## A Variational Approach to Problems in Calibration of Multiple Cameras (2004)

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Venue: | PROC. IEEE CONF. COMPUTER VISION AND PATTERN RECOGNITION |

Citations: | 6 - 2 self |

### BibTeX

@INPROCEEDINGS{Unal04avariational,

author = {Gozde Unal and Anthony Yezzi},

title = {A Variational Approach to Problems in Calibration of Multiple Cameras},

booktitle = {PROC. IEEE CONF. COMPUTER VISION AND PATTERN RECOGNITION},

year = {2004},

pages = {172--178},

publisher = {}

}

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### Abstract

This paper addresses the problem of calibrating camera parameters using variational methods. One problem addressed in this paper is the severe lens distortion in wide angle/inexpensive camera lenses. The camera distortion effects lead to inaccurate 3D reconstructions and geometrical measurements if not accounted for. A second problem is the color calibration problem caused by variations in camera responses which results in different color measurements and affects the algorithms that depend on these measurements. We present multi-view stereo techniques based on variational ideas to address these calibration problems. To reduce computational complexity of such algorithms, we utilize a prior knowledge on the calibration object which is used in the process, and evolve the pose, orientation, and scale parameters of such a 3D model object. We derive the evolution equations for the distortion coefficients, the color calibration parameters of the cameras, and present experimental results which demonstrate their potential use.

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Citation Context ...and intrinsic camera parameters are first obtained by a pinhole camera model neglecting lens distortion. Then, distortion calibration is performed while holding the other parameters fixed [17], [18], =-=[19]-=-. This is possible because the mapping from 3D world coordinates to the 2D image plane can be decomposed into a perspective projection and a mapping that models the deviations from the ideal pinhole c... |

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Citation Context ...trinsic camera parameters as well as camera pose and orientation (extrinsic camera parameters) are estimated by a minimization of an overall cost functional [5], [6], [7], [8], [9], [10], [11], [12], =-=[13]-=-. Many calibration techniques use both nonlinear minimization and closed-form solutions as in [14]. In this paper, we develop a coordinated refinement technique for the extrinsic and intrinsic camera ... |

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Citation Context ... constraints are arranged into a tensor, which is computed with estimated distortion parameters at each step to minimize a reprojection error in an iterative manner. In another group of methods as in =-=[25]-=-, [26], [27], a direct solution strategy is employed to find camera calibration parameters by incorporating lens distortion as well. Our contribution is a new distortion calibration technique that doe... |

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Citation Context ...uch each detected segment is distorted. The curved lines in the image that do not really correspond to 3D line segments will constitute outliers in this optimization procedure [17], [20], [21], [22], =-=[23]-=-. Other techniques such as [24] rely on point correspondences. Given a set of 3D points, the associated epipolar and trilinear constraints are arranged into a tensor, which is computed with estimated ... |

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Citation Context ...ly variational approaches to the 3D reconstruction problem were pioneered by Faugeras and Keriven [1] who also relied on local feature matching. A more recent variational approach by Yezzi and Soatto =-=[2]-=-, [3] proposed a joint region-based image segmentation and simultaneous 3D stereo reconstruction technique. This paper addresses camera calibration techniques built on this latter stereo reconstructio... |

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Citation Context ...r extrinsic and intrinsic camera parameters are first obtained by a pinhole camera model neglecting lens distortion. Then, distortion calibration is performed while holding the other parameters fixed =-=[17]-=-, [18], [19]. This is possible because the mapping from 3D world coordinates to the 2D image plane can be decomposed into a perspective projection and a mapping that models the deviations from the ide... |

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Citation Context ...storted. The curved lines in the image that do not really correspond to 3D line segments will constitute outliers in this optimization procedure [17], [20], [21], [22], [23]. Other techniques such as =-=[24]-=- rely on point correspondences. Given a set of 3D points, the associated epipolar and trilinear constraints are arranged into a tensor, which is computed with estimated distortion parameters at each s... |

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Citation Context ...raints are arranged into a tensor, which is computed with estimated distortion parameters at each step to minimize a reprojection error in an iterative manner. In another group of methods as in [25], =-=[26]-=-, [27], a direct solution strategy is employed to find camera calibration parameters by incorporating lens distortion as well. Our contribution is a new distortion calibration technique that does not ... |

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Citation Context ...Fig. 1 on the left. We capture its views before a dark background with the multiview stereo rig system, a desktop multicamera system designed for remote multimedia collaboration, developed by HP Labs =-=[28]-=-. The images of the calibration object captured from three of the five cameras in the rig are given in Fig. 1. Many desktop multicamera systems use wideangle and inexpensive cameras that produce sever... |

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Citation Context ...constructing reliable digital representations of 3D scenes, accurate camera calibrations are essential. There has been a great deal of research on the camera calibration problem as early as the 1970s =-=[4]-=-. In most of the previous techniques, some sets of features were extracted from images of a known calibration pattern and intrinsic camera parameters as well as camera pose and orientation (extrinsic ... |

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Citation Context ...riational approaches to the 3D reconstruction problem were pioneered by Faugeras and Keriven [1] who also relied on local feature matching. A more recent variational approach by Yezzi and Soatto [2], =-=[3]-=- proposed a joint region-based image segmentation and simultaneous 3D stereo reconstruction technique. This paper addresses camera calibration techniques built on this latter stereo reconstruction fra... |

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Citation Context ...n calibration pattern and intrinsic camera parameters as well as camera pose and orientation (extrinsic camera parameters) are estimated by a minimization of an overall cost functional [5], [6], [7], =-=[8]-=-, [9], [10], [11], [12], [13]. Many calibration techniques use both nonlinear minimization and closed-form solutions as in [14]. In this paper, we develop a coordinated refinement technique for the ex... |

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Citation Context ...ure of how much each detected segment is distorted. The curved lines in the image that do not really correspond to 3D line segments will constitute outliers in this optimization procedure [17], [20], =-=[21]-=-, [22], [23]. Other techniques such as [24] rely on point correspondences. Given a set of 3D points, the associated epipolar and trilinear constraints are arranged into a tensor, which is computed wit... |

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Citation Context ... how much each detected segment is distorted. The curved lines in the image that do not really correspond to 3D line segments will constitute outliers in this optimization procedure [17], [20], [21], =-=[22]-=-, [23]. Other techniques such as [24] rely on point correspondences. Given a set of 3D points, the associated epipolar and trilinear constraints are arranged into a tensor, which is computed with esti... |

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Citation Context ...ttern and intrinsic camera parameters as well as camera pose and orientation (extrinsic camera parameters) are estimated by a minimization of an overall cost functional [5], [6], [7], [8], [9], [10], =-=[11]-=-, [12], [13]. Many calibration techniques use both nonlinear minimization and closed-form solutions as in [14]. In this paper, we develop a coordinated refinement technique for the extrinsic and intri... |

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4 |
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Citation Context ...ion pattern and intrinsic camera parameters as well as camera pose and orientation (extrinsic camera parameters) are estimated by a minimization of an overall cost functional [5], [6], [7], [8], [9], =-=[10]-=-, [11], [12], [13]. Many calibration techniques use both nonlinear minimization and closed-form solutions as in [14]. In this paper, we develop a coordinated refinement technique for the extrinsic and... |

3 |
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Citation Context ...ome these unwanted effects. A common approach taken toward this problem is to calibrate each camera independently through comparisons with known colors on a color calibration object/environment [28], =-=[29]-=-. The color calibration object we use, shown in Fig. 2, is a color cube with patches of known colors whose images are captured from each camera. Demosaicing coefficients are calculated independently f... |

2 |
Stereoscopic segmentation,” Int
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(Show Context)
Citation Context ...tween the reprojection of the 3D calibration object and the image measurements by evolving the distortion parameters of the cameras. This is based on a recent variational approach by Yezzi and Soatto =-=[21, 22]-=- which proposed a joint region-based image segmentation and simultaneous 3D stereo reconstruction technique. Note that early variational approaches to the 3D reconstruction problem were pioneered by F... |

1 |
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(Show Context)
Citation Context ... known calibration pattern and intrinsic camera parameters as well as camera pose and orientation (extrinsic camera parameters) are estimated by a minimization of an overall cost functional [5], [6], =-=[7]-=-, [8], [9], [10], [11], [12], [13]. Many calibration techniques use both nonlinear minimization and closed-form solutions as in [14]. In this paper, we develop a coordinated refinement technique for t... |

1 |
A variational approach to calibration of multiple cameras
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(Show Context)
Citation Context ...nd their correct estimation is one of the first phases of a camera calibration system. 1. An initial version of this work that addresses lens distortion and color calibration can be found in [15] and =-=[16]-=-, and an initial work addressing extrinsic camera calibration appears in [3]. 0162-8828/07/$25.00 ß 2007 IEEE Published by the IEEE Computer SocietysUNAL ET AL.: A VARIATIONAL APPROACH TO PROBLEMS IN ... |