An Efficient Normal-Error Iterative Algorithm for Line Triangulation

Qiang Zhang, Yan Wu, Ming Liu, Licheng Jiao

Abstract: In this paper, we address the problem of line triangulation, which is to find the position of a line in space given its three projections taken with cameras with known camera matrices. Because of measurement error in line extraction, the problem becomes difficult so that it is necessary to estimate a 3D line to optimally fit measured lines. In this work, the normal errors of measured line are presented to describe the measurement error and based on their statistical property a new geometric-distance optimality criterion is constructed. Furthermore, a simple iterative algorithm is proposed to obtain suboptimal solution of the optimality criterion, which ensures that the solution satisfies the trifocal tensor constraint. Experiments show that our iterative algorithm can achieve the estimation accuracy comparable with the Gold Standard algorithm, but its computational load is substantially reduced.