Characterizing Depth Distortion under Different Generic Motions

Abstract

Given that errors in the estimates for the intrinsic and extrinsic camera parameters are inevitable, it is important to understand the behaviour of the resultant distortion in depth recovered under different motion-scene configurations. The main interest in this study is to look for generic motion type that can render depth recovery more robust and reliable. To this end, lateral and forward motions are compared both under calibrated and uncalibrated scenarios. For lateral motion, we found that although Euclidean reconstruction is difficult, ordinal depth information is obtainable; while for forward motion, depth information (even partial one) is difficult to recover. In the uncalibrated case, with fixed intrinsic parameters, the preceding statements still hold. However, if intrinsic parameter variations are allowed, then for lateral motion, depth relief can only be preserved locally. In general, lateral motion yields a distortion relationship that belongs to the projective transformation of a very simple type, while the distortion transformations for general motions including forward motion belong to the Cremona transformation. As an aside, we also provide an analysis of the distortion in the depth recovered using the least square procedure as compared to the epipolar reconstruction approach.