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## Minimal solutions for pose estimation of a multi-camera system (2013)

Venue: | in International Symposium on Robotics Research (ISRR |

Citations: | 6 - 6 self |

### Citations

3924 |
Random Sample Consensus: A Paradigm for Model Fitting
- Fischler, Bolles
- 1981
(Show Context)
Citation Context ...a system. In addition, it is important that the proposed approach is a minimal solution and requires minimal correspondences that makes it efficient to be used within robust estimators such as RANSAC =-=[5]-=- (see Section 5 for more detail). In this paper, we proposed a novel formulation to solve the pose estimation problem of a multi-camera system. In particular, we adopt the representation of noncentral... |

1050 | Scalable Recognition with a Vocabulary Tree
- Nister, Stewenius
- 2006
(Show Context)
Citation Context ...GPS/INS ground truth readings from the second datasets for testing our pose estimation algorithm on both areas. A total of 2500 and 2100 frames are used for testing. We first create a vocabulary-tree =-=[15]-=- with all the SURF features from the map. For every frame from the test dataset, we extract the SURF features, and query for the frame from the map with the highest similarity score with the vocabular... |

405 |
Ideals, Varieties and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra
- Cox, little, et al.
- 1991
(Show Context)
Citation Context ... signed distance from qi×q′i to XGi . Note that λ always has to be positive for the 3D point to appear in front of the camera. 4.2 Minimal Solution for Depths The distances di j where (i, j) ∈ {(1,2),=-=(1,3)-=-,(2,3)} between the 3D points Xi in the world frame FW shown in Figure 2 have to be the same as the distances between the 3D points XGi in the multi-camera frame FG , i.e. ||Xi−X j||2 = ||XGi −XGj ||2... |

313 | Gool, “Speeded-up robust features (SURF
- Bay, Ess, et al.
- 2008
(Show Context)
Citation Context ...ly from each of the test area, i.e. 2× 2 datasets - one for building a map and the other for testing our pose estimation algorithm on the map in each test area. To build the maps, we extract the SURF =-=[1]-=- features, and triangulate the 3D points based on the GPS/INS readings. We apply bundle adjustment (implemented with Google Ceres solver) on the GPS/INS poses and triangulated 3D points to get the fin... |

259 |
Review and Analysis of Solutions of the Three Point Perspective Pose Estimation Problem.
- Haralick, Lee, et al.
- 1994
(Show Context)
Citation Context ... and the images from the multicamera system mounted on it. The fact that the light rays from a multi-camera system do not meet at a single center of projection means that all the classical approaches =-=[6, 17, 13]-=- for solving the perspective pose problem cannot be used. An alternative approach has to be proposed to handle the non-central nature of the multi-camera system. In addition, it is important that the ... |

169 | Linear Pushbroom Cameras
- Gupta, Hartley
- 1997
(Show Context)
Citation Context ...e need for SVD. The proposed method computes the transformation R and t to align the two point sets P and Q consisting of three correspondence 3D points as shown in Equation 7. Pi = RQi+ t, i = 1,2,3 =-=(7)-=- First, two local frames FM and FN are defined on the point sets P and Q respectively. The origins of the local frames are defined on the first points, i.e. P1 and Q1. We can now write the transformed... |

126 |
Closed form solutions of absolute orientation using unit quaternions,”
- Horn
- 1987
(Show Context)
Citation Context ... for solving the pose estimation problem - (a) solve for the unknown depth of the points along the Plücker lines and (b) compute the multi-camera pose from the known depths with absolute orientation =-=[6, 8]-=-. We show that with a minimal number of 3-point correspondences, it leads to an 8 degree polynomial minimal solution that yields up to a maximum of 8 real solutions for the unknown depths. Each of the... |

120 | Linear n-point camera pose determination.
- Quan, Lan
- 1999
(Show Context)
Citation Context ... and the images from the multicamera system mounted on it. The fact that the light rays from a multi-camera system do not meet at a single center of projection means that all the classical approaches =-=[6, 17, 13]-=- for solving the perspective pose problem cannot be used. An alternative approach has to be proposed to handle the non-central nature of the multi-camera system. In addition, it is important that the ... |

82 | Using many cameras as one.
- Pless
- 2003
(Show Context)
Citation Context ...pose estimation problem of a multi-camera system. In particular, we adopt the representation of noncentral light rays from a multi-camera system with the Plücker line coordinates from existing works =-=[16, 12, 10, 11]-=- for relative motion estimation of the multi-camera system. We show that this allows us do a two-step approach for solving the pose estimation problem - (a) solve for the unknown depth of the points a... |

56 | Accurate non-iterative o (n) solution to the pnp problem
- Moreno-Noguer, Lepetit, et al.
- 2007
(Show Context)
Citation Context ... and the images from the multicamera system mounted on it. The fact that the light rays from a multi-camera system do not meet at a single center of projection means that all the classical approaches =-=[6, 17, 13]-=- for solving the perspective pose problem cannot be used. An alternative approach has to be proposed to handle the non-central nature of the multi-camera system. In addition, it is important that the ... |

41 |
A minimal solution to the generalised 3-point pose problem
- Nistér, Stewénius
(Show Context)
Citation Context ...rays as the Plücker lines is holistic and does not require any alternative formulation in any case. In addition, we also derive an efficient closed-form minimal solution for absolute orientation. In =-=[14]-=-, Nister proposed a formulation that directly solves for the rotation and translation parameters. His formulation gives an 8 degree polynomial minimal solution. This method is of special interest as t... |

24 | On pose recovery for generalized visual sensors
- Chen, Chang
(Show Context)
Citation Context ...n 6 for more detail). We verify our approach by showing comparisons with other existing approaches and results from large-scale real-world datasets. 2 Related Works The method proposed by Chen et al. =-=[2]-=- is most related to our method. In this work, they proposed a 3-point minimal solution and N-point solution to the multicamera pose estimation problem. Similar to our method, their proposed solution i... |

22 | A linear approach to motion estimation using generalized camera models,”
- Li, Hartley, et al.
- 2008
(Show Context)
Citation Context ...pose estimation problem of a multi-camera system. In particular, we adopt the representation of noncentral light rays from a multi-camera system with the Plücker line coordinates from existing works =-=[16, 12, 10, 11]-=- for relative motion estimation of the multi-camera system. We show that this allows us do a two-step approach for solving the pose estimation problem - (a) solve for the unknown depth of the points a... |

15 | Globally optimal O(n) solution to the PnP problem for general camera models
- Schweighofer, Pinz
- 2008
(Show Context)
Citation Context ... order of microseconds as noted in Nister’s paper [14]. In contrast to the minimal solvers for the pose estimation problem of the multicamera system, there also exist linear [4] and iterative N-point =-=[18, 19]-=- solutions. The linear solution needs 6 or more point correspondences and thus less efficient in RANSAC [5] compared to our minimal solution which requires only 3 point correspondences. Since the iter... |

12 |
A multi-camera 6-DOF pose tracker
- Tariq, Dellaert
- 2004
(Show Context)
Citation Context ... order of microseconds as noted in Nister’s paper [14]. In contrast to the minimal solvers for the pose estimation problem of the multicamera system, there also exist linear [4] and iterative N-point =-=[18, 19]-=- solutions. The linear solution needs 6 or more point correspondences and thus less efficient in RANSAC [5] compared to our minimal solution which requires only 3 point correspondences. Since the iter... |

5 |
Using multi-camera systems in robotics: Efficient solutions to the NPnP problem
- Kneip, Furgale, et al.
- 2013
(Show Context)
Citation Context ...can also be solved 4 Gim Hee Lee, Bo Li, Marc Pollefeys, and Friedrich Fraundorfer with the Sturm sequencing to achieve the same execution time. Despite the computational efficiency, as also noted in =-=[9]-=-, the derivation of Nister’s method is not intuitive and requires laborious geometry and algebraic reasonings. Kneip et al. presented that most recent work on pose estimation using a multicamera syste... |

4 | Motion estimation for self-driving cars with a generalized camera - Lee, Fraundorfer, et al. - 2013 |

2 |
Structureless pose-graph loop-closures with a multi-camera system on a self-driving car
- Lee, Fraundorfer, et al.
- 2013
(Show Context)
Citation Context ...pose estimation problem of a multi-camera system. In particular, we adopt the representation of noncentral light rays from a multi-camera system with the Plücker line coordinates from existing works =-=[16, 12, 10, 11]-=- for relative motion estimation of the multi-camera system. We show that this allows us do a two-step approach for solving the pose estimation problem - (a) solve for the unknown depth of the points a... |

1 | Gool. Generalised linear pose estimation
- Ess, Neubeck, et al.
- 2007
(Show Context)
Citation Context ...al that can be done in the order of microseconds as noted in Nister’s paper [14]. In contrast to the minimal solvers for the pose estimation problem of the multicamera system, there also exist linear =-=[4]-=- and iterative N-point [18, 19] solutions. The linear solution needs 6 or more point correspondences and thus less efficient in RANSAC [5] compared to our minimal solution which requires only 3 point ... |