A Practical Rank-Constrained Eight-Point Algorithm for Fundamental Matrix Estimation

Due to its simplicity, the eight-point algorithm has been widely used in fundamental matrix estimation. Unfortunately, the rank-2 constraint of a fundamental matrix is enforced via a posterior rank correction step, thus leading to non-optimal solutions to the original problem. To address this drawback, existing algorithms need to solve either a very high order polynomial or a sequence of convex relaxation problems, both of which are computationally ineffective and numerically unstable. In this work, we present a new rank-2 constrained eight-point algorithm, which directly incorporates the rank-2 constraint in the minimization process. To avoid singularities, we propose to solve seven sub problems and retrieve their globally optimal solutions by using tailored polynomial system solvers. Our proposed method is noniterative, computationally efficient and numerically stable. Experiment results have verified its superiority over existing algebraic error based algorithms in terms of accuracy, as well as its advantages when used to initialize geometric error based algorithms.