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Forward projection model of non-central catadioptric cameras with spherical mirrors

  • Nuno Goncalves (a1), Ana Catarina Nogueira (a1) and Andre Lages Miguel (a1)
Summary
SUMMARY

Non-central catadioptric vision is widely used in robotics and vision but suffers from the lack of an explicit closed-form forward projection model (FPM) that relates a 3D point with its 2D image. The search for the reflection point where the scene ray is projected is extremely slow and unpractical for real-time applications. Almost all methods thus rely on the assumption of a central projection model, even at the cost of an exact projection.

Two recent methods are able to solve this FPM, presenting a quasi-closed form FPM. However, in the special case of spherical mirrors, further enhancements can be made. We compare these two methods for the computation of the FPM and discuss both approaches in terms of practicality and performance. We also derive new expressions for the FPM on spherical mirrors (extremely useful to robotics and graphics) which speed up its computation.

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Corresponding author
*Corresponding author. E-mail: nunogon@isr.uc.pt
References
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3. M. Baker , “Alhazen's problem,” Am. J. Math. 4 (1), 327331 (1881).

4. J. Barreto and H. Araujo , “Geometric properties of central catadioptric line images and their application in calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 27 (8) (2005) 13271333.

6. J. F. Blinn and M. E. Newell , “Texture and reflection in computer generated images,” Commun. ACM 19 (10), 542547 (1976).

8. M. Chen and J. Arvo , “Perturbation methods for interactive specular reflections,” IEEE Trans. Vis. Comput. Graph. 6, 253264 (2000).

9. M. Chen and J. Arvo , “Theory and application of specular path perturbation,” ACM Trans. Graph. 19 (4), 246278 (2000).

12. L. Dupont , D. Lazard , S. Lazard and S. Petitjean , “Near-optimal parameterization of the intersection of quadrics: I. The generic algorithm,” J. Symb. Comput. 43 (3), 168191 (2008).

17. N. Goncalves , “On the reflection point where light reflects to a known destination in quadric surfaces,” Opt. Lett. 35 (2), 100102 (Jan. 2010).

20. J. Levin , “A parametric algorithm for drawing pictures of solid objects composed of quadric surfaces,” Commun. ACM 19 (10), 555563 (1976).

21. J. Levin , “Mathematical models for determining the intersection of quadric surfaces,” Comput. Graph. Image Process. 11 (1), 7387 (1979).

22. M. Lhuillier , “Automatic scene structure and camera motion using a catadioptric system,” Comput. Vis. Image Underst. 109 (2), 186203 (2008).

26. D. Mitchell and P. Hanrahan , “Illumination from curved reflectors,” SIGGRAPH Comput. Graph. 26 (2) (1992) 283291.

29. D. Roger and N. Holzschuch , “Accurate specular reflections in real-time,” Comput. Graph. Forum 25 (3), 293302 (2006).

33. R. Swaminathan , M. Grossberg and S. Nayar , “Non-single viewpoint catadioptric cameras: Geometry and analysis,” Int. J. Comput. Vis. 66 (3), 211229 (2006).

35. T. Whitted , “An improved illumination model for shaded display,” Commun. ACM 23 (6), 343349 (Jun. 1980).

36. X. Ying and Z. Hu , “Catadioptric camera calibration using geometric invariants,” IEEE Trans. Pattern Anal. Mach. Intell. 26 (10), 12601271 (2004).

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Robotica
  • ISSN: 0263-5747
  • EISSN: 1469-8668
  • URL: /core/journals/robotica
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