Uniqueness of Solutions to Structure and Motion from Combinations of Point and Line Correspondences

Abstract A great deal of dynamic computer vision literature deals with the determination of motion and structure of rigid objects by observing points or lines on objects at two or more time instants. In this paper we determine circumstances under which a unique solution to structure and motion is almost always guaranteed when various combinations of point and line correspondences among several snapshots of an object are known. The case given the most consideration is that in which the object is moving with constant motion, that is, with constant rotation about an unknown center which itself is moving with constant translation. In this case we show that there is a unique solution for motion and structure when either two point and one line or one point and two line correspondences are known over three frames with known timing. There is also a unique solution when one point and one line correspondence are known over four frames. Several examples are given to illustrate our results.