  Aligning two partially-overlapped 3D line reconstructions in Euclidean space
is challenging, as we need to simultaneously solve correspondences and relative
pose between line reconstructions. This paper proposes a neural network based
method and it has three modules connected in sequence: (i) a Multilayer
Perceptron (MLP) based network takes Pluecker representations of lines as
inputs, to extract discriminative line-wise features and matchabilities (how
likely each line is going to have a match), (ii) an Optimal Transport (OT)
layer takes two-view line-wise features and matchabilities as inputs to
estimate a 2D joint probability matrix, with each item describes the matchness
of a line pair, and (iii) line pairs with Top-K matching probabilities are fed
to a 2-line minimal solver in a RANSAC framework to estimate a six
Degree-of-Freedom (6-DoF) rigid transformation. Experiments on both indoor and
outdoor datasets show that the registration (rotation and translation)
precision of our method outperforms baselines significantly.
