Estimation of motion and structure of planar surfaces from a sequence of monocular images

An algorithm is presented which estimates 10 parameters for motion and structure of a rigid planar patch given point correspondences in a monocular image sequence under perspective projection. The rotational velocity is assumed constant and the rotation center arbitrary. The algorithm mainly consists of two steps. First, the 3-D space of (ω_x, ω_y, ω_z) is searched exhaustively and for each (ω_x, ω_y, ω_z) all the other parameters with the value of an objective function are computed linearly. Some of the (ω_x, ω_y, ω_z) and the corresponding structure values are used as the initial guesses in the second step. The objective function is iteratively minimized with respect to five variables for rotation and structure. The solution corresponding to the global minimum is used to obtain least squares estimates of the remaining unknowns, for translation and rotation center. It was experimentally found that the objective function converges well so that the 3-D space need not be densely searched. Results are presented for three image sequences, two simulated and one real.