# PlueckerNet: Learn to Register 3D Line Reconstructions

arXiv: https://arxiv.org/abs/2012.01096 · HTML: https://mlsanity.com/paper/2012.01096/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Dec 2020.

## Built on by (most cited first, 4 of 4)

- [Holistically-Attracted Wireframe Parsing: From Supervised to Self-Supervised Learning](https://mlsanity.com/paper/2210.12971/) (2022)
- [ColabSfM: Collaborative Structure-from-Motion by Point Cloud Registration](https://mlsanity.com/paper/2503.17093/) (2025)
- [Registration beyond Points: General Affine Subspace Alignment via Geodesic Distance on Grassmann Manifold](https://mlsanity.com/paper/2507.17998/) (2025)
- [Co-PLNet: A Collaborative Point-Line Network for Prompt-Guided Wireframe Parsing](https://mlsanity.com/paper/2601.18252/) (2026)

## Abstract (arXiv)

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.