# Minimal Problems in Computer Vision

**This page provides a list of papers, software, data, and evaluations for solving minimal problems in computer vision, which is concerned with finding parameters of (geometrical) models from as small (minimal) data sets by solving systems of algebraic equations.**

Please send links to papers that should be listed here to Tomas Pajdla (pajdla@gmail.com) or Zuzana Kukelova (kukelova@gmail.com).

`Title | Authors | Published | Year | Links | Problem |
---|---|---|---|---|---|

Zur Ermittlung eines Objektes aus zwei Perspektiven mit Innerer Orientierung | E. Kruppa | Z. Sitz.-Ber. Akad.Wiss.,Wien, Math. Naturw. Kl., Abt. IIa., 122:1939-1948 | 1918 | [pdf(EN)] | Relative camera pose |

An alternative formulation for five point relative pose problem | D. Batra, B. Nabbe, M. Hebert | IEEE Workshop on Motion and Video Computing | 2007 | [pdf http] | Relative camera pose, 5pt, calibrated camera |

Automatic Generator of Minimal Problem Solvers | Z. Kukelova, M. Bujnak, T. Pajdla | ECCV 2008, Marseille, France, October 12-18 | 2008 | [pdf code] | Solver generator, GB |

An Efficient Hidden Variable Approach to Minimal-Case Camera Motion Estimation | R. Hartley, H. Li | IEEE Transactions On Pattern Analysis And Machine Intelligence, 34(12):2303-2314, Dec 2012 | 2012 | [pdf code] | Relative camera pose, 5pt, 6pt, calibrated camera, focal length, HV |

Polynomial eigenvalue solutions to minimal problems in computer vision | Z. Kukelova, M. Bujnak, T. Pajdla | IEEE Transactions on Pattern Analysis and Machine Intelligence,34(7):1381-1393, 2012 | 2012 | [pdf code1 code2] | Relative camera pose, 5pt, 6pt, calibrated camera, focal length, HV |

Five-point motion estimation made easy | H. Li, R. Hartley | ICPR 2006, volume 1, pages 630-633 | 2006 | [pdf code] | Relative camera pose, 5pt, calibrated camera, HV |

An efficient solution to the five-point relative pose problem | D. Nister | IEEE Transactions on Pattern Analysis and Machine Intelligence, 26(6):756-777, June 2004 | 2004 | [pdf] | Relative camera pose, 5pt, calibrated camera, CF |

Recent developments on direct relative orientation | H. Stewenius, C. Engels, D. Nister | ISPRS Journal of Photogrammetry and Remote Sensing, 60(4):284-94, 2006 | 2006 | [pdf http] | Relative camera pose, 5pt, calibrated camera, GB |

A non-iterative algorithm for determining all essential matrices corresponding to five point pairs | J. Philip | Photogrammetric Record, 15(88):589-599, 1996 | 1996 | [http] | Relative camera pose, 5pt, calibrated camera |

Four points in two or three calibrated views: Theory and practice | D. Nister, F. Schaffalitzky | International Journal of Computer Vision, Volume 67, Number 2, April, 2006 | 2006 | [pdf http] | 4 points in 3 views, calibrated camera |

Some results on minimal euclidean reconstruction from four points | L. Quan, B. Triggs, B. Mourrain | J. Math. Imaging Vis., 24(3)::341–348, 2006 | 2006 | [pdf http] | 4 points in 3 views, calibrated camera |

Multi-View Structure Computation without Explicitly Estimating Motion | H. Li | CVPR 2010 | 2010 | [pdf] | 4 points in 3 views, calibrated camera |

Improving numerical accuracy of Gröbner basis polynomial equation solver | M. Byröd, K. Josephson, K. Åström | ICCV 2007 | 2007 | [pdf] | Gröbner basis solvers, Relative camera pose, generalized camera, 6pt, focal length, three-view triangulation, GB |

A simple solution to the six-point two-view focal-length problem | H. Li | ECCV 2006 | 2006 | [pdf code] | Relative camera pose, 6pt, focal length, HV |

Random Sample Consensus: A Paradigm for Model Fitting with Applications to Image Analysis and Automated Cartography | M. A. Fischler, R. C. Bolles | Comm. of the ACM, Vol 24, pp 381-395 | 1981 | [http] | Absolute camera pose, P3P, calibrated camera, CF |

A general solution to the P4P problem for camera with unknown focal length | M. Bujnak, Z. Kukelova, T. Pajdla | CVPR 2008, Anchorage, Alaska, USA, | 2008 | [pdf code] | Absolute camera pose, P4Pf, focal length, GB |

Camera Pose and Calibration from 4 or 5 Known 3D Points | B. Triggs | ICCV 1999 | 1999 | [pdf] | Absolute camera pose, P4Pf, focal length, uncalibrated camera |

A new efficient and direct solution for pose estimation using quadrangular targets: Algorithm and evaluation | M. A. Abidi, T. Chandra | IEEE PAMI, 17(5):534–538, 1995 | 1995 | [http] | Absolute camera pose, P4Pf, focal length, planar scene |

Pose Estimation with Radial Distortion and Unknown Focal Length | K. Josephson, M. Byröd, K. Åström | CVPR 2009, Florida, USA | 2009 | [pdf code] | Absolute camera pose, P4Pfr, focal length. radial distortion, GB |

New efficient solution to the absolute pose problem for camera with unknown focal length and radial distortion | M. Bujnak, Z. Kukelova, Pajdla T. | ACCV 2010, Queenstown, NZ | 2010 | [pdf code] | Absolute camera pose, P4Pfr, focal length. radial distortion, GB |

Real-time solution to the absolute pose problem with unknown radial distortion and focal length. | Z. Kukelova, M. Bujnak, T. Pajdla | ICCV 2013, Sydney, Australia | 2013 | [pdf] | Absolute camera pose, P5Pfr, focal length. radial distortion, CF |

Closed-form solutions to the minimal absolute pose problems with known vertical direction | Z. Kukelova, M. Bujnak, T. Pajdla | ACCV 2010, Queenstown, NZ, November 8-12, 2010 | 2010 | [pdf code1 code2] | Absolute camera pose, uP2P, uP3Pfr, known vertical direction, IMU, calibrated camera, focal length, radial distortion CF |

Pose estimation using both points and lines for geo-localization | S. Ramalingam, S. Bouaziz, P. Sturm | ICRA 2011 | 2011 | [pdf] | Absolute camera pose, calibrated camera, P2P1L, P1P2L, points, lines |

3D reconstruction from image collections with a single known focal length | M. Bujnak, Z.Kukelova, T. Pajdla | ICCV 2009, Kyoto, Japan, September 29 – October 2, 2009 | 2009 | [pdf] | Relative camera pose, 6pt-on-off, calibrated-uncalibrated, focal length, GB |

Minimal Solutions for Panoramic Stitching | M. Brown, R. Hartley, D. Nister | CVPR 2007. Minneapolis, USA | 2007 | [pdf http] | Camera rotation, panorama, homography, focal length, CF, HV |

Minimal Solutions for Panoramic Stitching with Radial Distortion | M. Byröd, M. Brown, K. Åström | BMVC 2009, London, UK | 2009 | [pdf http] | Camera rotation, panorama, homography, focal length, radial distortion, GB |

Solutions to minimal generalized relative pose problems | H. Stewenius, D. Nister, M. Oskarsson, K. Åström | OMNIVIS 2005 | 2005 | [pdf] | Relative camera pose, generalized camera, calibrated camera, GB |

Fast and robust numerical solutions to minimal problems for cameras with radial distortion | Z. Kukelova, M. Byröd, K. Josephson, T. Pajdla, K. Åström | Computer Vision and Image Understanding, Volume 114, Issue 2, Pages 234-244, ISSN 1077-3142, February 2010 | 2010 | [http code] | Relative camera pose, 6ptr, 9ptr1r2, radial distortion, calibrated camera, uncalibrated camera, different distortions, GB |

Fast and robust numerical solutions to minimal problems for cameras with radial distortion | M. Byröd, Z. Kukelova, K. Josephson, T. Pajdla, K. Åström | CVPR 2008 | 2008 | [pdf code] | Relative camera pose, 6ptr, 9ptr1r2, radial distortion, calibrated camera, uncalibrated camera, different distortions, GB |

Two minimal problems for cameras with radial distortion | Z. Kukelova, T. Pajdla | OMNIVIS 2007, Rio de Janeiro | 2007 | [pdf] | Relative camera pose, 6ptr, 9ptr1r2, radial distortion, calibrated camera, uncalibrated camera, different distortions, GB |

A minimal solution to the autocalibration of radial distortion | Z. Kukelova, T. Pajdla | CVPR 2007 | 2007 | [pdf] | Relative camera pose, 8ptr, radial distortion, uncalibrated camera, GB |

Simultaneous Linear Estimation of Multipleview Geometry and Lens Distortion | A. Fitzgibbon | CVPR 2001 | 2001 | [pdf] | Relative camera pose, 9ptr, radial distortion, uncalibrated camera, non-miniml, HV |

A Non-iterative Method for Correcting Lens Distortion from 9 Point Correspondences | H. Li, R. Hartley | OMNIVIS 2005 | 2005 | [pdf] | Relative camera pose, 9ptr, radial distortion, uncalibrated camera, non-miniml, HV |

P2Pi: A minimal solution for the registration of 3D points to 3D planes | S. Ramalingam, Y. Taguchi, T. Marks, O.Tuzel | ECCV 2011 | 2011 | [pdf] | 3D points to 3D planes registration |

Hand-Eye Calibration without Hand Orientation Measurement Using Minimal Solution | Z. Kukelova, J. Heller, T. Pajdla | ACCV 2012, Daejeon, Korea, November 2012 | 2012 | [pdf] | Hand-eye calibration, known translation, robotics, GB |

Fast Optimal Three View Triangulation | M. Byröd, K. Josephson, Kalle Åström | ACCV 2007, Tokyo, Japan | 2007 | [pdf code] | Three view triangulation, L2, GB |

A Column-Pivoting Based Strategy for Monomial Ordering in Numerical Gröbner Basis Calculations | M. Byröd, K. Josephson, K. Åström | ECCV 2008 | 2008 | [pdf] | Gröbner basis solvers, Relative camera pose, generalized camera, 6pt, focal length, three-view triangulation, GB |

How hard is three-view triangulation really? | H. Stewénius, F. Schaffalitzky, D. Nister | ICCV 2005 , volume 1, pages 686-693, Beijing China, October 2005 | 2005 | [http] | Three view triangulation, L2, GB |

Radial Distortion Homography | Z. Kukelova, J. Heller M. Bujnak, T. Pajdla | CVPR 2015, Boston, USA | 2015 | [pdf code] | Homography, H5r1r2, radial distortion, different distortions, GB |

Making minimal solvers fast | M. Bujnak, Z. Kukelova, T. Pajdla | CVPR 2012, Providence, USA, June 16-21, 2012 | 2012 | [pdf] | Gröbner basis solvers, Relative camera pose, 6pt, 6pt, focal length, P4Pf, GB |

Fast and stable algebraic solution to L2 three-view triangulation | Z. Kukelova, M. Bujnak, T. Pajdla | 3DV 2013, Seattle, USA, June, 2013 | 2013 | [pdf] | Three view triangulation, L2, GB |

Singly-Bordered Block-Diagonal Form for Minimal Problem Solvers | Z. Kukelova, M. Bujnak, J. Heller, T. Pajdla | ACCV 2014, Singapore, November, 2014 | 2014 | [pdf] | Gröbner basis solvers, Relative camera pose, Absolute camera pose, 9pt, P4Pf, P4Pfr, focal length, radial distortion, GB |

P3.5P: Pose Estimation with Unknown Focal Length | Ch. Wu | CVPR 2015, Boston, USA | 2015 | [pdf] | Absolute camera pose, P3.5f, focal length, HV |

Relative Pose Estimation for a Multi-Camera System with Known Vertical Direction |
G. H. Lee, M. Pollefeys, F. Fraundorfer | CVPR 2014 | 2014 | [pdf] | Relative camera pose, multicamera system, known vertical direction, IMU, HV |

Minimal Solutions for Pose Estimation of a Multi-Camera System | G. H. Lee, B. Li., M. Pollefeys, F. Fraundorfer | ISRR 2014 | 2014 | [pdf] | Absolute camera pose, multicamera system |

A 4-Point Algorithm for Relative Pose Estimation of a Calibrated Camera with a Known Relative Rotation Angle | B. Li, L. Heng, G. H. Lee, M. Pollefeys | IROS 2013 | 2013 | [pdf] | Relative camera pose, calibrated camera, known relative rotation angle |

A Minimal Solution to the Rolling Shutter Pose Estimation Problem | O. Saurer, M. Pollefeys, G. H. Lee | IROS 2015 | 2015 | [pdf] | Absolute camera pose, rolling shutter camera |

Minimal Solutions for Pose Estimation of a Multi-Camera System | G. H. Lee, B. Li., M. Pollefeys, F. Fraundorfer | International Journal of Robotics Research | 2015 | [http] | Absolute camera pose, multicamera system |

R6P – Rolling Shutter Absolute Camera Pose | C. Albl, Z. Kukelova, T. Pajdla | CVPR 2015 | 2015 | [pdf http code] | Absolute camera pose, rolling shutter camera, R6P, GB |

A homography formulation to the 3pt plus a common direction relative pose problem |
O. Saurer, P. Vasseur, C. Demonceaux, F. Fraundorfer | ACCV 2014 | 2014 | [pdf] | Relative camera pose, known vertical direction, IMU, 3pt |

A new solution to the relative orientation problem using only 3 points and the vertical direction |
M. Kalantari, A. Hashemi, F. Jung, J.P. Guedon |
Journal of Mathematical Imaging and Vision 39, 2011 |
2011 | [http] | Relative camera pose, known vertical direction, IMU, 3pt, GB |

Two Efficient Solutions for Visual Odometry Using Directional Correspondence | O. Naroditsky, X.S. Zhou, J.H. Gallier, S.I. Roumeliotis, K. Daniilidis | IEEETrans. Pattern Anal. Mach. Intell. 34, 2012 | 2012 | [http] | Relative camera pose, known vertical direction, IMU, 3pt, GB |

Algebraic solutions to absolute pose problems | M. Bujnak | PhD Thesis, Czech Technical University in Prague | 2012 | [pdf http] | Absolute camera pose, P3P, P4Pf, P4Pfr, uP2P, uP3Pfr, calibrated camera, focal length, radial distortion, known vertical direction, GB |

Algebraic Methods in Computer Vision | Z. Kukelova | PhD Thesis, Czech Technical University in Prague | 2013 | [pdf http] | Gröbner basis solvers, Relative camera pose, 6pt, 8ptr, 9ptr1r2, 6ptr, focal length, radial distortion, GB |

Tractable Algorithms for Robust Model Estimation | O. Enqvist , E. Ask, F. Kahl, K. Åström | International Journal of Computer Vision | 2015 | [pdf] | Robust fitting using minimal solvers |

On the Minimal Problems of Low-Rank Matrix Factorization | F. Jiang, M. Oskarsson, K. Åström | CVPR 2015 | 2015 | [pdf] | Low rank matrix factorization, missing data |

Absolute Pose for Cameras Under Flat Refractive Interfaces | S. Haner, K. Åström | CVPR 2015 | 2015 | [pdf code] | Absolute pose, refractive surfaces |

Revisiting Trifocal Tensor Estimation using Lines | Y. Kuang, M. Oskarsson, K. Åström | ICPR 2014 | 2014 | [pdf] | Trifocal tensor, Uncalibrated cameras, 10 lines in 3 views |

Prime Rigid Graphs and Multidimensional Scaling with Missing Data | M. Oskarsson, K. Åström, A. Torstensson | ICPR 2014 | 2014 | [pdf] | MDS, missing data |

Partial Symmetry in Polynomial Systems and Its Application in Computer Vision | Y. Kuang, Y. Zheng, K. Åström | CVPR 2014 | 2014 | [pdf] | Gröbner basis solvers, symmetry |

Minimal Solvers for Relative Pose with a Single Unknown Radial Distortion | Y. Kuang, J.E. Solem, F. Kahl, K. Åström | CVPR 2014 | 2014 | [pdf] | Relative camera pose, radial distortion |

Minimal Solutions for Dual Microphone Rig Self-Calibration | S. Zhayida, S. Burgess, Y. Kuang, Yubin, K. Åström | European Signal Processing Conference (EUSIPCO 2014) | 2014 | [pdf] | Time-of-arrival, relative pose, MDS , missing data |

An Automatic System for Microphone Self-Localization Using Ambient Sound | S. Zhayida, F. Andersson, Y. Kuang, K. Åström | European Signal Processing Conference (Eusipco 2014) | 2014 | [pdf] | Time-difference-of-arrival, relative pose, MDS, missing data |

A Unifying Approach to Minimal Problems in Collinear and Planar TDOA Sensor Network Self-Calibration | E. Ask, Y. Kuang, K. Åström | European Signal Processing Conference (Eusipco 2014) | 2014 | [pdf] | Time-difference-of-arrival, relative pose, MDS, missing data |

A Minimal Solution to Relative Pose with Unknown Focal Length and Radial Distortion | F. Jiang, Y. Kuang, J.F. Solem, K. Åström | ACCV 2014 | 2014 | [pdf] | Relative camera pose, radial distortion, focal length |

Stratified Sensor Network Self-Calibration From TDOA Measurements | Y. Kuang, K. Åström | 21st European Signal Processing Conference 2013 | 2013 | [pdf] | Time-difference-of-arrival, relative pose, MDS, missing data |

Revisiting the PnP Problem: A Fast, General and Optimal Solution | Y. Zheng, Y. Kuang, S. Sugimoto, K. Åström, M. Okutomi | ICCV 2013 | 2013 | [pdf] | Absolute camera pose, PnP, optimal |

Pose Estimation with Unknown Focal Length using Points, Directions and Lines | Y. Kuang, K. Åström | ICCV 2013 | 2013 | [pdf] | Absolute camera pose, points, lines, quivers |

Optimal Geometric Fitting Under the Truncated L2 -Norm | E. Ask, O. Enqvist, F. Kahl | CVPR 2013 | 2013 | [pdf] | Optimal truncated L2-fitting using minimal solvers |

Minimal Structure and Motion Problems for TOA and TDOA Measurements with Collinearity Constraints | E. Ask, S. Burgess, K. Åström | 2nd International Conference on Pattern Recognition Applications | 2013 | [pdf] | Time-of-arrival, time-difference-of-arrival, relative pose, collinearity |

A Complete Characterization and Solution to the Microphone Position Self-Calibration Problem | Y. Kuang, S. Burgess, A. Torstensson, K. Åström | The 38th International Conference on Acoustics, Speech, and Signal Processing | 2013 | [pdf] | Time-of-arrival, 3D, 4-6 solver, 5-5 solver |

Pose Estimation from Minimal Dual-Receiver Configurations | S. Burgess, Y. Kuang, K. Åström | ICPR 2012 | 2012 | [pdf] | time-of-arrival, pose |

Numerically Stable Optimization of Polynomial Solvers for Minimal Problems | E. Ask, Y. Kuang, K. Åström | ECCV 2012 | 2012 | [pdf] | Gröbner basis solvers, making templates small and numerically stable |

Exploiting p-Fold Symmetries for Faster Polynomial Equation Solving | E. Ask, Y. Kuang, K. Åström | ICPR 2012 | 2012 | [pdf] | Gröbner basis solvers, symmetry |

Fast and Stable Polynomial Equation Solving and Its Application to Computer Vision | M. Byröd, K. Josephson, K. Åström | International Journal of Computer Vision | 2009 | [pdf] | Gröbner basis solvers, Numerical stability, GB |

The Minimal Structure and Motion Problems with Missing Data for 1D Retina Vision | M. Oskarsson, K. Åström, N.Chr. Overgaard | Journal of Mathematical Imaging and Vision | 2006 | [http] | |

A minimal solution for relative pose with unknown focal length | H. Stewenius, D. Nister, F. Kahl, F. Schaffalitzky | CVPR 2005 | 2005 | [pdf code] | Relative camera pose, 6pt, focal length, GB |

A minimal solution to the generalized 3-point pose problem | Nister, D., Stewenius, H. | Journal of Mathematical Imaging and Vision (JMIV) 27(1):67-79 | 2006 | [pdf] | Generalized P3P |

Computing similarity transformations from only image correspondences | Sweeney, C., Kneip, L., Höllerer, T. & Turk, M. | CVPR 2015 | 2015 | [pdf] | Generalized relative pose and scale with known directional correspondence |

UPnP: An Optimal O(n) Solution to the Absolute Pose Problem with Universal Applicability | Kneip, L., Li, H. & Seo, Y. | ECCV 2014 | 2014 | [pdf] | P3P & PnP (normal and generalized) |

Using multi-camera systems in robotics: Efficient solutions to the NPnP problem | Kneip, L., Furgale, P. T. & Siegwart, R. | ICRA 2013 | 2013 | [pdf] | Generalized PnP |

Finding the exact rotation between two images independently of the translation | Kneip, L., Roland, S. & Marc, P. | ECCV 2012 | 2012 | [pdf] | Relative Pose problem |

A novel parametrization Of the perspective-three-point problem for a direct computation of absolute camera position and orientation | Kneip, L., Scaramuzza, D. & Siegwart, R. | CVPR 2013 | 2013 | [pdf] | P3P |

A Minimal Case Solution to the Calibrated Relative Pose Problem for the Case of Two Known Orientation Angles | Fraundorfer, F., Tanskanen, P. & Pollefeys M. | ECCV 2010 | 2010 | [pdf] | Relative Pose with known direction |

An Efficient Minimal Solution for Multi-Camera Motion | Ventura, J., Arth, C. & Lepetit, V. | ICCV 2015 | 2015 | [pdf] | Generalized relative pose |

A Minimal Solution to the Generalized Pose-and-Scale Problem | Ventura, J., Arth, G., Reitmayr, G. & Schmalstieg. D. | CVPR 2014 | 2014 | [pdf] | generalized P3P + unknown scale |

gDLS: A Scalable Solution to the Generalized Pose and Scale Problem | Sweeney, C., Fragoso, V., Hollerer, T. & Turk, M. | ECCV 2014 | 2014 | [pdf] | Generalized P3P/PnP + unknown scale |

Solving for Relative Pose with a Partially Known Rotation is a Quadratic Eigenvalue Problem | Sweeney, C., Flynn, J. & Turk, M. | 3DV 2014 | 2014 | [pdf] | Relative pose with known direction |

Efficient Computation of Absolute Pose for Gravity-Aware Augmented Reality | Sweeney, C., Flynn, J., Nuernberger, B., Turk, M. & Hollerer, T. | IEEE International Symposium on Mixed and Augmented Reality (ISMAR 2015). | 2015 | [pdf] | P3P with known direction |

A Direct Least-Squares (DLS) Method for PnP | Hesch, J.A. & Roumeliotis, S.I. | ICCV 2011 | 2011 | [pdf] | P3P/PnP |

Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commuta- tive Algebra. | D. A. Cox, J. Little, D. O’Shea. | Springer | 2015 | [book] | An Introduction to Algebraic Geometry. New edition! |

Using Algebraic Geometry. | D. A. Cox, J. Little, D. O’Shea. | Springer | 1998 | [book] | More advanced Algebraic Geometry |

Computing All Solutions to Polynomial Equations in Economics | F. Kubler, P. Renner, K. Schmedders | Handbook of Computational Economics, vol 4, Elsevier | 2014 | [pdf] | Very lightweight intro to polynomial system solving |

Estimating the fundamental matrix under pure translation and radial distortion | C. Steger | ISPRS Journal of Photogrammetry and Remote Sensing, 74:202-217 | 2012 | [pdf] | Relative pose, radial distortion, pure translation |

A Robust Least Squares Solution to the Calibrated Two-View Geometry with Two Known Orientation Angles | G. Nakano and J. Takada | VISIGRAPP 2013, Revised Selected Papers | 2013 | [pdf] | Relative camera pose with known vertical direction |

Globally Optimal DLS Method for PnP Problem with Cayley Parameterization | G. Nakano | BMVC | 2015 | [pdf] | P3P and PnP |

Indoor robot motion based on monocular images | D. Ortin, J. M. M. Montiel | Robotica 19:331-342 | 2001 | [pdf] | Relative pose for planar motion of a calibrated camera from 2pt |

Monocular Visual Odometry and Dense 3D Reconstruction for On-Road Vehicles | M. Zhu, S. Ramalingam, Y. Taguchi, T. Garaas | ECCV | 2012 | [pdf] | Relative pose for planar motion of a calibrated camera from 2pt, closed form |

1-Point-RANSAC Structure from Motion for Vehicle-Mounted Cameras by Exploiting Non-holonomic Constraints | D. Scaramuzza | IJCV 95:74–85 | 2011 | [pdf] | Relative pose for planar non-holonomic motion of a calibrated camera from 1pt |

Classifying and solving minimal structure and motion problems with missing data | M. Oskarsson, K. Astrom, N. C. Overgaard | ICCV | 2001 | [pdf] | 1D and 2D camera, SfM n points in m views classification |

Structure from Motion with Wide Circular Field of View Cameras | B. Micusik, T. Pajdla | IEEE PAMI 18(7):1-15 | 2006 | [pdf] | Catadioptric cameras, radial distortion, generalized cameras, PolyEig |

Minimal solution for uncalibrated absolute pose problem with a known vanishing point | B. Micusik, H. Wildenauer | 3DV | 2013 | [pdf] | Absolute pose, known vertical direction, PolyEig |

Closed form solution for radial distortion estimation from a single vanishing point | B. Micusik, H. Wildenauer | BMVC | 2013 | [pdf] | Radial distortion, focal length, known vertical direction, orthogonal vanishing points, PolyEig |

Relative pose problem for non-overlapping surveillance cameras with known gravity vector | B. Micusik | CVPR | 2011 | [pdf] | Relative pose, non-overlapping cameras, PolyEig |

Rolling Shutter Absolute Pose Problem With Known Vertical Direction | C. Albl, Z. Kukelova, T. Pajdla | CVPR 2016 | 2016 | [pdf] | Absolute pose, Rolling Shutter |

Rolling Shutter Camera Relative Pose: Generalized Epipolar Geometry | Y. Dai, H. Li, L. Kneip | CVPR 2016 | 2016 | [pdf] | Relative pose, Rolling Shutter |

Minimal Solvers for 3D Geometry From Satellite Imagery | E. Zheng, K. Wang, E. Dunn, J-M. Frahm | ICCV 2015 | 2015 | [pdf] | |

A Linear Generalized Camera Calibration From Three Intersecting Reference Planes | M. Nishimura, S. Nobuhara, T. Matsuyama, S. Shimizu, K. Fujii | ICCV 2015 | 2015 | [pdf] | Camera calibration |

Efficient Solvers for Minimal Problems by Syzygy-Based Reduction | V. Larsson, K. Astrom, M. Oskarsson | CVPR 2017 | 2017 | [pdf] | Solver generator |

A Clever Elimination Strategy for Efficient Minimal Solvers | Z. Kukelova, J. Kileel, B. Sturmfels, T. Pajdla | CVPR 2017 | 2017 | [pdf] | elimination, template, minimal solver |

Distortion Varieties | J. Kileel, Z. Kukelova, T. Pajdla, B. Sturmfels | Foundations of Computational Mathematics (2018) 18:1043 | 2018 | [paper] | Radial distortion, relative pose |

A Minimal Solution for Two-View Focal-Length Estimation Using Two Affine Correspondences | D. Barath, T. Toth, L. Hajder | CVPR 2017 | 2017 | [pdf] | Relative pose, focal length |

The Misty Three Point Algorithm for Relative Pose | T. Palmer, K. Astrom, J-M. Frahm | CVPR 2017 | 2017 | [pdf] | Relative pose, underwater |

Toroidal Constraints for Two-Point Localization Under High Outlier Ratios | F. Camposeco, T. Sattler, A. Cohen, A. Geiger, M. Pollefeys | CVPR 2017 | 2017 | [pdf] | Absolute pose, P2P, Outlier rejection |

On the Two-View Geometry of Unsynchronized Cameras | C. Albl, Z. Kukelova, A. Fitzgibbon, J. Heller, M. Smid, T. Pajdla | CVPR 2017 | 2017 | [pdf] | |

A Minimal Solution for Non-Perspective Pose Estimation from Line Correspondences | G. H. Lee | ECCV 2016 | 2016 | ||

Minimal Solvers for Generalized Pose and Scale Estimation from Two Rays and One Point | F. Camposeco, T. Sattler, M. Pollefeys | ECCV 2016 | 2016 | ||

Uncovering Symmetries in Polynomial Systems | V. Larsson, K. Astrom | ECCV 2016 | 2016 | ||

A Versatile Approach for Solving PnP | G. Nakano | ECCV 2016 | 2016 | Absolute Pose, Focal length, Radial distortion, PnPf, PnPfr | |

Accurate and Linear Time Pose Estimation from Points and Lines | A. Vakhitov, J. Funke, F. Moreno-Noguer | ECCV 2016 | 2016 | PnPL | |

Robust and Accurate Line- and/or Point-Based Pose Estimation without Manhattan Assumptions | Y. Salaun, R. Marlet, P. Monasse | ECCV 2016 | 2016 | ||

Using Sparse Elimination for Solving Minimal Problems in Computer Vision | J. Heikkila | ICCV 2017 | 2017 | [pdf] | Resultant |

Polynomial Solvers for Saturated Ideals | V. Larsson, K. Astrom, M. Oskarsson | ICCV 2017 | 2017 | ||

Making Minimal Solvers for Absolute Pose Estimation Compact and Robust | V. Larsson, Z. Kukelova, Y. Zheng | ICCV 2017 | 2017 | P3.5Pf, P4Pfr | |

Beyond Grobner Bases: Basis Selection for Minimal Solvers | V. Larsson, M. Oskarsson, K. Astrom, A. Wallis, Z. Kukelova, T. Pajdla | CVPR 2018 | 2018 | [pdf] | Basis selection |

Five-Point Fundamental Matrix Estimation for Uncalibrated Cameras | D. Barath | CVPR 2018 | 2018 | ||

Hybrid Camera Pose Estimation | F. Camposeco, A. Cohen, M. Pollefeys, T. Sattler | CVPR 2018 | 2018 | Absolute Pose | |

Camera Pose Estimation With Unknown Principal Point | V. Larsson, Z. Kukelova, Y. Zheng | CVPR 2018 | 2018 | Absolute Pose, P4.5Puv, P5Pfuva, P7Pfruv | |

Solving the Perspective-2-Point Problem for Flying-Camera Photo Composition | Z. Lan, D. Hsu, G. H. Lee | CVPR 2018 | 2018 | ||

A Direct Least-Squares Solution to the PnP Problem With Unknown Focal Length | Y. Zheng, L. Kneip | CVPR 2016 | 2016 | [pdf] | |

Efficient Intersection of Three Quadrics and Applications in Computer Vision | Z. Kukelova, J. Heller, A. Fitzgibbon | CVPR 2016 | 2016 | [pdf] | |

Radial Distortion Triangulation | Z. Kukelova, V. Larsson | CVPR 2019 | 2019 | ||

Resultant Based Incremental Recovery of Camera Pose From Pairwise Matches | Y. Kasten, M. Galun, R. Basri | WACV 2019 | 2019 | Generalized relative pose | |

Radially-Distorted Conjugate Translations | J. Pritts, Z. Kukelova, V. Larsson, O. Chum | CVPR 2018 | 2018 | ||

Rectification from Radially-Distorted Scales | J. Pritts, Z. Kukelova, V. Larsson, O. Chum | ACCV 2018 | 2018 | ||

Optimal Trilateration Is an Eigenvalue Problem | M. Larsson, V. Larsson, K. Astrom, M. Oskarsson | ICASSP 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) | 2019 | [pdf] | |

Robust Self-calibration of Constant Offset Time-difference-of-arrival | K. Batstone, G. Flood, T. Beleyur, V. Larsson, H. Goerlitz, M. Oskarsson, K. Astrom | ICASSP 2019-2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) | 2019 | [pdf] | |

Registration and merging maps with uncertainties | M. Larsson, K. Astrom, M. Oskarsson | 2018 IEEE International Conference on Indoor Positioning and Indoor Navigation (IPIN), pp. 206–212 | 2018 | [pdf] | |

City-scale localization for cameras with known vertical direction | L. Svarm, O. Enqvist, F. Kahl, M. Oskarsson | IEEE transactions on Pattern Analysis and Machine Intelligence, 39(7):1455-1461 | 2016 | [pdf] | |

A fast minimal solver for absolute camera pose with unknown focal length and radial distortion from four planar points | M. Oskarsson | arXiv preprint arXiv:1805.10705 | 2018} | [pdf] | |

Two-View Orthographic Epipolar Geometry: Minimal and Optimal Solvers | M. Oskarsson | Journal of Mathematical Imaging and Vision, Springer, 60(2):163-173 | 2018 | [paper] | |

Trust no one: Low rank matrix factorization using hierarchical RANSAC | Oskarsson, Magnus and Batstone, Kenneth and Astrom, Kalle | IEEE Conference on Computer Vision and Pattern Recognition, pp. 5820-5829 | 2016} | [pdf] | |

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Solving polynomial systems via homotopy continuation and monodromy | T. Duff, C. Hill, A. Jensen, K. Lee, A. Leykin, J. Som- mars | IMA Journal of Numerical Analysis | 2018 | [pdf] | General polynomial solving techniques |

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Minimal problems for the calibrated trifocal variety | J. Kileel | SIAM J. Appl. Algebra Geometry | 2018 | [pdf] | Calibrated trifocal minimal problems, linear constraints on the trifocal tensor |

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A minimal closed-form solution for multi-perspective pose estimation using points and lines. | P. Miraldo, T. Dias, S. Ramalingam | ECCV | 2018 | [pdf] | absolute pose, points and lines |

Using galois theory to prove structure from motion algorithms are optimal | D. Nister, R. I. Hartley, and H. Stewenius | CVPR | 2007 | [paper] | relative pose, calibrated, 5 points |

Minimal projective reconstruction for combinations of points and lines | M. Oskarsson, A. Zisserman, K. Astrom | Image Vision Comput | 2004 | [pdf] | projective reconstruction, points and lines |

Trinocular geometry revisited | M. Trager, J. Ponce, and M. Hebert | IJCV | 2016 | [paper] | three views |

Minimal case relative pose computation using ray-point-ray features | J. Zhao, L. Kneip, Y. He, and J. Ma | PAMI | 2019 | [paper] | relative pose, points and lines |

Linear solution to the minimal absolute pose rolling shutter problem. | C. Albl, Z. Kukelova, A. Sugimoto, T. Pajdla | ACCV | 2018 | [paper] | absolute pose, rolling shutter |

Rolling Shutter Camera Relative Pose: Generalized Epipolar Geometry | Y. Dai, H. Li, L. Kneip | CVPR | 2016 | [pdf] | Problem |

A minimal solution to the rolling shutter pose estimation problem | O. Saurer, M. Pollefeys, and G. H. Lee | IROS | 2015 | [pdf] | pose estimation, rolling shutter |

Das pothenotische Problem in erweiterter Gestalt nebst uberseine Anwendungen in der Geodasie | J. A. Grunert | Grunerts Archiv fur Mathematik und Physik, 1:238–248 | 1841 | [pdf] | |

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A computer algorithm for reconstructing a scene fromtwo projections | H. C. Longuet-Higgins | Nature, 293(5828) | 1981 | [] | relative pose, 5 points |

Minimal solutions for generic imaging models | S. Ramalingam, P. Sturm | CVPR | 2008 | [] | generalized non-central cameras |

Optimizing polynomial solvers for minimalgeometry problems | O. Naroditsky, K. Daniilidis | ICCV | 2011 | [] | |

The ideal of the trifocal variety | C. Aholt, L. Oeding | Math. Comput. | 2014 | [] | three views, algebraic geometry |

Efficient solution to the epipolar geometry for radially distorted cameras | Z. Kukelova, J. Heller, M. Bujnak, A. W. Fitzgibbon, and T. Pajdla. | ICCV | 2015 | [] | reative pose, radial distortion |

Rigid multi-view varieties | M. Joswig, J. Kileel, B. Sturmfels, A. Wagne | IJAC 26(4):775-788 | 2016 | [pdf] | multiview algebraic geometry |

Multiview absolute pose using 3D-2D perspective line correspondences and vertical direction | N. Horanyi, Z. Kato | ICCV | 2017 | [pdf] | absolute pose, lines |

On the existence of epipolar matrices | S. Agarwal, H-L. Lee, B. Sturmfels, R. R. Thomas | IJCV | 2017 | [pdf] | multiview algebraic geometry |

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Ideals of the Multiview Variety | S. Agarwal, A, Pryhuber, R. R. Thomas | arXiv:1812:09470 | 2018 | [pdf] | multiview algebraic geometry |

PLMP – Point-Line Minimal Problems in Complete Multi-View Visibility | T Duff, K Kohn, A Leykin, T Pajdla | ICCV | 2019 | [paper,arXiv] | minimal problem classification, complete visibility, point line incidences, homotopy continuation, monodromy |

Rolling Shutter Camera Absolute Pose | C Albl, Z Kukelova, V Larsson, T Pajdla | IEEE PAMI | 2019 | [pdf] | Absolute camera pose, rolling shutter camera, R6P, GB |

Minimal Solutions for Relative Pose with a Single Affine Correspondence | B Guan, J Zhao, Z Li, F Sun, F Fraundorfer | arXiv 1912.10776 | 2019 | [pdf] | relative pose, known vertical direction, planar motion, affine cirrespondence |

A sparse resultant based method for efficient minimal solvers | S Bhayani, Z Kukelova, J Heikkila | arXiv | 2019 | [pdf] | sparse resultant, template, solver |

Trifocal Relative Pose from Lines at Points and its Efficient Solution | R Fabbri, T Duff, H Fan, M Regan, D da Costa de Pinho, E Tsigaridas, C Wampler, J Hauenstein, B Kimia, A Leykin, T Pajdla | arXiv | 2018 | [pdf] | relative pose, calibrated trifocal geometry, homotopy continuation |