The 3D Line Motion Matrix and Alignment of Line Reconstructions

We study the problem of aligning two 3D line reconstructions in projective, affine, metric or Euclidean space. We introduce the 6 × 6 3D line motion matrix that acts on Plucker coordinates. We characterize its algebraic properties and its relation to the usual 4 × 4 point motion matrix, and propose various methods for estimating 3D motion from line correspondences, based on cost functions defined in images or 3D space. We assess the quality of the different estimation methods using simulated data and real images.