New Rank Deficiency Condition for Multiple View Geometry of Line Features

In this paper, a new rank deficiency condition for multiple images of a line is presented. It is shown that a set of m image lines correspond to a unique 3-D line if and only if an associated (m-1 x 4 matrix Hl is of maximum rank 1. This condition is shown to be equivalent to all multilinear constraints among image lines, but it tremendously simplifies previously known derivations. Since rank deficiency is a purely linear algebraic condition, it gives rise to a set of natural linear algorithms for line matching, line transfer to a new view and motion estimation from images of multiple lines. These linear algorithms use all available data simultaneously without specifying a particular choice of image triplets. Hence apart from the initialization, the algorithms allow us to bypass trifocal tensors used for similar purposes. The theory and algorithms for the line case are developed in exact parallel to that for the point case. Geometric interpretation of the Hl matrix and the duality between point and line are also clearly revealed through this approach.Ope