Depth Factor and Sensitivity Coefficient in Active Stereo‐Camera Imaging

Abstract

A non‐linear epipole‐featured model was developed and evaluated for structure computation in active convergent stereovision. In this paper, using the developed analytic model, the terms virtual depth and depth factor are introduced, which together define the depth of a world point relative to the coordinate frame of the reference camera. Furthermore, an equivalence relation between coplanar–parallel and convergent stereo‐camera imaging systems was established, in which baseline‐to‐depth‐factor ratio is introduced and termed as convergent stereo disparity. This convergent stereo disparity can be equated with the image rectification process in a practical conventional coplanar–parallel stereo‐camera setup. Subsequently, generalised mathematical analyses were done to model and study the variation of the depth sensitivity coefficient and relative depth uncertainty with respect to convergent stereovision system parameters using the developed model. It was observed that different values of the left and right focal lengths are required to achieve a high sensitivity coefficient, a condition that is not conformable with the conventional practice of having the same left and right focal lengths in stereo‐camera imaging. Regarding the variation of the stereo projection and stereo convergence angles, there are trade‐offs between the sensitivity coefficient and relative depth uncertainty. Finally, it was found that a stereo convergence angle of 90° yields the best relative depth uncertainty value at which the focal length–normalized epipole‐to‐principal point distances on both image planes are reciprocals.