A clever elimination strategy for efficient minimal solvers
This work addresses the need for more efficient minimal solvers in computer vision, particularly for partially calibrated cameras, though it appears incremental as it builds on existing solver generation methods.
The paper tackles the problem of generating minimal solvers in computer vision by introducing an elimination strategy that first removes unknowns not in linear equations, leading to smaller and faster solvers. It demonstrates efficiency gains in three relative camera pose problems with unknown parameters, producing new constraints on fundamental matrices.
We present a new insight into the systematic generation of minimal solvers in computer vision, which leads to smaller and faster solvers. Many minimal problem formulations are coupled sets of linear and polynomial equations where image measurements enter the linear equations only. We show that it is useful to solve such systems by first eliminating all the unknowns that do not appear in the linear equations and then extending solutions to the rest of unknowns. This can be generalized to fully non-linear systems by linearization via lifting. We demonstrate that this approach leads to more efficient solvers in three problems of partially calibrated relative camera pose computation with unknown focal length and/or radial distortion. Our approach also generates new interesting constraints on the fundamental matrices of partially calibrated cameras, which were not known before.