## The design and implementation of a generic sparse bundle adjustment software package based on the levenberg-marquardt algorithm (2004)

Citations: | 92 - 4 self |

### BibTeX

@TECHREPORT{Lourakis04thedesign,

author = {Manolis I. A. Lourakis and Manolis I. A. Lourakis and Antonis A. Argyros and Antonis A. Argyros},

title = {The design and implementation of a generic sparse bundle adjustment software package based on the levenberg-marquardt algorithm},

institution = {},

year = {2004}

}

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### Abstract

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### Citations

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Numerical Recipes: The Art of Scientific Computing
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(Show Context)
Citation Context ...the LM algorithm based on the material in [16] is supplied next. Note, however, that a detailed analysis of the LM algorithm is beyond the scope of this paper and the interested reader is referred to =-=[16, 20, 22]-=- for more comprehensive treatments. In the following, vectors and arrays appear in boldface and T is used to denote transposition. Also, jj:jj and jj:jj1 denote the 2 and infinity norms respectively. ... |

843 |
An Algorithm for Least-Squares Estimation of nonlinear Parameters
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Citation Context ...evenberg-Marquardt Algorithm The LM algorithm is an iterative technique that locates the minimum of a multivariate function that is expressed as the sum of squares of non-linear real-valued functions =-=[13, 17]-=-. It has become a standard technique for non-linear least-squares problems, widely adopted in the field of computer vision. LM can be thought of as a combination of steepest descent and the Gauss-Newt... |

413 | Bundle adjustment – a modern synthesis
- Triggs, McLauchlan, et al.
- 2000
(Show Context)
Citation Context ...ed in the field of photogrammetry [24] and has increasingly been used by vision researchers during the last decade. An excellent overview of its application to vision-based reconstruction is given in =-=[25]-=-. BA is a technique for simultaneously refining the 3D structure and viewing parameters (i.e. camera pose and possibly intrinsic calibration and radial distortion), to obtain a reconstruction which is... |

334 | An Introduction to the Conjugate Gradient Method Without the Agonizing Pain", www.cs.cmu.edu
- Shewchuk
- 1994
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Citation Context ... to employing a solver based on the conjugate gradients (CG) method. Thus, sba incorporates an iterative linear systems solver that is based on conjugate gradients with jacobi or SSOR preconditioning =-=[23, 2]-=-. sba motstr levmar x() implements a forward communication mechanism; its arguments are explained one by one in the following, where I and O denote input and output arguments respectively: n : The num... |

66 |
User guide for MINPACK-1
- Moré, Garbow, et al.
- 1980
(Show Context)
Citation Context ...h computation of the solution to a dense linear system has complexity O(N 3) in the number of parameters, it is clear that general purpose implementations of the LM algorithm, such as MINPACK's lmder =-=[19]-=- or PORT3's dn2g 1 [5] routines for example, are computationally very demanding when employed to minimize functions depending on many parameters. Fortunately, when solving minimization problems arisin... |

28 |
Manual of Photogrammetry
- Slama, ed
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(Show Context)
Citation Context ...iably used as the last step of every featurebased multiview structure and motion estimation algorithm; see, for example, [10, 3, 6, 21, 27]. BA was originally conceived in the field of photogrammetry =-=[24]-=- and has increasingly been used by vision researchers during the last decade. An excellent overview of its application to vision-based reconstruction is given in [25]. BA is a technique for simultaneo... |

17 | Incremental Motion Estimation Through Local Bundle Adjustment
- Zhang, Shan
- 2001
(Show Context)
Citation Context ...ndle Adjustment Package 1 1 Introduction Bundle Adjustment (BA) is almost invariably used as the last step of every featurebased multiview structure and motion estimation algorithm; see, for example, =-=[10, 3, 6, 21, 27]-=-. BA was originally conceived in the field of photogrammetry [24] and has increasingly been used by vision researchers during the last decade. An excellent overview of its application to vision-based ... |

15 |
Damping parameter in marquardt's method
- Nielsen
- 1999
(Show Context)
Citation Context ...the LM algorithm based on the material in [16] is supplied next. Note, however, that a detailed analysis of the LM algorithm is beyond the scope of this paper and the interested reader is referred to =-=[16, 20, 22]-=- for more comprehensive treatments. In the following, vectors and arrays appear in boldface and T is used to denote transposition. Also, jj:jj and jj:jj1 denote the 2 and infinity norms respectively. ... |

10 |
Visual modeling with a hand-held camera,” Int
- Pollefeys, Gool, et al.
- 2004
(Show Context)
Citation Context ...ndle Adjustment Package 1 1 Introduction Bundle Adjustment (BA) is almost invariably used as the last step of every featurebased multiview structure and motion estimation algorithm; see, for example, =-=[10, 3, 6, 21, 27]-=-. BA was originally conceived in the field of photogrammetry [24] and has increasingly been used by vision researchers during the last decade. An excellent overview of its application to vision-based ... |

5 | Quaternions and Rotations in 3-Space: The Algebra and its Geometric Interpretation
- Vicci
- 2001
(Show Context)
Citation Context ...ion of a 3D rotation and a 3D translation. A 3D rotation by an angle ` about a unit vector u = (u1; u2; u3)T is represented by the quaternion R = (cos( `2 ); u1 sin( `2 ); u2 sin( `2 ); u3 sin( `2 )) =-=[26]-=-. A 3D translation is defined by a vector t. A 3D point is represented by its Euclidean coordinate vector M. Thus, the parameters of each camera j and point i are aj = (Rj; tjT )T and bi = Mi, respect... |

2 |
The Least Squares Problem. [web page] http://plato.asu.edu/topics/problems/nlolsq.html
- Mittelmann
- 2004
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Citation Context ...erved and predicted image points, which is expressed as the sum of squares of a number of nonlinear real-valued functions. Thus, the minimization is achieved using non-linear least squares algorithms =-=[4, 18]-=-, of which the Levenberg-Marquardt (LM) has proven to be the most successful due to its use of an effective damping strategy that lends it the ability to converge promptly from a wide range of initial... |

1 | The Design and Implementation of a Sparse Bundle Adjustment Package 21 [16 - Madsen, Nielsen, et al. - 2004 |