Estimation of Motion and Structure of 3-d Objects from a Sequence of Images

In this article we analyze the motion of 3-D objects either in terms of image contours or intensity gradients. We make the assumption that the objects viewed are locally rigid and planar. We suppose that the projection is perspective and use the "perspective" velocity vector, which has been introduced by G.L.Scott. We give spatial relations on the "perspective" velocity field both in the case of points lying on a contour and in the case of dense image points. We utilize these spatial relations to estimate the "perspective" velocity field using the normal velocity component on a contour or the motion constraint equation in the 2D image. In the first case the Kalman filter is used. In the second case a Gauss-Seidel relaxation algorithm is proposed. We demonstrate that if the "perspective" velocity vector is known at three points, one can reconstruct the 3-D motion parameters and the plane orientation. We also demonstrate that if the "perspective" velocity vector is known at four points the 3-D motion parameters and the relative depths can be reconstructed solving two systems of three linear equations and a system of four linear equations.