#### DMCA

## Recovering The Vanishing Self-Polar Triangle From A Single View Of A Planar Pattern (2000)

Venue: | Proc. ICIP’00 |

Citations: | 1 - 0 self |

### Citations

1509 |
Three-dimensional computer vision: a geometric viewpoint
- Faugeras
- 1993
(Show Context)
Citation Context ...angle with vanishing points as vertices that is self-polar, which means that the three (vanishing) points are mutually conjugated with respect to the absolute conic. Fundamentally, the absolute conic =-=[1]-=- is the key object for (self-)calibration and its image, represented by a 3\Theta3 symmetric matrix ! with five degrees of freedom, carries the metric information of the projective space. Consequently... |

1380 | A flexible new technique for camera calibration - Zhang - 2000 |

244 |
Algebraic Projective Geometry
- Semple, Kneebone
- 1952
(Show Context)
Citation Context ...zero-skew s = 0 and squared pixels u =sv (or equivalently known aspect ratio ), we can write: ( ! 12 = 0 ! 11 = ! 22 (4) Indeed, with respect to an image orthonormal coordinate system, circular points=-=[8]-=- have image complex projective coordinatess[1; \Sigmai; 0] T and, since they lie on the imaged absolute conic, we have (4). Like we did for the known principal point constraints, we solve system (4) w... |

235 | Single View Metrology
- Reid, Zisserman
(Show Context)
Citation Context ...able. Given a single view, a planeto -plane mapping (ie the world plane to image homography) can be estimated and a lot of highly interesting techniques have been recently developped for this purpose =-=[6]-=- [7]. While the image of the absolute conic can be given by a set of three mutually conjugated (vanishing) points [3] v 1 ; v 2 ; v 3 associated with three additional factors ff : fi : fl, the homogra... |

229 |
Using vanishing points for camera calibration.
- Caprile, Torre
- 1990
(Show Context)
Citation Context ...ation of the projective space. Consequently, the recovery of the vanishing self-polar triangle is closely connected to the problem of recovering the metric structure of the scene and it has been shown=-=[2]-=- [3] that a natural camera calibration (ie with a square-pixel with zero-skew constraint) can be done, in a single view, from the vanishing self-polar triangle. In this paper, we are concerned with th... |

167 | Metric rectification for perspective images of planes.
- Liebowitz, Zisserman
- 1998
(Show Context)
Citation Context .... Given a single view, a planeto -plane mapping (ie the world plane to image homography) can be estimated and a lot of highly interesting techniques have been recently developped for this purpose [6] =-=[7]-=-. While the image of the absolute conic can be given by a set of three mutually conjugated (vanishing) points [3] v 1 ; v 2 ; v 3 associated with three additional factors ff : fi : fl, the homography ... |

148 | Autocalibration from planar scenes.
- Triggs
- 1998
(Show Context)
Citation Context ... at least two perpendicular planar patterns[3] or three images of a single planar pattern were required [4]. This calibration problem from a planar pattern recently arouse interest in computer vision =-=[5]-=- because, in many man-made environments, planes are widely present and easily identifiable. Given a single view, a planeto -plane mapping (ie the world plane to image homography) can be estimated and ... |

65 | Combining scene and auto-calibration constraints
- Liebowitz, Zisserman
- 1999
(Show Context)
Citation Context ...n of the projective space. Consequently, the recovery of the vanishing self-polar triangle is closely connected to the problem of recovering the metric structure of the scene and it has been shown[2] =-=[3]-=- that a natural camera calibration (ie with a square-pixel with zero-skew constraint) can be done, in a single view, from the vanishing self-polar triangle. In this paper, we are concerned with the re... |

8 | About conditions for recovering the metric structure of perpendicular planes from the single ground plane to image homography
- Gurdjos, Payrissat
(Show Context)
Citation Context ... this information is not available, a partial knowledge of the camera orientation is equivalent. It includes the special case where the horizontal axis of the camera is "almost" parallel to =-=the ground[9]-=-, which is very likely regarding the camera orientation in some applications (TV broadcast sport images for instance). 3. EXPERIMENTS We applied our technique for recovering the direction orthogonal t... |