## 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@google.com) or Zuzana Kukelova (kukelova@google.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 | 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 | 2105 | [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 | [] | An Introduction to Algebraic Geometry. New edition! |

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

Computing All Solutions to Polynomial Equations in Economics | F. Kubler, P. Renner, K. Schmedders | [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 |

Title | Authors | Published | Year | [pdf] | Problem |

(c) Maintained by Tomas Pajdla (pajdla@google.com) and Zuzana Kukelova (kukelova@google.com). Last update on 28 May 2019.