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We present gP4Pc, a new method for computing the absolute pose of ageneralized camera with unknown internal scale from four corresponding 3Dpoint-and-ray pairs. Unlike most pose-and-scale methods, gP4Pc is based onconstraints arising from the congruence of shapes defined by two sets of fourpoints related by an unknown similarity transformation. By choosing a novelparametrization for the problem, we derive a system of four quadratic equationsin four scalar variables. The variables represent the distances of 3D pointsalong the rays from the camera centers. After solving this system via Groebnerbasis-based automatic polynomial solvers, we compute the similaritytransformation using an efficient 3D point-point alignment method. We alsopropose a specialized variant of our solver for the case of coplanar points,which is computationally very efficient and about 3x faster than the fastestexisting solver. Our experiments on real and synthetic datasets, demonstratethat gP4Pc is among the fastest methods in terms of total running time whenused within a RANSAC framework, while achieving competitive numericalstability, accuracy, and robustness to noise.

Generalized Pose-and-Scale Estimation using 4-Point Congruence Constraints