## Fast and Globally Convergent Pose Estimation From Video Images (1998)

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Citations: | 119 - 5 self |

### BibTeX

@MISC{Lu98fastand,

author = {Chien-ping Lu and Gregory D. Hager and Eric Mjolsness},

title = {Fast and Globally Convergent Pose Estimation From Video Images},

year = {1998}

}

### Years of Citing Articles

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### Abstract

Determining the rigid transformation relating 2D images to known 3D geometry is a classical problem in photogrammetry and computer vision. Heretofore, the best methods for solving the problem have relied on iterative optimization methods which cannot be proven to converge and/or which do not effectively account for the orthonormal structure of rotation matrices. We show that the pose estimation problem can be formulated as that of minimizing an error metric based on collinearity in object (as opposed to image) space. Using object space collinearity error, we derive an iterative algorithm which directly computes orthogonal rotation matrices and which is globally convergent. Experimentally, we show that the method is computationally efficient, that it is no less accurate than the best currently employed optimization methods, and that it outperforms all tested methods in robustness to outliers. Chien-Ping Lu, Silicon Graphics Inc. cplu@engr.sgi.com y Greg Hager, Department of Computer...

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Citation Context ...0 ß 2000 IEEE problem and to solve it by nonlinear optimization algorithms, most typically, the Gauss-Newton method [13], [14], [15]. In the vision literature, the work by Lowe and its variants [16], =-=[17]-=- is an example of applying the Gauss-Newton method to the pose estimation problem. As with most nonlinear optimizations, these methods rely on a good initial guess to converge to the correct solution.... |

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Citation Context ...cations of the reference points on the object by slight modification of the objective function. The optimization could also be easily extended to perform a robust optimization step using IRLS methods =-=[44]-=-, making it yet more robust to outliers. In addition, our results suggest that OI tends to find the correct pose solution, suggesting that there are few, if any, spurious local minima. We are currentl... |

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Citation Context ...thods for pose estimation has been developed by relaxing the orthogonality constraint on rotation matrices and/or by simplifying the perspective camera model [18], [19], [20], [21], [22], [23], [24], =-=[25]-=-. In iterative reduced perspective methods [23], [26], an approximate solution computed using a simplified camera model is iteratively refined to approach a full perspective solution. In these methods... |

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Citation Context ... be computed: A fourth- or fifth-degree polynomial system can be formulated using geometrical invariants of the observed points and the problem can be solved by finding roots of the polynomial system =-=[7]-=-, [8], [9], [10], [11], [12]. However, the resulting methods can only be applied to a limited number of points and are thus sensitive to additive noise and possible outliers. For more than four points... |

3 |
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Citation Context ...omputed: A fourth- or fifth-degree polynomial system can be formulated using geometrical invariants of the observed points and the problem can be solved by finding roots of the polynomial system [7], =-=[8]-=-, [9], [10], [11], [12]. However, the resulting methods can only be applied to a limited number of points and are thus sensitive to additive noise and possible outliers. For more than four points, clo... |

3 |
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Citation Context ... fourth- or fifth-degree polynomial system can be formulated using geometrical invariants of the observed points and the problem can be solved by finding roots of the polynomial system [7], [8], [9], =-=[10]-=-, [11], [12]. However, the resulting methods can only be applied to a limited number of points and are thus sensitive to additive noise and possible outliers. For more than four points, closed form so... |

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2 |
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Citation Context ...puter graphics, it plays a central role in tasks that combine computer-generated objects with photographic scenesÐe.g., landmark tracking for determining head pose in augmented reality [2], [3], [4], =-=[5]-=- or interactive manipulation of objects. In computer vision, pose estimation is central to many approaches to object recognition [6]. The information available for solving the pose estimation problem ... |

2 |
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Citation Context ...to: tpami@computer.org, and reference IEEECS Log Number 107625. æ 0162-8828/00/$10.00 ß 2000 IEEE problem and to solve it by nonlinear optimization algorithms, most typically, the Gauss-Newton method =-=[13]-=-, [14], [15]. In the vision literature, the work by Lowe and its variants [16], [17] is an example of applying the Gauss-Newton method to the pose estimation problem. As with most nonlinear optimizati... |

2 |
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Citation Context ...ate methods for pose estimation has been developed by relaxing the orthogonality constraint on rotation matrices and/or by simplifying the perspective camera model [18], [19], [20], [21], [22], [23], =-=[24]-=-, [25]. In iterative reduced perspective methods [23], [26], an approximate solution computed using a simplified camera model is iteratively refined to approach a full perspective solution. In these m... |

2 |
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Citation Context ...ALLY CONVERGENT POSE ESTIMATION FROM VIDEO IMAGES 613 Gauss-Newton method. It has become a standard technique for nonlinear least-squares problems and has been widely adopted in computer vision [30], =-=[31]-=- and computer graphics [3]. 2.3 Why Another Iterative Algorithm? Classical optimization techniques are currently the only choice when observed data is noisy and a high accuracy solution to the pose es... |

1 |
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Citation Context ...ami@computer.org, and reference IEEECS Log Number 107625. æ 0162-8828/00/$10.00 ß 2000 IEEE problem and to solve it by nonlinear optimization algorithms, most typically, the Gauss-Newton method [13], =-=[14]-=-, [15]. In the vision literature, the work by Lowe and its variants [16], [17] is an example of applying the Gauss-Newton method to the pose estimation problem. As with most nonlinear optimizations, t... |

1 |
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Citation Context ...ion. A class of approximate methods for pose estimation has been developed by relaxing the orthogonality constraint on rotation matrices and/or by simplifying the perspective camera model [18], [19], =-=[20]-=-, [21], [22], [23], [24], [25]. In iterative reduced perspective methods [23], [26], an approximate solution computed using a simplified camera model is iteratively refined to approach a full perspect... |

1 |
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Citation Context ...ing the orthogonality constraint on rotation matrices and/or by simplifying the perspective camera model [18], [19], [20], [21], [22], [23], [24], [25]. In iterative reduced perspective methods [23], =-=[26]-=-, an approximate solution computed using a simplified camera model is iteratively refined to approach a full perspective solution. In these methods, the rotation matrix is computed in two steps: First... |

1 |
et al., ªPose Estimation from Corresponding Point Data,º
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Citation Context ...ds there is no guarantee that they will eventually converge to the correct solution when applied iteratively. The developments in this article were originally motivated by the work of Haralick et al. =-=[28]-=-. They introduced a pose estimation algorithm which simultaneously computes both object pose and the depths of the observed points. The algorithm seems to be globally convergent, although a complete p... |

1 |
Computer and Robot Vision, chapter 14
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Citation Context ...However, when the current solution is far from the correct one and/or the linear system is illconditioned, it may converge slowly or even fail to converge altogether. It has been empirically observed =-=[29]-=- that, for the Gauss-Newton method to work, the initial approximate solutions have to be within 10 percent of scale for translation and within 15 o for each of the three rotation angles. The Levenberg... |

1 |
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Citation Context ...rmediate absolute orientation problem can now be formulated as a scalar-weighted least squares X n iˆ1 1 d …k† i 2 kRp i ‡ t ^Vi R …k† p i ‡ t …k† k 2 : …46† Such weighting schemes were used in [40], =-=[41]-=- and can be easily incorporated into the algorithm developed above. Note, however, that this kind of bias is significant only when the object is very close to the camera or the depth of the object is ... |

1 |
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Citation Context ... determine the conditions under which the pose computed by OI is unique and the error of OI can be analytically determined. We are currently implementing a version of the algorithm within the XVision =-=[45]-=- environment for use in robotic applications, as well as augmented and virtual reality. An initial implementation described in [46] has shown that, by combining efficient local tracking with efficient... |

1 |
ªOnline Pose Estimation and Model Matching,º
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Citation Context ...currently implementing a version of the algorithm within the XVision [45] environment for use in robotic applications, as well as augmented and virtual reality. An initial implementation described in =-=[46]-=- has shown that, by combining efficient local tracking with efficient pose estimation, it is relatively simple to construct a real-time object tracking system which runs on typical desktop hardware. A... |

1 | An automatic registration method for frameless stereotaxy, image guided surgery, and enhanced reality visualization - al - 1994 |