Line Matching and Pose Estimation for Unconstrained Model-to-Image Alignment

This paper has two contributions in the context of line based camera pose estimation, 1) 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, 2) We eliminate a degenerate case due to the type of rotation representation in arguably the best line based pose estimation method currently available. For establishing line correspondences we perform exhaustive search on the space of camera pose values till we obtain a pose (position and rotation) which is geometrically consistent with the given set of 2D, 3D lines. For this highly complex search we design a strategy which performs precomputations on the 3D model using separate set of constraints on position and rotation values. During runtime, the set of different rotation values are ranked independently and combined with each position values in the order of their ranking. Then successive geometric constraints which are much simpler when compared to computing reprojection error are used to eliminate incorrect pose values. We show that the ranking of rotation values reduces the number of trials needed by a huge factor and the simple geometric constraints avoid the need for computing the reprojection error in most cases. Though the execution time for the current MATLAB implementation is far from real time requirement, our method can be accelerated significantly by exploiting simplicity and parallelizability of the operations we employ. For eliminating the degenerate case in the state of art pose estimation method, we reformulate the rotation representation. We use unit quaternions instead of CGR parameters used by the method.