Abstract
This paper presents fundamental theory and design of central panoramic cameras. Panoramic cameras combine a convex hyperbolic or parabolic mirror with a perspective camera to obtain a large field of view. We show how to design a panoramic camera with a tractable geometry and we propose a simple calibration method. We derive the image formation function for such a camera. The main contribution of the paper is the derivation of the epipolar geometry between a pair of panoramic cameras. We show that the mathematical model of a central panoramic camera can be decomposed into two central projections and therefore allows an epipolar geometry formulation. It is shown that epipolar curves are conics and their equations are derived. The theory is tested in experiments with real data.
This research was supported by the Czech Ministry of Education grant VS96049, the internal grant of the Czech Technical University 3097472/335, the Grant Agency of the Czech Republic, grants 102/97/0480, 102/97/0855 and European Union grant Copernicus CP941068.
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Simon Baker and Shree K. Nayar. A theory of catadioptric image formation. Submitted to IJCV, 1997. Also appears in ICCV98, and exists as TR CUCS-015-97, and it was presented in Darpa IUW 1997.
R. Benosman, T. Maiere, and J. Devars. Multidirectional stereovision sensor, calibration and scenes reconstruction. In International Conference on Pattern Recognition 1996, Vienna, Austria, pages 161–165. IEEE Computer Society Press, September 1996.
T. Brodský, C. Fernmüller, and Y. Aloimonos. Directions of motion fields are hardly ever ambiguous. In Buxton. B. and R. Cipola, editors, 4th European Conference on Computer Vision, Cambridge UK, volume 2, pages 119–128, 1996.
J.S. Chahl and M.V. Srinivasan. Range estimation with a panoramic visual sensor. Journal of the Optical Society of America, 14(9):2144–2151, September 1997.
J.S. Chahl and M.V. Srinivasan. Reflective surfaces for panoramic imaging. Applied Optics, 36(31):8275–8285, November 1997.
K. Daniilidis and H.-H. Nagel. The coupling of rotation and translation in motion estimation of planar surfaces. In IEEE Conf. on Computer Vision and Pattern Recognition, pages 188–193, New York, NY, June 1993.
Olivier Faugeras. 3-D Computer Vision, A Geometric Viewpoint. MIT Press, 1993.
Margaret M. Fleck. Perspective projection: The wrong imaging model. Research report 95-01, Department of Computer Science, University of Iowa, Iowa City, USA, 1995.
Joshua Gluckman and Shree K. Nayar. Ego-motion and omnidirectional cameras. In Sharat Chandran and Uday Desai, editors, The Sixth International Conference on Computer Vision in Bombay, India, pages 999–1005, 6 Community Centre, Panscheel Park, New Delhi 110 017, January 1998. N. K. Mehra for Narosa Publishing House.
Francis Hamit. New video and still cameras provide a global roaming viewpoint. Advance Imaging, pages 50–52, March 1997.
Richard I. Hartley. Euclidean reconstruction from uncalibrated views. In Workshop on Invariants in Computer Vision, pages 187–202, October 1993.
Richard I. Hartley. In defence of the 8-point algorithm. In Fifth International Conference on Computer Vision, MIT Cambridge Massachusetts, pages 1064–1070. IEEE Copmuter Society Press, 1995.
Hiroshi Ishiguro, Masashi Yamamoto, and Saburo Tsuji. Omni-directional stereo. IEEE Transactions on Pattern Analysis and Machine Inteligence, 14(2):257–262, February 1992.
Shree K. Nayar. Catadioptric omnidirectional camera. In International Conference on Computer Vision and Pattern Recognition 1997, Puerto Rico USA, pages 482–488. IEEE Computer Society Press, June 1997.
Sameer A. Nene and Shree K. Nayar. Stereo with mirrors. In Sharat Chandran and Uday Desai, editors, The Sixth International Conference on Computer Vision in Bombay, India, pages 1087–1094, 6 Community Centre, Panscheel Park, New Delhi 110 017, January 1998. N. K. Mehra for Narosa Publishing House.
Tomáš Pajdla. BCRF — Binary Illumination Coded Range Finder: Reimplementation. ESAT MI2 Technical Report Nr. KUL/ESAT/MI2/9502, Katholieke Universiteit Leuven, Belgium, April 1995.
David Southwell, Anup Basu, Mark Fiala, and Jereome Reyda. Panoramic stereo. In International Conference on Pattern Recognition 1996, Vienna, Austria, volume A, pages 378–382. IEEE Computer Society Press, August 1996.
Tomáš Svoboda, Tomáš Pajdla, and Václav Hlaváč. Central panoramic cameras: Geometry and design. Research report K335/97/147, Czech Technical University, Faculty of Electrical Engineering, Center for Machine Perception, December 1997. Available at ftp://cmp.felk.cvut.cz/pub/cmp/articles/svoboda/TR-K335-97-147.ps.gz.
Yasushi Yagi, Yoshimitsu Nishizawa, and Masahiko Yachida. Map-based navigation for a mobile robot with omnidirectional images sensor COPIS. IEEE Transaction on Robotics and Automation, 11(5):634–648, October 1995.
Yasushi Yagi, Kazuma Yamazawa, and Masahiko Yachida. Rolling motion estimation for mobile robot by using omnidirectional image sensor hyperomnivision. In International Conference on Pattern Recognition 1996, Vienna, Austria, pages 946–950. IEEE Computer Society Press, September 1996.
Zhengyou Zhang, Rachid Deriche, Olivier Faugeras, and Quang-Tuang Luog. A robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry. Artificial Inteligence, 78:87–119, October 1995. Also Research Report No.2273, INRIA Sophia-Antipolis.
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Svoboda, T., Pajdla, T., Hlaváč, V. (1998). Epipolar geometry for panoramic cameras. In: Burkhardt, H., Neumann, B. (eds) Computer Vision — ECCV'98. ECCV 1998. Lecture Notes in Computer Science, vol 1406. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055669
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