This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Paracatadioptric Camera Calibration
May 2002 (vol. 24 no. 5)
pp. 687-695

Catadioptric sensors refer to the combination of lens-based devices and reflective surfaces. These systems are useful because they may have a field of view which is greater than hemispherical, providing the ability to simultaneously view in any direction. Configurations which have a unique effective viewpoint are of primary interest, among these is the case where the reflective surface is a parabolic mirror and the camera is such that it induces an orthographic projection and which we call paracatadiotpric. We present an algorithm for the calibration of such a device using only the images of lines in space. In fact, we show that we may obtain all of the intrinsic parameters from the images of only three lines and that this is possible without any metric information. We propose a closed-form solution for focal length, image center, and aspect ratio for skewless cameras and a polynomial root solution in the presence of skew. We also give a method for determining the orientation of a plane containing two sets of parallel lines from one uncalibrated view. Such an orientation recovery enables a rectification which is impossible to achieve in the case of a single uncalibrated view taken by a conventional camera. We study the performance of the algorithm in simulated set-ups and compare results on real images with an approach based on the image of the mirror's bounding circle.

[1] E. Hecht and A. Zajac, Optics. 3rd ed., Addison-Wesley, 1997.
[2] G. Toomer, “Diocles On Burning Mirrors,” Sources in the History of Mathematics and the Physical Sciences, Springer-Verlag, 1976.
[3] S.K. Nayar, “Catadioptric Omnidirectional Cameras,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 482-488, June 1997.
[4] S. Baker and S. Nayar, “A Theory of Single-Viewpoint Catadioptric Image Formation,” Int'l J. Computer Vision, vol. 35, pp. 175-196, 1999.
[5] T. Svoboda, T. Pajdla, and V. Hlavac, “Epipolar Geometry for Panoramic Cameras,” Proc. European Conf. Computer Vision, pp. 218-232, 1998.
[6] A. Bruckstein and T. Richardson, “Omniview Cameras with Curved Surface Mirrors,” Proc. IEEE Workshop Omnidirectional Vision, pp. 79-86, June 2000, Originally published as Bell Labs technical memo, 1996.
[7] C. Geyer and K. Daniilidis, “A Unifying Theory for Central Panoramic Systems,” Proc. Sixth European Conf. Computer Vision, pp. 445-462, 2000.
[8] C.J. Taylor, “Video Plus,” Proc. IEEE Workshop Omnidirectional Vision, K. Daniilidis, ed., pp. 3-11, June 2000.
[9] P. Sturm, “A Method for 3D-Reconstruction of Piecewise Planar Objects from Single Panoramic Images,” Proc. IEEE Workshop Omnidirectional Vision, pp. 119-126, June 2000.
[10] T. Boult, “Remote Reality Demonstration,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 966-967, June 1998.
[11] Y. Onoe, K. Yamazawa, H. Takemura, and N. Yokoya, “Telepresence by Real-Time View-Dependent Image Generation from Omnidirectional Video Streams,” Computer Vision and Image Understanding vol. 71, pp. 588-592, 1998.
[12] N. Winters, J. Gaspar, G. Lacey, and J. Santos-Victor, “Omnidirectional Vision for Navigation,” Proc. IEEE Workshop Omnidirectional Vision, pp. 21-28, June 2000.
[13] A. Leonardis and M. Jogan, “Robust Localization Using Eigenspace of Spinning-Images,” Proc. IEEE Workshop Omnidirectional Vision, pp. 37-46, June 2000.
[14] R. Benosman, E. Deforas, and J. Devars, “A New Catadioptric Sensor for Panoramic Vision of Mobile Robots,” Proc. IEEE Workshop Omnidirectional Vision, pp. 112-118, June 2000.
[15] V. Nalwa, “A True Omnidirectional Viewer,” technical report, Bell Labs, Holmdel, NJ 1996.
[16] Y. Yagi, “Omnidirectional Sensing and Its Application,” IEICE Trans. Information&Systems, vol. 3, pp. 568-579, 1999.
[17] Proc. IEEE Workshop Omnidirectional Vision. K. Daniilidis, ed., June 2000.
[18] R. Benosman and S. Kang, Panoramic Vision. Springer-Verlag, 2000.
[19] Y. Yagi, S. Kawato, and S. Tsuji, “Real-Time Omnidirectional Image Sensor (copis) for Vision-Guided Navigation,” IEEE J. Robotics and Automation, vol. 10, no. 1, pp. 11-21, Feb. 1994.
[20] S. Kang, “Catadioptric self-calibration,” IEEE Conf. Computer Vision and Pattern Recognition, pp. I-201-207, June 2000.
[21] S.A. Nene and S.K. Nayar, “Stereo with Mirrors,” Proc. 6th Int'l Conf. Computer Vision, Jan. 1998.
[22] I. Coope, “Circle Fitting by Linear and Nonlinear Least Squares,” J. Optimetric Theory Applications, vol. 76, pp. 381-388, 1993.
[23] L. Moura and R. Kitney, “A Direct Method for Least-Squares Circle Fitting,” Computer Physics Comm., vol. 64, pp. 57-63, 1991.
[24] Z. Zhang, “Parameter-Estimation Techniques: A Tutorial with Application to Conic Fitting,” Image and Vision Computing, vol. 15, pp. 59-76, 1997.
[25] M.A. Fischler and R.C. Bolles, “Random Sample Consensus: A Paradigm for Model Fitting with Applications to Image Analysis and Automated Cartography,” Graphics and Image Processing, vol. 24, no. 6, pp. 381–395, June 1981.

Index Terms:
Omnidirectional vision, panoramic vision, catadioptric camera, vanishing points, calibration
Citation:
C. Geyer, K. Daniilidis, "Paracatadioptric Camera Calibration," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 24, no. 5, pp. 687-695, May 2002, doi:10.1109/34.1000241
Usage of this product signifies your acceptance of the Terms of Use.