Closed-form Linear Solution To Motion Estimation In Disparity Space

Real-time stereovision systems play an important role in automotive related applications. This paper concerns the problem of rigid motion estimation with a stereovision sensor. Given a set of corresponding 3D points in Euclidean space reconstructed from stereovision, efficient linear algorithms exist to solve for the rigid motion. However it has been well known that the noise in the Euclidean reconstruction from stereovision is heteroscedastic and anisotropic, therefore the linear algorithms are only sub-optimal. Recently a d-motion based algorithm has been developed to solve for the rigid motion directly in the disparity space, in which the noise can be approximated to be homogenous and isotropic. However this algorithm is nonlinear and requires iterative least-squares solution. By reformulating the problem, a closed-form linear solution is presented in this paper to solve for the rigid motion in disparity space. Synthetic experimental results show that this new algorithm outperforms the d-motion based algorithm in terms of both accuracy and computational cost. We believe that the closed-form linear solution is potentially very useful for applications making use of stereovision to estimate rigid motion.