MOTION AND STRUCTURE FROM LINE CORRESPONDENCES - SOME FURTHER RESULTS

A great deal of dynamic computer vision literature deals with the determination of motion and structure of rigid objects by observing points on objects at two or more time instants. In some situations point correspondences may not be available but line correspondences may be, such as when edges on the objects are visible. In this article we investigate the multiplicity of solutions when various numbers of 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 given three line correspondences over three frames, two line correspondences over four frames, and one line correspondence over five or more frames. With fewer line correspondences there are infinitely many solutions. In the more general case where the motion is allowed to vary between successive frames, we show that there can be no more than 600 solutions to motion and structure with six line correspondences over three views, and that there is a unique solution with seven line correspondences. Several examples are given to illustrate our results. (C) 1994 John Wiley and Sons, Inc.