Behaviour of SFM algorithms with erroneous calibration

This paper presents an algorithm-independent geometrical analysis of the behavior of differential Structure from Motion (SFM) algorithms when there are errors in intrinsic parameters of the camera. We demonstrate both analytically and in simulation how uncertainty in the calibration parameters gets propagated to motion estimates in a differential setting. In particular, we studied how erroneous focal length and principal point estimates affect the behavior of the bas-relief ambiguity and introduce additional biasing to the translation estimate in a non-simple manner not revealed by previous analyses. Our formulation allows us to characterize the influence of various factors such as different scene-motion configurations and field of views in an analytically tractable manner. Guidelines are given as to whether one should err on the low or the high side in the estimation of the focal length depending on various operating conditions such as the feature density and the noise level. Simulations with synthetic data and real images were conducted to support our findings.