Propagation of uncertainty for an epipole-dependent model for convergent stereovision structure computation

Abstract

An analytic model incorporating stereo epipoles is proposed for structure computation using a convergent stereovision setup. The developed model is predicated on the image parameters of both CCD camera sensors, together with two extrinsic parameters, namely the stereo baseline distance and the stereo projection angle of the scene point of interest. In the model, the points on the image planes are measured relative to the principal points, stereo epipoles are featured, and only focal length-normalized camera sensor coordinates are required for structure computation. The reconstruction model could be employed in active vision-based metrology in which the stereo imaging cameras are systematically rotated about their vertical axes relative to each other. The performance of the model is studied, and its accuracy tested by comparing the 3-space coordinates it predicted to the those obtained by a gold standard triangulation and to the ground truth results. In terms of execution speed the proposed reconstruction model exhibited a computation time of 0.6 ms compared to 6.2 ms and 9.9 ms recorded for the direct linear transformation and gold standard triangulation algorithms respectively. The coordinate measurement uncertainties determined by experimental methods are subsequently compared with those obtained by a theoretical approach based on the analytic reconstruction model. Strong correlations were found to exist between the two sets of uncertainty values obtained.