RT Journal Article
T1 A Tighter Relaxation for the Relative Pose Problem Between Cameras
A1 García-Salguero, Mercedes
A1 Briales Garcia, Jesus
A1 González-Jiménez, Antonio Javier
K1 Matrices (Matemáticas)
AB This paper tackles the resolution of the Relative Pose problem with optimality guarantees by stating it as an optimization problem over the set of essential matrices that minimizes the squared epipolar error. We relax this non-convex problem with its Shor’s relaxation, a convex program that can be solved by off-the-shelf tools. We follow the empirical observation that redundant but independent constraints tighten the relaxation. For that, we leverage equivalent definitions of the set of essential matrices based on the translation vectors between the cameras. Overconstrained characterizations of the set of essential matrices are derived by the combination of these definitions. Through extensive experiments on synthetic and real data, our proposal is empirically proved to remain tight and to require only 7 milliseconds to be solved even for the overconstrained formulations, finding the optimal solution under a wide variety of configurations, including highly noisy data and outliers. The solver cannot certify the solution only in very extreme cases, e.g.noise 100 pix and number of pair-wise correspondences under 15. The proposal is thus faster than other overconstrained formulations while being faster than the minimal ones, making it suitable for real-world applications that require optimality certification.
PB Springer
YR 2022
FD 2022-04-06
LK https://hdl.handle.net/10630/24607
UL https://hdl.handle.net/10630/24607
LA eng
NO Garcia-Salguero, M., Briales, J. & Gonzalez-Jimenez, J. A Tighter Relaxation for the Relative Pose Problem Between Cameras. J Math Imaging Vis 64, 493–505 (2022). https://doi.org/10.1007/s10851-022-01085-z
NO Open Access funded by Universidad de Malaga / CBUA.
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 20 ene 2026