This Article 
 Bibliographic References 
 Add to: 
Rectified Catadioptric Stereo Sensors
February 2002 (vol. 24 no. 2)
pp. 224-236

Abstract—It has been previously shown how mirrors can be used to capture stereo images with a single camera, an approach termed catadioptric stereo. In this paper, we present novel catadioptric sensors that use mirrors to produce rectified stereo images. The scan-line correspondence of these images benefits real-time stereo by avoiding the computational cost and image degradation due to resampling when rectification is performed after image capture. First, we develop a theory which determines the number of mirrors that must be used and the constraints on those mirrors that must be satisfied to obtain rectified stereo images with a single camera. Then, we discuss in detail the use of both one and three mirrors. In addition, we show how the mirrors should be placed in order to minimize sensor size for a given baseline, an important design consideration. In order to understand the feasibility of building these sensors, we analyze rectification errors due to misplacement of the camera with respect to the mirrors.

[1] O. Faugeras, B. Hotz, H. Mathieu, T. Vieville, , Z. Zhang, P. Fau, E. Theron, L. Moll, G. Berry, J. Vuillemin, P. Bertin, and C. Proy, “Real-Time Correlation-Based Stereo: Algorithm, Implementation and Application,” Technical Report 2013, INRIA Sophia Antipolis, 1993.
[2] J. Gluckman and S.K. Nayar, “Planar Catadioptric Stereo: Geometry and Calibration,” Proc. 1999 Conf. Computer Vision and Pattern Recognition, 1999.
[3] A. Goshtasby and W.A. Gruver, “Design of a Single-Lens Stereo Camera System,” Pattern Recognition, vol. 26, no. 6, pp. 923–937, 1993.
[4] E. Hecht and A. Zajac, Optics. Addison-Wesley, 1974.
[5] M. Inaba, T. Hara, and H. Inoue, “A Stereo Viewer Based on a Single Camera with View-Control Mechanism,” Proc. Int'l Conf. Robots and Systems, July 1993.
[6] F. Isgro and E. Trucco, “Projective Rectification Without Epipolar Geometry,” Proc. 1999 Conf. Computer Vision and Pattern Recognition, 1999.
[7] D.H. Lee, I.S. Kweon, and R. Cipolla, “A Biprism Stereo Camera System,” Proc. 1999 Conf. Computer Vision and Pattern Recognition, 1999.
[8] C. Loop and Z. Zhang, “Computing Rectifying Homographies for Stereo Vision,” Proc. Computer Vision and Pattern Recognition '99, vol. I, pp. 125-131, 1999.
[9] H. Mathieu and F. Devernay, “Systeme de Miroirs pour la Stereoscopie,” Technical Report 0172, INRIA Sophia-Antipolis, 1995.
[10] H. Mitsumoto,S. Tamura,K. Okazaki,N. Kajimi,, and Y. Fukui,“3D reconstruction using mirror images based on a plane symmetry recoveringmethod,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 14, no. 9, pp. 941-946, 1992.
[11] S.K. Nayar, Robotic Vision System, United States Patent 4,893,183, Aug. 1988.
[12] S.A. Nene and S.K. Nayar, “Stereo with Mirrors,” Proc. 6th Int'l Conf. Computer Vision, Jan. 1998.
[13] M. Pollefeys, R. Koch, and L. Van Gool, "A Simple and Efficient Rectification Method for General Motion," Proc. 7th IEEE Int'l Conf. Computer Vision (ICCV99), IEEE CS Press, 1999, pp. 496- 501.
[14] L. Robert, M. Buffa, and M. Herbert, “Weakly-Calibrated Stereo Perception for Rover Navigation,” Proc. Fifth Int'l Conf. Computer Vision, 1995.
[15] D. Southwell, A. Basu, M. Fiala, and J. Reyda, “Panoramic Stereo,” Proc. Int'l Conf. Pattern Recognition, 1996.
[16] Z.Y. Zhang and H.T. Tsui, “3D Reconstruction from a Single View of an Object and Its Image in a Plane Mirror,” Proc. Int'l Conf. Pattern Recognition, 1998.

Index Terms:
Stereo imaging, image sensors, stereo rectification.
Joshua Gluckman, Shree K. Nayar, "Rectified Catadioptric Stereo Sensors," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 24, no. 2, pp. 224-236, Feb. 2002, doi:10.1109/34.982902
Usage of this product signifies your acceptance of the Terms of Use.