Linear differential algorithm for motion recovery: A geometric approach

The aim of this paper is to explore a linear geometric algorithm for recove ring the three dimensional motion of a moving camera from image velocities. Generic similarities and differences between the discrete approach and the differential approach are clearly revealed through a parallel development of an analogous motion estimation theory previously explored in Vieville, T . and Faugeras, O.D. 1995. In Proceedings of Fifth International Conference on Computer Vision, pp. 750-756; Zhuang, X. and Haralick, R.M. 1984. In Pr oceedings of the First International Conference on Artificial Intelligence Applications, pp. 366-375. We present a precise characterization of the spa ce of differential essential matrices, which gives rise to a novel eigenval ue-decomposition-based 3D velocity estimation algorithm from the optical fl ow measurements. This algorithm gives a unique solution to the motion estim ation problem and serves as a differential counterpart of the well-known SV D-based 3D displacement estimation algorithm for the discrete case. Since t he proposed algorithm only involves linear algebra techniques, it may be us ed to provide a fast initial guess for more sophisticated nonlinear algorit hms (Ma et al., 1998c. Electronic Research Laboratory Memorandum, UC Berkel ey, UCB/ERL(M98/37)). Extensive simulation results are presented for evalua ting the performance of our algorithm in terms of bias and sensitivity of t he estimates with respect to different noise levels in image velocity measu rements.