## Algorithms for Plane-Based Pose Estimation (2000)

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Citations: | 26 - 7 self |

### BibTeX

@INPROCEEDINGS{Sturm00algorithmsfor,

author = {Peter Sturm},

title = {Algorithms for Plane-Based Pose Estimation},

booktitle = {},

year = {2000},

pages = {706--711}

}

### Years of Citing Articles

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### Abstract

We present several methods for the estimation of relative pose between planes and cameras, based on projections of sets of coplanar features in images. While such methods exist for simple cases, especially one plane seen in one or several views, the aim of this paper is to propose solutions for multi-plane multi-view situations, possibly with little overlap. We propose a factorization-based method for the general case of n planes seen in m views. A mechanism for computing missing data, i.e. when one or several of the planes are not visible in one or several of the images, is described. Finally, a bundle adjustment procedure is developed that optimizes camera and plane pose as well as camera calibration. 1 Introduction The work presented in this paper is part of a project on multi-view 3D modeling based on scene regularities. Scene regularities like coplanarity of points or lines, perpendicularity and parallelism of lines or planes etc. are increasingly used for interactive 3D modeling...

### Citations

1077 |
A versatile camera calibration technique for high accuracy 3D machine vision using off-the-shell TV cameras and lenses
- Tsai
- 1987
(Show Context)
Citation Context ... environments. Pose estimation from planar objects turns out to be rather harder than camera calibration: calibration constraints based on the projection of planar objects with known metric structure =-=[8, 15, 18, 19, 20]-=- can be accumulated over many images. As for pose estimation however, the goal is to obtain relative camera (and plane) pose in a global reference frame: estimation of relative pose of two cameras see... |

928 | Shape and motion from image streams under orthography: A factorization method
- Tomasi, Kanade
- 1992
(Show Context)
Citation Context ...n) quicker, for the small price of subsequent computation of the third columns of the resulting rotation matrices. 4.3 Computing Missing Data Our method suffers, as all factorization approaches (e.g. =-=[17]-=-), from the problem of missing data. As mentioned above, in practice we will very often meet the case where several planes are not visible in several cameras, thus the matrix to factorize is not entir... |

926 | Modeling and rendering architecture from photographs: A hybrid geometry- and image-based approach
- Debevec, Taylor, et al.
- 1996
(Show Context)
Citation Context ...ene regularities. Scene regularities like coplanarity of points or lines, perpendicularity and parallelism of lines or planes etc. are increasingly used for interactive 3D modeling of man-made scenes =-=[1, 2, 3, 12, 14, 16]-=-. Typically, the entire scene (very often a building) is depicted by hand in one or several images; the geometric constraints representing scene regularities allow then to obtain a 3D reconstruction o... |

743 | Closed-form Solution of Absolute Orientation using Unit Quaternions
- Horn
- 1987
(Show Context)
Citation Context ...d matrix coefficients. Concretely, the problem may be formulated as: min T;w; kM \Gamma T 0 @ 1 0 0 1 w 0 0 1 A k 2 F subject to \Gamma T T \Delta T = I 3 : (4) It is easy to show, along the lines of =-=[5]-=-, that the optimal solution for the rotation T can be obtained independently fromsand w, and that the latter may then be obtained from T. The optimal solution for T is obtained by solving the followin... |

398 | Photorealistic scene reconstruction by voxel coloring - Seitz, Dyer - 1999 |

334 | Flexible camera calibration by viewing a plane from unknown orientations
- Zhang
- 1999
(Show Context)
Citation Context ... environments. Pose estimation from planar objects turns out to be rather harder than camera calibration: calibration constraints based on the projection of planar objects with known metric structure =-=[8, 15, 18, 19, 20]-=- can be accumulated over many images. As for pose estimation however, the goal is to obtain relative camera (and plane) pose in a global reference frame: estimation of relative pose of two cameras see... |

136 | In Defence of the 8-point Algorithm
- Hartley
- 1995
(Show Context)
Citation Context ...mputed from point matches between planes and the images (in our experiments the matches are mainly obtained by hand); we use a linear method analogous to the 8-point method for the fundamental matrix =-=[4]-=-. 1 This is simply the matrix of equation (1), the third column being dropped. 2 Notations. As already mentioned above, for a 3 \Theta 3 matrix A, A is the 3 \Theta 2 submatrix consisting of its first... |

136 |
Techniques for Calibration of the Scale Factor and Image Center for High Accuracy 3-D Machine Vision Metrology
- Lenz, Tsai
- 1988
(Show Context)
Citation Context ... environments. Pose estimation from planar objects turns out to be rather harder than camera calibration: calibration constraints based on the projection of planar objects with known metric structure =-=[8, 15, 18, 19, 20]-=- can be accumulated over many images. As for pose estimation however, the goal is to obtain relative camera (and plane) pose in a global reference frame: estimation of relative pose of two cameras see... |

127 | On plane-based camera calibration: A general algorithm, singularities, applications
- Sturm, Maybank
- 1999
(Show Context)
Citation Context |

101 |
Principal component analysis with missing data and its applications to polyhedral object modeling
- Shum, Ikeuchi, et al.
- 1995
(Show Context)
Citation Context ...n practice we will very often meet the case where several planes are not visible in several cameras, thus the matrix to factorize is not entirely defined. Solutions to this problem have been proposed =-=[7, 11, 17]-=-; these are either of an ad hoc or heuristic nature or rely on an initialization by some means. We propose another ad hoc approach for our problem. Our situation is not too bad, since the missing entr... |

62 |
Linear fitting with missing data: Applications to structure-from-motion and to characterizing intensity images
- Jacobs
- 1997
(Show Context)
Citation Context ...n practice we will very often meet the case where several planes are not visible in several cameras, thus the matrix to factorize is not entirely defined. Solutions to this problem have been proposed =-=[7, 11, 17]-=-; these are either of an ad hoc or heuristic nature or rely on an initialization by some means. We propose another ad hoc approach for our problem. Our situation is not too bad, since the missing entr... |

55 | Geometrically constrained structure from motion: Points on planes. 3D Structure from Multiple Images of Large-Scale Environments
- Szeliski, Torr
- 1998
(Show Context)
Citation Context ...ene regularities. Scene regularities like coplanarity of points or lines, perpendicularity and parallelism of lines or planes etc. are increasingly used for interactive 3D modeling of man-made scenes =-=[1, 2, 3, 12, 14, 16]-=-. Typically, the entire scene (very often a building) is depicted by hand in one or several images; the geometric constraints representing scene regularities allow then to obtain a 3D reconstruction o... |

47 | A method for interactive 3D reconstruction of piecewise planar objects from single images
- Sturm, Maybank
- 1999
(Show Context)
Citation Context ...ene regularities. Scene regularities like coplanarity of points or lines, perpendicularity and parallelism of lines or planes etc. are increasingly used for interactive 3D modeling of man-made scenes =-=[1, 2, 3, 12, 14, 16]-=-. Typically, the entire scene (very often a building) is depicted by hand in one or several images; the geometric constraints representing scene regularities allow then to obtain a 3D reconstruction o... |

36 | 3D models of architectural scenes from uncalibrated images and vanishing points
- Cipolla, Robertson
- 1999
(Show Context)
Citation Context |

17 | Interactive 3D Modeling from Multiple Images Using Scene Regularities
- Shum, Szeliski, et al.
- 1998
(Show Context)
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15 |
A complete two-plane camera calibration method and experimental comparisons
- Wei, Ma
- 1993
(Show Context)
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4 |
A Complete Two-Plane Camera Calibration
- Wei, Ma
- 1993
(Show Context)
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3 |
Camera Calibration Problem: Some
- Holt, Netravali
- 1991
(Show Context)
Citation Context ...nar objects with known metric structure: each image of such an object provides two constraints on calibration and, if calibration can be fully determined, relative pose up to two solutions in general =-=[6]-=-. Especially rectangles are very useful since determining their metric structure is done by simply measuring their edge lengths and since they abound in man-made environments. Pose estimation from pla... |

2 |
Duality, Rigidity and Planar Parallax," ECCV
- Criminisi, Reid, et al.
- 1998
(Show Context)
Citation Context |

2 |
Camera Calibration Problem: Some New Results
- Holt, Netravali
- 1991
(Show Context)
Citation Context ...nar objects with known metric structure: each image of such an object provides two constraints on calibration and, if calibration can be fully determined, relative pose up to two solutions in general =-=[6]-=-. Especially rectangles are very useful since determining their metric structure is done by simply measuring their edge lengths and since they abound in man-made environments. Pose estimation from pla... |

1 |
Manual of Photogrammetry," Fourth Edition
- Slama
- 1980
(Show Context)
Citation Context ...0 m 1 C C C C C C C C A = 0 B B B B B B B B @ P i w 0 i1 . . . P i w 0 in P j w 0 1j . . . P j w 0 mj 1 C C C C C C C C A We use a special method to solve this sparse equation system, as described in =-=[13]-=-. The solution is of course only unique up to a translation: adding a 3-vector to all the v j and subtracting it from all the t 0 i does not affect the criterion (8). 4.5 Complete Algorithm 1. Compute... |