# Minimal Perspective Autocalibration

arXiv: https://arxiv.org/abs/2405.05605 · HTML: https://mlsanity.com/paper/2405.05605/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 51 references that are in the map.
- First posted on arXiv 9 May 2024.

## Builds on (most cited first, 9 of 9)

- [Learning to Solve Hard Minimal Problems](https://mlsanity.com/paper/2112.03424/) (2021)
- [PLMP -- Point-Line Minimal Problems in Complete Multi-View Visibility](https://mlsanity.com/paper/1903.10008/) (2019)
- [Algebraic Characterization of Essential Matrices and Their Averaging in Multiview Settings](https://mlsanity.com/paper/1904.02663/) (2019)
- [PL1P -- Point-line Minimal Problems under Partial Visibility in Three Views](https://mlsanity.com/paper/2003.05015/) (2020)
- [Minimal Problems for the Calibrated Trifocal Variety](https://mlsanity.com/paper/1611.05947/) (2016)
- [Galois/monodromy groups for decomposing minimal problems in 3D reconstruction](https://mlsanity.com/paper/2105.04460/) (2021)
- [Averaging Essential and Fundamental Matrices in Collinear Camera Settings](https://mlsanity.com/paper/1912.00254/) (2019)
- [Translation of "Zur Ermittlung eines Objektes aus zwei Perspektiven mit innerer Orientierung" by Erwin Kruppa (1913)](https://mlsanity.com/paper/1801.01454/) (2017)
- [A Minimal Six-Point Auto-Calibration Algorithm](https://mlsanity.com/paper/1307.3759/) (2013)

## Built on by (most cited first, 3 of 3)

- [Minimal Solvers for Full DoF Motion Estimation from Asynchronous Tracks](https://mlsanity.com/paper/2508.17537/) (2025)
- [Three-view Focal Length Recovery From Homographies](https://mlsanity.com/paper/2501.07499/) (2025)
- [Multiprojective Geometry of Compatible Triples of Fundamental and Essential Matrices](https://mlsanity.com/paper/2602.23450/) (2026)

## Abstract (arXiv)

We introduce a new family of minimal problems for reconstruction from multiple views. Our primary focus is a novel approach to autocalibration, a long-standing problem in computer vision. Traditional approaches to this problem, such as those based on Kruppa's equations or the modulus constraint, rely explicitly on the knowledge of multiple fundamental matrices or a projective reconstruction. In contrast, we consider a novel formulation involving constraints on image points, the unknown depths of 3D points, and a partially specified calibration matrix K. For 2 and 3 views, we present a comprehensive taxonomy of minimal autocalibration problems obtained by relaxing some of these constraints. These problems are organized into classes according to the number of views and any assumed prior knowledge of K. Within each class, we determine problems with the fewest -- or a relatively small number of -- solutions. From this zoo of problems, we devise three practical solvers. Experiments with synthetic and real data and interfacing our solvers with COLMAP demonstrate that we achieve superior accuracy compared to state-of-the-art calibration methods. The code is available at https://github.com/andreadalcin/MinimalPerspectiveAutocalibration