# Calibrated and Partially Calibrated Semi-Generalized Homographies

arXiv: https://arxiv.org/abs/2103.06535 · HTML: https://mlsanity.com/paper/2103.06535/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 59 references that are in the map.
- First posted on arXiv 11 Mar 2021.

## Builds on (most cited first, 14 of 14)

- [ORB-SLAM: a Versatile and Accurate Monocular SLAM System](https://mlsanity.com/paper/1502.00956/) (2015)
- [ORB-SLAM2: an Open-Source SLAM System for Monocular, Stereo and RGB-D Cameras](https://mlsanity.com/paper/1610.06475/) (2016)
- [From Coarse to Fine: Robust Hierarchical Localization at Large Scale](https://mlsanity.com/paper/1812.03506/) (2018)
- [Understanding the Limitations of CNN-based Absolute Camera Pose Regression](https://mlsanity.com/paper/1903.07504/) (2019)
- [Graph-Cut RANSAC](https://mlsanity.com/paper/1706.00984/) (2017)
- [Camera Relocalization by Computing Pairwise Relative Poses Using Convolutional Neural Network](https://mlsanity.com/paper/1707.09733/) (2017)
- [Expert Sample Consensus Applied to Camera Re-Localization](https://mlsanity.com/paper/1908.02484/) (2019)
- [To Learn or Not to Learn: Visual Localization from Essential Matrices](https://mlsanity.com/paper/1908.01293/) (2019)
- [Progressive-X: Efficient, Anytime, Multi-Model Fitting Algorithm](https://mlsanity.com/paper/1906.02290/) (2019)
- [Why Having 10,000 Parameters in Your Camera Model is Better Than Twelve](https://mlsanity.com/paper/1912.02908/) (2019)
- [Beyond Controlled Environments: 3D Camera Re-Localization in Changing Indoor Scenes](https://mlsanity.com/paper/2008.02004/) (2020)
- [A clever elimination strategy for efficient minimal solvers](https://mlsanity.com/paper/1703.05289/) (2017)
- [Five-point Fundamental Matrix Estimation for Uncalibrated Cameras](https://mlsanity.com/paper/1803.00260/) (2018)
- [Homography from two orientation- and scale-covariant features](https://mlsanity.com/paper/1906.11927/) (2019)

## Built on by (most cited first, 12 of 12)

- [ViewFormer: NeRF-free Neural Rendering from Few Images Using Transformers](https://mlsanity.com/paper/2203.10157/) (2022)
- [SceneGraphLoc: Cross-Modal Coarse Visual Localization on 3D Scene Graphs](https://mlsanity.com/paper/2404.00469/) (2024)
- [Visual Localization using Imperfect 3D Models from the Internet](https://mlsanity.com/paper/2304.05947/) (2023)
- ["Where am I?" Scene Retrieval with Language](https://mlsanity.com/paper/2404.14565/) (2024)
- [Gaussian Splatting Feature Fields for Privacy-Preserving Visual Localization](https://mlsanity.com/paper/2507.23569/) (2025)
- [A Guide to Structureless Visual Localization](https://mlsanity.com/paper/2504.17636/) (2025)
- [Finding Geometric Models by Clustering in the Consensus Space](https://mlsanity.com/paper/2103.13875/) (2021)
- [Lazy Visual Localization via Motion Averaging](https://mlsanity.com/paper/2307.09981/) (2023)
- [Self-supervised Learning of Neural Implicit Feature Fields for Camera Pose Refinement](https://mlsanity.com/paper/2406.08463/) (2024)
- [A Scene is Worth a Thousand Features: Feed-Forward Camera Localization from a Collection of Image Features](https://mlsanity.com/paper/2510.00978/) (2025)
- [Combining Absolute and Semi-Generalized Relative Poses for Visual Localization](https://mlsanity.com/paper/2409.14269/) (2024)
- [Partially calibrated semi-generalized pose from hybrid point correspondences](https://mlsanity.com/paper/2209.15072/) (2022)

## Abstract (arXiv)

In this paper, we propose the first minimal solutions for estimating the semi-generalized homography given a perspective and a generalized camera. The proposed solvers use five 2D-2D image point correspondences induced by a scene plane. One of them assumes the perspective camera to be fully calibrated, while the other solver estimates the unknown focal length together with the absolute pose parameters. This setup is particularly important in structure-from-motion and image-based localization pipelines, where a new camera is localized in each step with respect to a set of known cameras and 2D-3D correspondences might not be available. As a consequence of a clever parametrization and the elimination ideal method, our approach only needs to solve a univariate polynomial of degree five or three. The proposed solvers are stable and efficient as demonstrated by a number of synthetic and real-world experiments.