Geometric construction of the caustic surface of catadioptric non-central sensors

Imaging Beyond the Pinhole Camera

Volumn , Issue , 2006, Pages 39-54

  Ieng, S H ^a,b   Benosman, R ^a  

^a SORBONNE UNIVERSITÉ   (France)

^b ECE   (France)

Author keywords

caustic curve; non central catadioptric camera

Indexed keywords

EID: 84892211281     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-1-4020-4894-4_3     Document Type: Chapter

References (25)

1. Hamilton, W.R.: Theory of systems of rays. Trans. Royal Irish Academy, 15: 69-174, 1828.
2. Rees, D.: Panoramic television viewing system. United States Patent No.3,505,465, April 1970.
3. Burkhard, D.G. and D.L. Shealy: Flux density for ray propagation in geometric optics. J. Optical Society of America, 63: 299-304, 1973.
4. Bruce, J.W., P.J. Giblin, and C.G. Gibson: On caustics of plane curves. American Mathematical Monthly, 88: 651-667, 1981.
5. Mitchell, D. and P. Hanrahan: Illumination from curved reflectors. In Proc. SIGGRAPH, pages 283-291, 1992.
6. Yamazawa, K., Y. Yagi, and M. Yachida: Omnidirectional imaging with hyperboloidal projection. In Proc. Int. Conf. Intelligent Robots and Systems, pages 1029-1034, 1993
7. Bellver-Cebreros, C., E. Gómez-González, and M. Rodríguez-Danta: Obtention of meridian caustics and catacaustics by means of stigmatic approximating surfaces. Pure Applied Optics, 3: 7-16, 1994.
8. Jensen, H.W.: Rendering caustics on non-Lambertian surfaces. In Proc. Graphics Interface, pages 116-121, 1996.
9. Nalwa, V.: A true omnidirectional viewer. Technical report, Bell Laboratories, Holmdel, NJ 07733, U.S.A., February 1996.
10. Nayar, S.: Catadioptric omnidirectional cameras. In Proc. CVPR, pages 482-488, 1997.
11. Peri, V. and S.K. Nayar: Generation of perspective and panoramic video from omnidirectional video. In Proc. DARPA-IUW, vol. I, pages 243-245, December 1997.
12. Chahl, J.S. and M.V. Srinivasan: Reflective surfaces for panoramic imaging: Applied Optics, 36: 8275-8285, 1997.
13. Baker, S. and S.K. Nayar: A theory of catadioptric image formation. In Proc. ICCV, pages 35-42, 1998.
14. Vstone Corporation, Japan: http://www.vstone.co.jp/ (last visit: 12 Feb. 2006).
15. Gluckman, J. and S.K. Nayar: Planar catadioptric stereo: geometry and calibration. In Proc. CVPR, Vol. I, pages 22-28, 1999.
16. Baker, S. and S.K. Nayar: A theory of single-viewpoint catadioptric image formation. Int. J. Computer Vision, 35: 175-196, 1999.
17. Conroy, J. and J. Moore: Resolution invariant surfaces for panoramic vision systems. In Proc. ICCV, pages 392-397, 1999.
18. Ollis, M., H. Herman, and S. Singh: Analysis and design of panoramic stereo vision using equi-angular pixel cameras. Technical Report, The Robotic Institute, Carnegie Mellon University, 5000 Forbes Avenue Pittsburgh, PA 15213, 1999.
19. Rutter, J.W.: Geometry of Curves, Chapman & Hall/CRC, 2000.
20. Hicks, R.A. and R. Bajcsy: Catadioptric sensors that approximate wide-angle perspective projections. In Proc. CVPR, pages 545-551, 2000.
21. Swaminathan, R., M.D. Grossberg, and S.K. Nayar: Caustics of catadioptric cameras. In Proc. ICCV, pages 2-9, 2001.
22. Backstein, H. and T. Padjla: Non-central cameras: a review. In Proc. Computer Vision Winter Workshop, Ljubljana, pages 223-233, 2001.
23. Gaetcher, S. and T. Pajdla: Mirror design for an omnidirectional camera with space variant imager. In Proc. Workshop on Omnidirectional Vision Applied to Robotic Orientation and Nondestructive Testing, Budapest, 2001.
24. Hicks, R. A., R. K. Perline, and M. Coletta: Catadioptric sensors for panoramic viewing. In Proc. Int. Conf. Computing Information Technology, 2001.
25. Fabrizio, J., P. Tarel, and R. Benosman: Calibration of panoramic catadioptric sensors made easier. In Proc. IEEE Workshop on Omnidirectional Vision, June 2002.