Recently, we have seen a proliferation in research addressing the motion estimation problem and its practical applications based on coplanar point configurations [10,14,12,9,6,7,13]. This paper introduces a new approach where following an estimation of the full projection matrix from non-coplanar points in one reference frame, the system provides better motion estimation results based on coplanar point configurations without estimating the camera intrinsic parameters. The new mathematical framework allows us to directly estimate the rigid transformation between a full projection matrix and a homography. Experimental results compare the accuracy of this and the homography decomposition approach, proposed in [14], in the context of an augmented reality application where three cameras are calibrated for real-time image augmentation.