Necessary and sufficient conditions for a unique solution of plane motion and structure

This paper presents necessary and sufficient conditions for uniquely determining the motion and structure of a planar surface from any number of monocular images. The authors first show an uncertain situation for the two-view plane motion problem in which an infinite number of solutions may result. Although this situation rarely occurs in real situations, it does raise visual ambiguities under certain circumstances, e.g., when some images are observed through a mirror. The understanding of this situation therefore helps analyze reflected images which are often seen in daily life. Then, the authors present necessary and sufficient conditions for a unique solution of plane motion and structure from any number of views. These algorithm-independent conditions enhance understanding about the problem of estimating plane motion and structure from image sequences and may be used to determine the uniqueness of the solution of the motion and structure of a planar surface