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Mathematical Problems in Engineering - Volume 2014 2014, Article ID 689429, 9 pages -

Research Article

North Carolina Central University, Durham, NC 27707, USA

Old Dominion University, Norfolk, VA 23529, USA

Received 3 October 2013; Accepted 24 December 2013; Published 11 February 2014

Academic Editor: Yi-Hung Liu

Copyright © 2014 Mingpei Liang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Cameras with telephoto lens are usually used to recover details of an object that is either small or located far away from the cameras. However, the calibration of this kind of cameras is not as accurate as the one of cameras with short focal lengths that are commonly used in many vision applications. This paper has two contributions. First, we present a first-order error analysis that shows the relation between focal length and estimation uncertainties of camera parameters. To our knowledge, this error analysis with respect to focal length has not been studied in the area of camera calibration. Second, we propose a robust algorithm to calibrate the camera with a long focal length without using additional devices. By adding a regularization term, our algorithm makes the estimation of the image of the absolute conic well posed. As a consequence, the covariance of camera parameters can be reduced greatly. We further used simulations and real data to verify our proposed algorithm and obtained very stable results.

Autor: Mingpei Liang, Xinyu Huang, Chung-Hao Chen, Gaolin Zheng, and Alade Tokuta



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