Geometry based exhaustive line correspondence determination

Abstract

In this paper we propose a purely geometric approach to establish correspondence between 3D line segments in a given model and 2D line segments detected in an image. Contrary to the existing methods which use strong assumptions on camera pose, we perform exhaustive search in order to compute maximum number of geometrically permitted correspondences between a 3D model and 2D lines. We present a novel theoretical framework in which we sample the space of camera axis direction (which is bounded and hence can be densely sampled unlike the unbounded space of camera position) and show that geometric constraints arising from it reduce rest of the computation to simple operations of finding camera position as the intersection of 3 planes. These geometric constraints can be represented using indexed arrays which accelerate it further. The algorithm returns all sets of correspondences and associated camera poses having high geometric consensus. The obtained experimental results show that our method has better asymptotic behavior than conventional approach. We also show that with the inclusion of additional sensor information our method can be used to initialize pose in just few seconds in many practical situations.