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Nonmetric Calibration of Wide-Angle Lenses and Polycameras
October 2000 (vol. 22 no. 10)
pp. 1172-1178

Abstract—Images taken with wide-angle cameras tend to have severe distortions which pull points towards the optical center. This paper proposes a simple method for recovering the distortion parameters without the use of any calibration objects. Since distortions cause straight lines in the scene to appear as curves in the image, our algorithm seeks to find the distortion parameters that map the image curves to straight lines. The user selects a small set of points along the image curves. Recovery of the distortion parameters is formulated as the minimization of an objective function which is designed to explicitly account for noise in the selected image points. Experimental results are presented for synthetic data as well as real images. We also present the idea of a polycamera which is defined as a tightly packed camera cluster. Possible configurations are proposed to capture very large fields of view. Such camera clusters tend to have a nonsingle viewpoint. We therefore provide analysis of what we call the minimum working distance for such clusters. Finally, we present results for a polycamera consisting of four wide-angle sensors having a minimum working distance of about $4$m. On undistorting the acquired images using our proposed technique, we create real-time high resolution panoramas.

[1] S. Becker and V.M. Bove, “Semi-Automatic 3-D Model Extraction from Uncalibrated 2-D Camera Views,” Proc. SPIE Visual Data Exploration and Analysis II, vol. 2,410, pp. 447-461, Feb. 1995.
[2] M. Born and E. Wolf, Principles of Optics. Permagon Press, 1965.
[3] D.C. Brown, “Decentering Distortion of Lenses,” Photogrammetric Eng., vol. 32, no. 3, pp. 444-462, May 1966.
[4] D.C. Brown, “Close Range Camera Calibration,” Photogrammetric Eng., vol. 37, no. 8, pp. 855-866, Aug. 1971.
[5] A. Conrady, “Decentering Lens Systems,” Monthly Notices of the Royal Astronomical Soc., vol. 79, pp. 384-390, 1919.
[6] A. Goshtasby, “Correction of Image Deformation from Lens Distortion Using Bezier Patches,” Computer Vision, Graphics, and Image Processing, vol. 47, pp. 385-394, 1989.
[7] S.B. Kang, “Semi-Automatic Methods for Recovering Radial Distortion Parameters from a Single Image,” Technical Reports Series CRL 97/3, DEC, Cambridge Research Labs, May 1997.
[8] D. McCutchen, “Method and Apparatus for Dodecahedral Imaging,” at United States Patent no. 5,023,725 http:/, 1991.
[9] V. Nalwa, “A True Omnidirectional Viewer,” technical report, Bell Laboratories, Holmdel, N.J., Feb. 1996.
[10] J.A. Nelder and R.A. Mead, “A Simplex Method for Function Minimization,” Computer J., vol. 7, pp. 308-313, 1965.
[11] H. Sawhney and R. Kumar, “True Multi-Image Alignment and Its Application to Mosaicing and Lens Distortion Correction,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 450-456, 1997.
[12] H.S. Sawhney and R. Kumar, “True Multi-Image Alignment and Its Application to Mosaicing and Lens Distortion Correction,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 21, no. 3, pp. 235-243, Mar. 1999.
[13] G.P. Stein, “Internal Camera Calibration Using Rotation and Geometric Shapes,” AITR-1,426, master's thesis, MIT, AI Laboratory, 1993.
[14] G. Stein, “Accurate Internal Camera Calibration Using Rotation, with Analysis of Sources of Error,” Proc. Fifth Int'l Conf. Computer Vision, pp. 230-236, June 1995.
[15] G.P. Stein, “Lens Distortion Calibration Using Point Correspondences,” Proc. 1997 Conf. Computer Vision and Pattern Recognition, pp. 143-148, June 1997.
[16] R. Szeliski, “Video Mosaics for Virtual Environments,” IEEE Computer Graphics and Applications, pp. 22-30, Mar. 1996.
[17] R. Tsai, "A Versatile Camera Calibration Technique for High-Accuracy 3D Machine Vision Metrology Using Off-the-Shelf TV Cameras and Lenses," IEEE J. Robotics and Automation, vol. 3, no. 4, pp. 323-344, Aug. 1987.
[18] “VNI,” IMSL Fortran Numerical Libraries, 1998.
[19] J. Weng, P. Cohen, and M. Herniou, “Camera Calibration with Distortion Models and Accuracy Evaluation,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 14, no. 10, pp. 965-980, Oct. 1992.

Index Terms:
Camera calibration, wide-angle lens, radial distortion, decentering distortion, camera clusters, polycamera, nonsingle viewpoint, minimum working distance, real-time panoramic sensor.
Rahul Swaminathan, Shree K. Nayar, "Nonmetric Calibration of Wide-Angle Lenses and Polycameras," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 22, no. 10, pp. 1172-1178, Oct. 2000, doi:10.1109/34.879797
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