estimation

Abstract Why is it that semidefinite relaxations have been so successful in numerous applications computer vision and robotics for solving non-convex optimization problems involving rotations? In studying the empirical performance, we note there are few failure cases reported literature, particular estimation with a single rotation, motivating us to gain further theoretical understanding. A general framework based on tools from algebraic geometry introduced analyzing power of quadratic objective functions rotational constraints. Applications include registration, hand–eye calibration, rotation averaging. We characterize extreme points show exist which relaxation not tight, even case rotation. also some problem classes always tight given an appropriate parametrization. Our findings accompanied numerical simulations, providing evidence understanding results.