Depth distortion under calibration uncertainty

There have been relatively little works to shed light on the effects of errors in the intrinsic parameters on motion estimation and scene reconstruction. Given that the estimation of the extrinsic and intrinsic parameters apts to be imprecise, it is important to study the resulting distortion on the recovered structure. By making use of the iso-distortion framework, we explicitly characterize the geometry of the distorted space recovered from 3D motion with freely varying focal length. This characterization allows us: (1) to investigate the effectiveness of the visibility constraint in disambiguating errors in calibration parameters by studying the negative distortion regions and (2) to make explicit those ambiguous error situations under which the visibility constraint is not effective. An important finding is that under these ambiguous situations, the direction of heading can be accurately recovered and the structure recovered experienced a well-behaved distortion. The distortion is given by a relief transformation which preserves ordinal depth relations. Thus in the case where the change in focal length is not well estimated, structure information in the form of depth relief can be obtained. Experiments were presented to support the use of the visibility constraint in obtaining such partial motion and structure solutions.