# On Incremental Structure-from-Motion using Lines

arXiv: https://arxiv.org/abs/2105.11196 · HTML: https://mlsanity.com/paper/2105.11196/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 May 2021.

## Built on by (most cited first, 5 of 5)

- [DeepLSD: Line Segment Detection and Refinement with Deep Image Gradients](https://mlsanity.com/paper/2212.07766/) (2022)
- [Robust Incremental Structure-from-Motion with Hybrid Features](https://mlsanity.com/paper/2409.19811/) (2024)
- [Vision-Based Environmental Perception for Autonomous Driving](https://mlsanity.com/paper/2212.11453/) (2022)
- [3D Reconstruction via Incremental Structure From Motion](https://mlsanity.com/paper/2508.01019/) (2025)
- [The Impact of Semi-Supervised Learning on Line Segment Detection](https://mlsanity.com/paper/2411.04596/) (2024)

## Abstract (arXiv)

Humans tend to build environments with structure, which consists of mainly planar surfaces. From the intersection of planar surfaces arise straight lines. Lines have more degrees-of-freedom than points. Thus, line-based Structure-from-Motion (SfM) provides more information about the environment. In this paper, we present solutions for SfM using lines, namely, incremental SfM. These approaches consist of designing state observers for a camera's dynamical visual system looking at a 3D line. We start by presenting a model that uses spherical coordinates for representing the line's moment vector. We show that this parameterization has singularities, and therefore we introduce a more suitable model that considers the line's moment and shortest viewing ray. Concerning the observers, we present two different methodologies. The first uses a memory-less state-of-the-art framework for dynamic visual systems. Since the previous states of the robotic agent are accessible -- while performing the 3D mapping of the environment -- the second approach aims at exploiting the use of memory to improve the estimation accuracy and convergence speed. The two models and the two observers are evaluated in simulation and real data, where mobile and manipulator robots are used.