Generalized Radial Alignment Constraint for Camera Calibration

In camera calibration, the radial alignment constraint (RAC) has been proposed as a technique to obtain closed form solution to calibration parameters when the image distortion is purely radial about an axis normal to the sensor plane. But, in real images this normality assumption might be violated due to manufacturing limitations or intentional sensor tilt. A misaligned optic axis results in traditional formulation of RAC not holding for real images leading to calibration errors. In this paper, we propose a generalized radial alignment constraint (gRAC), which relaxes the optic axis-sensor normality constraint by explicitly modeling their configuration via rotation parameters which form a part of camera calibration parameter set. We propose a new analytical solution to solve the gRAC for a subset of calibration parameters. We discuss the resulting ambiguities in the analytical approach and propose methods to overcome them. The analytical solution is then used to compute the intersection of optic axis and the sensor about which overall distortion is indeed radial. Finally, the analytical estimates from gRAC are used to initialize the nonlinear refinement of calibration parameters. Using simulated and real data, we show the correctness of the proposed gRAC and the analytical solution in achieving accurate camera calibration.