A dimensionality result for multiple homography matrices

Abstract

It is shown that the set of all I-element collections of interdependent homography matrices describing homographies induced by I planes in the 3D scene between two views has dimension 4I + 7. This improves on an earlier result which gave an upper bound for the dimension in question, and solves a long-standing open problem. The significance of the present result lies in that it is critical to the identification of the full set of constraints to which collections of interdependent homography matrices are subject, which in turn is critical to the design of constrained optimisation techniques for estimating such collections from image data.