We present a two step approach for estimating the motionand sturcture parameters from region orrespondences in two frames. Given four or more region corresondences on the same planar surface, the motion and planar orientation parameters are first linearly estimated based on second-order approximation of the displacement field of the image plane. Then, using this linear estimate as an initial guess, a nonlinear estimate is obtained by iteratively minimizing an objective function using the exact experession of the displacement field. The objective function involves the centroids of corresponding regions and relationships among low-order moments. Through simulations, we show that the two-step region-based approach gives robust estimates. The performance of nonlinear region-based estimation is compared with that of linear region-based and point-based methods. Experimental results for two image pairs, on esynthetic and one real, ar epresented to show the practical applicability of our approach.