### Citations

8928 | Distinctive image features from scale-invariant keypoints
- Lowe
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Citation Context ...own calibration matrices. 3 OVERVIEW Given n input images, we follow a standard global SfM pipeline. 1. A collection of key-points across the images is extracted and matched (typically by using SIFT (=-=Lowe, 2004-=-)); 2. The essential matrices Eij are computed from the matching points by using the 8−point Algorithm in combination with RANSAC, and subsequently refined by using a GaussNewton type algorithm on the... |

4732 |
Multiple View Geometry in Computer Vision, 2nd ed
- Hartley, Zisserman
- 2004
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Citation Context ...ee solvability. 2 BACKGROUND In this section we provide a brief summary of the main concepts in multi-view geometry, useful to define our method. A complete treatment of this subject can be found in (=-=Hartley and Zisserman, 2004-=-). The camera model is the pinhole camera, which is described by its centre c and the image plane. The distance of the image plane from c is the focal length. The line from the camera centre perpendic... |

1363 | Using sedumi 1.02, a matlab toolbox for optimization over symmetric cones. Optimization Methods and Software
- Sturm
- 1999
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Citation Context ...tter enforces the matrix G to be symmetric positive semidefinite and to have identity blocks along its diagonal. In our implementation, the MATLAB command eigs is used for EIG and the SeDuMi toolbox (=-=Sturm, 1999-=-) for SDP. We also include in our analysis the matrix completion algorithm OPTSPACE, whose MATLAB 1code has been provided by the authors of (Keshavan et al., 2009). To evaluate the accuracy of attitud... |

676 | Photo tourism: Exploring photo collections
- Snavely, Seitz, et al.
- 2006
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Citation Context ...here first stereo-models are built and co-registered, structure-and-motion methods, such as bundle block adjustment (e.g. (Triggs et al., 2000)), resection-intersection methods (Brown and Lowe, 2005, =-=Snavely et al., 2006-=-), hierarchical methods (Gherardi et al., 2010, Ni and Dellaert, 2012)), where “structure” and “motion” are solved simultaneously, and – more recently – motion-first methods (Govindu, 2001, Martinec a... |

562 | Bundle adjustment - a modern synthesis
- Triggs, McLauchlan, et al.
- 2000
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Citation Context ...ke independent models block adjustments (e.g. (Crosilla and Beinat, 2002)), where first stereo-models are built and co-registered, structure-and-motion methods, such as bundle block adjustment (e.g. (=-=Triggs et al., 2000-=-)), resection-intersection methods (Brown and Lowe, 2005, Snavely et al., 2006), hierarchical methods (Gherardi et al., 2010, Ni and Dellaert, 2012)), where “structure” and “motion” are solved simulta... |

354 | The power of convex relaxation: Near-optimal matrix completion - Cands, Tao |

285 | Matrix rank minimization with applications - Fazel - 2002 |

191 | Matrix completion from a few entries
- Keshavan, Oh, et al.
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Citation Context ...e incomplete matrix is known, as will be explained below. Many authors have proposed efficient methods to solve this problem, such as OPTSPACE, a gradient descent algorithm on the Grassmann manifold (=-=Keshavan et al., 2009-=-). 4.2 Proposed Algorithm LetRij ∈ SO(3) denote the relative rotation between coordinate frames indexed by j and i, and let bRij be an estimate of Rij , obtained through the essential matrix factoriza... |

128 | On benchmarking camera calibration and multi-view stereo for high resolution imagery”, - Strecha, Hansen, et al. - 2008 |

88 |
Unsupervised 3D object recognition and reconstruction in unordered datasets
- Brown, Lowe
- 2005
(Show Context)
Citation Context ... and Beinat, 2002)), where first stereo-models are built and co-registered, structure-and-motion methods, such as bundle block adjustment (e.g. (Triggs et al., 2000)), resection-intersection methods (=-=Brown and Lowe, 2005-=-, Snavely et al., 2006), hierarchical methods (Gherardi et al., 2010, Ni and Dellaert, 2012)), where “structure” and “motion” are solved simultaneously, and – more recently – motion-first methods (Gov... |

75 | Robust rotation and translation estimation in multiview reconstruction
- Martinec, Pajdla
- 2007
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Citation Context ... al., 2006), hierarchical methods (Gherardi et al., 2010, Ni and Dellaert, 2012)), where “structure” and “motion” are solved simultaneously, and – more recently – motion-first methods (Govindu, 2001, =-=Martinec and Pajdla, 2007-=-, Kahl and Hartley, 2008, Enqvist et al., 2011, ArieNachimson et al., 2012, Moulon et al., 2013) that first solve for the “motion” and then recover the “structure”. All these motionfirst methods are g... |

30 | Combining two-view constraints for motion estimation
- Govindu
- 2001
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Citation Context ...005, Snavely et al., 2006), hierarchical methods (Gherardi et al., 2010, Ni and Dellaert, 2012)), where “structure” and “motion” are solved simultaneously, and – more recently – motion-first methods (=-=Govindu, 2001-=-, Martinec and Pajdla, 2007, Kahl and Hartley, 2008, Enqvist et al., 2011, ArieNachimson et al., 2012, Moulon et al., 2013) that first solve for the “motion” and then recover the “structure”. All thes... |

28 |
A.: Improving the efficiency of hierarchical structure-and-motion
- Gherardi, Farenzena, et al.
(Show Context)
Citation Context ...istered, structure-and-motion methods, such as bundle block adjustment (e.g. (Triggs et al., 2000)), resection-intersection methods (Brown and Lowe, 2005, Snavely et al., 2006), hierarchical methods (=-=Gherardi et al., 2010-=-, Ni and Dellaert, 2012)), where “structure” and “motion” are solved simultaneously, and – more recently – motion-first methods (Govindu, 2001, Martinec and Pajdla, 2007, Kahl and Hartley, 2008, Enqvi... |

26 |
Metrics for 3D rotations: Comparison and analysis
- Huynh, Q
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Citation Context ... matrix completion algorithm OPTSPACE, whose MATLAB 1code has been provided by the authors of (Keshavan et al., 2009). To evaluate the accuracy of attitude estimation, any of the metrics analyzed in (=-=Huynh, 2009-=-) can be used, since they all are biinvariant and respect the topology of SO(3). In our experiments we choose the angular (chordal) distance, which takes values in the range [0, 180◦]. To generate the... |

18 | Non-sequential structure from motion. In:
- Enqvist, Kahl, et al.
- 2011
(Show Context)
Citation Context ... 2010, Ni and Dellaert, 2012)), where “structure” and “motion” are solved simultaneously, and – more recently – motion-first methods (Govindu, 2001, Martinec and Pajdla, 2007, Kahl and Hartley, 2008, =-=Enqvist et al., 2011-=-, ArieNachimson et al., 2012, Moulon et al., 2013) that first solve for the “motion” and then recover the “structure”. All these motionfirst methods are global, for they take into account the whole ep... |

18 | Cycle bases in graphs: Characterization, algorithms, complexity, and applications
- Kavitha, Liebchen, et al.
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Citation Context ...the EOK-Algorithm. To overcome this drawback, we propose a novel algorithm based on the notion of cycle basis. Indeed, cycles in a graph form a vector space over the field Z2 of dimension nE −nV +nC (=-=Kavitha et al., 2009-=-), where nE is the number of edges, nV is the number of vertices, and nC is the number of connected components of the graph. A basis for the vector space can be constructed by “completing a spanning f... |

16 | Rotation averaging
- Hartley, Trumpf, et al.
(Show Context)
Citation Context ...t be compatible. Thus an appropriate minimization problem is min R1,...,Rn∈SO(3) X (i,j)∈N ‖ bRij −RiRTj ‖2F . (10) Problem (10) is known as Multiple Rotation Averaging in computer vision literature (=-=Hartley et al., 2013-=-). Note that the solution is determined up to a global rotation, corresponding to a change in orientation of the external coordinate system. This fact is inherent to the problem and cannot be resolved... |

15 | Global motion estimation from point matches
- Arie-Nachimson, Kovalsky, et al.
- 2012
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Citation Context ...formulate a novel algorithm to remove the outliers among the relative rotations, presented in Section 5. Finally, in Section 6 we provide a theoretical analysis of the linear algorithm introduced in (=-=Arie-Nachimson et al., 2012-=-), that solve for exterior positions. The discussion carried out in the paper is supported by experimental results on both synthetic and real images, shown in Section 7. The conclusions along with pos... |

15 | Essential matrix estimation using Gauss-Newton iterations on a manifold
- Helmke, Hüper, et al.
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Citation Context ...computed from the matching points by using the 8−point Algorithm in combination with RANSAC, and subsequently refined by using a GaussNewton type algorithm on the Essential Manifold, as explained in (=-=Helmke et al., 2007-=-). Finally, they are factorized via Singular Value Decomposition (SVD) to obtain the relative rotations Rij of the cameras (Hartley and Zisserman, 2004); 3. Exterior camera orientation is computed as ... |

14 | Multiple-view geometry under the l∞-norm. Pattern Analysis and Machine Intelligence,
- Kahl, Hartley
- 2008
(Show Context)
Citation Context ...ethods (Gherardi et al., 2010, Ni and Dellaert, 2012)), where “structure” and “motion” are solved simultaneously, and – more recently – motion-first methods (Govindu, 2001, Martinec and Pajdla, 2007, =-=Kahl and Hartley, 2008-=-, Enqvist et al., 2011, ArieNachimson et al., 2012, Moulon et al., 2013) that first solve for the “motion” and then recover the “structure”. All these motionfirst methods are global, for they take int... |

14 |
Closest unitary, orthogonal and hermitian operators to a given operator
- Keller
- 1975
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Citation Context ...ach gradient descent step with a projection onto SO(3) of each 3 × 3 block in R. The nearest rotation (in the Frobenius norm sense) can be found through singular value decomposition, as explained in (=-=Keller, 1975-=-). 5 CYCLES AND CONSISTENCY In this section we explain how to detect the outliers among the relative rotations. The presence of false two-view geometries, which generate outliers, is a common situatio... |

8 |
Use of generalised Procrustes analysis for the photogrammetric block adjustment by independent models.
- Crosilla, Beinat
- 2002
(Show Context)
Citation Context ...ras are known, namely the focal length and the coordinates of the principal point. Structure-from-motion methods can be classified as: structurefirst, like independent models block adjustments (e.g. (=-=Crosilla and Beinat, 2002-=-)), where first stereo-models are built and co-registered, structure-and-motion methods, such as bundle block adjustment (e.g. (Triggs et al., 2000)), resection-intersection methods (Brown and Lowe, 2... |

8 | Global fusion of relative motions for robust, accurate and scalable structure from motion.
- Moulon, Monasse, et al.
- 2013
(Show Context)
Citation Context ...and “motion” are solved simultaneously, and – more recently – motion-first methods (Govindu, 2001, Martinec and Pajdla, 2007, Kahl and Hartley, 2008, Enqvist et al., 2011, ArieNachimson et al., 2012, =-=Moulon et al., 2013-=-) that first solve for the “motion” and then recover the “structure”. All these motionfirst methods are global, for they take into account the whole epipolar graph, whose nodes represent the views and... |

1 |
Robust absolute rotation estimation via low-rank and sparse matrix decomposition
- Arrigoni, Rossi, et al.
- 2014
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Citation Context ...oblem. As an alternative, we are developing a matrix completion algorithm which is robust both with respect to noise and outliers, avoiding the need of a demanding preliminary outlier rejection step (=-=Arrigoni et al., 2014-=-). Finally, we plan to investigate The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XL-5, 2014 ISPRS Technical Commission V Symposium, 23 – 25 ... |