3D motion estimation from combined 2D-3D data of line segments

Abstract

We present a new method of 3D motion estimation from line correspondence. The original idea is to explicitly take into account both 2D and 3D information of line segments. In such a way, a unique solution can be guaranteed by a linear estimation process if the correspondences of eight non-collinear line segments are known. In our method, the motion estimation can be performed in two sequential steps: The first consists in the estimation of the rotation matrix and the second in the estimation of the translation vector. The advantage of the presented method is twofold: First of all, we can have a closed-form solution which completely determines the 3D motion to be estimated. This is not the case if only 2D information of line segments is used (see Weng et al. (1992)). Secondly, our method is more elegant and needs less computation effort. In fact, our method just requires three perspective views. In contrast, the traditional methods which only employ 3D information of line segments require four perspective views and more computation effort (see Sabata and Aggarwal (1991) and Zhang and Faugeras (1991)). The experimental results presented at the end of this paper show the numerical stability and the usefulness of our method.