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## A neural approach to zoom-lens camera calibration from data with outliers

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### Citations

5963 |
Neural Networks: A comprehensive Foundations, Second edition
- Haykin
- 2001
(Show Context)
Citation Context ... use variable or adaptive sampling spacings, where more samples are taken in regions with high parameter variations. Another direction worth investigating is to use one of the network pruning methods =-=[16]-=- to find parameter MLFNs with minimum size and yet with good generalization. In this case, each MLFN starts with a large size then it is pruned by weakening or eliminating certain weights in a selecti... |

2970 |
Robust statistics
- Huber
- 2011
(Show Context)
Citation Context ...ion should be pursued; one bad outlier would skew the results of any approach based on the widely used least squares estimates. We therefore propose to use the maximum likelihood estimator Mestimator =-=[13]-=- as a more robust estimator. The rest of this paper is organized as follows. We describe the camera model and state the calibration problem in Section 2. In Section 3, we briefly describe the neurocal... |

1893 |
Multilayer feedforward networks are universal approximations,
- Hornik, Stinchcombe, et al.
- 1989
(Show Context)
Citation Context ...o represent any model function on continuous ranges of lens control space. In particular, we resort to the proven power of multi-layered feedforward neural networks (MLFNs) as universal approximators =-=[6]-=- to provide suitable parameter formulation/ fitting. This can take care of the second point, but one still needs to consider the interaction between these MLFNs in such way that minimizes the calibrat... |

1737 |
Robust Regression and Outlier Detection,
- Rousseeuw, Leroy
- 1987
(Show Context)
Citation Context ...twork training, one can make a good, robust estimate of the standard deviation of the errors of good data (inliers). This estimate is related to the median of the absolute values of the residuals, sˆ =-=[12]-=-. Any data item whose error is larger than a certain number (e.g. 2.5–3.0) of sˆ can be considered as an outlier and removed. We are currently investigating another approach based on LMedS estimates [... |

957 |
Robust statistics: The approach based on influence functions.
- Hampel, Ronchetti, et al.
- 1986
(Show Context)
Citation Context ...he residuals, P irðr iÞ, where r is a symmetric, positive-definite function with a unique minimum at zero, and is chosen to be less increasing than square. Many of such r function have been suggested =-=[13, 14]-=-, which yield breakdown points of about 1/p, where p is the number of unknowns (p 11 in case of camera calibration). M-estimators have high efficiencies, typically 0.9 [14] (efficiency is defined as... |

316 |
Camera calibration with distortion models and accuracy evaluation,’’
- Weng, Cohen, et al.
- 1992
(Show Context)
Citation Context ...wo scale factors au and av, and the skew c between the image axes. This camera model thus ignores lens distortion which is often accounted for in the camera model by adding some distortion parameters =-=[1]-=-. However, with the state of the art of the technology, camera distortion is reasonably small, and the pinhole model is thus a good approximation. On the other hand, if lens distortion is noticeable (... |

275 |
Robust regression methods for computer vision: A review.
- Meer, Mintz, et al.
- 1991
(Show Context)
Citation Context ..., many robust techniques have been proposed [12–14] to handle outliers and these techniques have gained popularity in computer vision M. Ahmed, A. Farag / Image and Vision Computing 20 (2002) 619–630 =-=[18]-=-. Robust estimates include M-estimates (maximum likelihood estimates), L-estimates (linear combination of order statistics), R-estimates (estimates based on rank transformations) and LMedS estimates (... |

102 | Non-metric calibration of wide-angle lenses and polycameras.
- Swaminathan, Nayar
- 1999
(Show Context)
Citation Context ...On the other hand, if lens distortion is noticeable (this may be thescase at small camera focal length), the distortion parameters can be estimated in the captured images by a pre-calibration process =-=[3,7]-=- keeping in mind that these parameters may vary with lens settings. Then the images or image features can be undistorted before calibration proceeds. In this work, we follow this strategy for a couple... |

102 | Modeling and Calibration of Automated Zoom Lenses
- Willson
(Show Context)
Citation Context ...calibration techniques. The calibrated model parameters at each lens setting are then stored in lookup tables [2,8], or polynomials (or perhaps other functions) are formulated to model the parameters =-=[4,5,9]-=-. The following remarks can be drawn on the previous approaches: † Using interpolation to obtain each model parameter at intermediate lens settings in tables or fitting a function to each parameter in... |

40 |
Line-Based Correction of Radial Lens Distortion
- Prescott, McLean
- 1997
(Show Context)
Citation Context ...On the other hand, if lens distortion is noticeable (this may be thescase at small camera focal length), the distortion parameters can be estimated in the captured images by a pre-calibration process =-=[3,7]-=- keeping in mind that these parameters may vary with lens settings. Then the images or image features can be undistorted before calibration proceeds. In this work, we follow this strategy for a couple... |

34 | Some aspects of zoom lens camera calibration
- Li, Lavest
- 1996
(Show Context)
Citation Context ...e model) at a number of lens settings which span the lens control space using traditional calibration techniques. The calibrated model parameters at each lens setting are then stored in lookup tables =-=[2,8]-=-, or polynomials (or perhaps other functions) are formulated to model the parameters [4,5,9]. The following remarks can be drawn on the previous approaches: † Using interpolation to obtain each model ... |

22 | Calibration of an Active Binocular Head.
- Shih, Hung, et al.
- 1998
(Show Context)
Citation Context ...does not consider the interaction between all the model parameters to represent the underlying camera model. † Polynomials in many cases fail to follow the complex variations in some model parameters =-=[2,10]-=-. Although other alternatives such as exponential functions, Chebyshev polynomials and Legendre polynomials can be exploited, the question about the optimal (or best)s620 Fig. 1. CardEye trinocular ac... |

13 |
Calibration of a computer controlled robotic vision sensor with a zoom lens
- Tarabanis, Tsai, et al.
- 1994
(Show Context)
Citation Context ...e model) at a number of lens settings which span the lens control space using traditional calibration techniques. The calibrated model parameters at each lens setting are then stored in lookup tables =-=[2,8]-=-, or polynomials (or perhaps other functions) are formulated to model the parameters [4,5,9]. The following remarks can be drawn on the previous approaches: † Using interpolation to obtain each model ... |

12 |
Geometric calibration of zoom lenses for computer vision metrology. Photogrammetric Engineering and Remote Sensing,
- Wiley, Wong
- 1995
(Show Context)
Citation Context ...e interaction between the different camera model parameters and to improve the calibration accuracy. We believe that this approach has the following key features, as opposed to other techniques (e.g. =-=[4,5,9,10]-=-): 1. It is general; it can consider, in a straightforward manner, any number/combination of lens control parameters, e.g. zoom, focus and/or aperture. 2. Since no a priori knowledge about how lens se... |

11 | Neurocalibration: A Neural Network That Can Tell Camera Calibration Parameters, Computer Vision
- Ahmed, Hemayed, et al.
- 1999
(Show Context)
Citation Context ...twork. SettingError 0. for all input–output patterns at si do Compute calibration error, 1, from Eq. (7). All weights of central network are updated according to the neurocalibration updating rules =-=[11]-=-. SettingError þ1. end for CycleError þSettingError. The updated 5 network weights are taken as new desired values and propagated back to the corresponding MLFNs. Each parameter MLFN k updates its o... |

3 | Active-camera calibration using iterative image feature localization
- Seales, Eggert
- 1995
(Show Context)
Citation Context ...calibration techniques. The calibrated model parameters at each lens setting are then stored in lookup tables [2,8], or polynomials (or perhaps other functions) are formulated to model the parameters =-=[4,5,9]-=-. The following remarks can be drawn on the previous approaches: † Using interpolation to obtain each model parameter at intermediate lens settings in tables or fitting a function to each parameter in... |

1 |
Zoom-lens camera calibration for an active vision system
- Ahmed
(Show Context)
Citation Context ... other function such as Huber’s function [13]. The updating rules for network weights will be different from those used in Ref. [11] and are re-derived according to the new error in Eq. (8), see Ref. =-=[17]-=- for more details. It is important to note that M-estimate methods tend to be extremely susceptible to the initial solution to the non-linear optimization method. Most calibration approaches found in ... |