Error Characteristics of SFM with Erroneous Focal Length

This paper presents a theoretical analysis of the behavior of “Structure from Motion” (SFM) algorithms with respect to the 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. We studied the behavior of the estimation of the focus of expansion (FOE) in the case that the camera is well calibrated except that the focal length is estimated with error. The results suggest that the behavior of the bas-relief ambiguity is affected by the erroneous focal length. The amount of influence depends on the relative direction of the translation and rotation parameters of the camera, the field of view and scene depth. Simulation with synthetic data was conducted to support our findings.