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Caustics of Catadioptric Cameras

This paper explores the caustics formed in catadioptric cameras, particularly those with a single viewpoint. It investigates the geometry of viewpoints and the impact on imaging characteristics. The study also delves into techniques for calibrating non-single viewpoint cameras. The importance of caustics in graphics rendering is also discussed.

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Caustics of Catadioptric Cameras

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  1. Caustics of Catadioptric Cameras Rahul Swaminathan, Michael D. Grossberg and Shree K. Nayar CAVE Lab, Columbia University ICCV Conference Vancouver, July 2001

  2. Camera Imaging Systems.

  3. Effective Viewpoint The Single Viewpoint All incoming rays of light meet at a point. Camera Detector Incoming light rays

  4. Catadioptric Systems: Single Viewpoint. (Nayar , Baker Peri ) Only combinations of conic reflectors produce single viewpoint systems. Parabolic mirror Telecentric lens. Parashot 360 Acquired image.

  5. What about such systems?

  6. Non-Single Viewpoint Cameras. • No single viewpoint. – Locus of Viewpoints formed. • Can we elegantly describe the geometry of viewpoints? • Effect of new geometry on imaging characteristics. • Is there a simple technique to calibrate such systems?

  7. Locus of Viewpoints: Caustics. Adapted from [ Jensen, 1997 ]

  8. Caustic How is a Caustic formed? Incoming light rays Reflector

  9. Caustic Computing the Caustic. Burkhard & Shealy, 1973 Entry Pupil At the caustic, there exists a singularity : r Reflector

  10. Ellipse : e < 1 Parabola : e = 1 Hyperbola : e > 1 Conic Catadioptrics Imaging plane d (t) O p Reflector z(t)

  11. Imaging plane d Conic Catadioptric Cameras Imaging plane d  O O p p Reflector Reflector Perspective lens based Telecentric lens based

  12. Some Caustics. Pinhole Elliptical Reflector : e =.75 , p = 1.0 , d = 0.5 d p Caustic Reflector

  13. Some Caustics. Pinhole Parabolic Reflector : e =1.0 , p = 1.0 , d = 1.0 d Reflector p Caustic

  14. Some Caustics. Reflector Elliptical Reflector : e =.75 , p = 1.0 , d =  Caustic

  15. Some Caustics. Reflector Elliptical Reflector : e =.75 , p = 1.0 , d =  Caustic

  16. Reflector surface Reflector surface Caustic surface Caustic surface Some Caustics. Lens pinhole

  17. 3D Caustic Surfaces. Caustic for a parabola, source outside the reflector and along the axis of symmetry. Caustic surface for a source placed off-axis with respect to the reflector. All caustics are computed in closed form, then plotted.

  18. 3D Caustic Surfaces. Caustic for a parabola, source outside the reflector and along the axis of symmetry. Caustic surface for a source placed off-axis with respect to the reflector. All caustics are computed in closed form, then plotted.

  19. Caustic Deriving Resolution Characteristics. f Reflector Z

  20. Resolution Characteristics. (t) O p Reflector z(t)

  21. Resolution Characteristics. (t) O p Reflector z(t)

  22. Calibration.

  23. Calibration.

  24. Calibration.

  25. Calibration.

  26. Importance of Caustics to Graphics. Caustics formed by the refracting water surface,lead to such exotic light patterns. Realistic reproduction, requires modeling of caustics

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