1. What is a Camera? Jean Ponce (ponce@di.ens.fr) http://www.di.ens.fr/~ponce Willow project-team Laboratoire d’informatique ENS/INRIA/CNRS UMR 8548 Ecole normale supérieure, Paris, FRANCE

2. Computational photography © M. Levoy, Stanford © R. Raskar, MIT © S. Nayar, CU (Pajdla, 2002) (Seitz and Kim, 2002) ( Yu and McMillan, 2004)

3. The two-plane parameterization of lines (Durand et al., 1996; Gortler et al., 1996; Levoy & Hanrahan, 1996; Gu et al., 1997) © Gu et al. (2007)

4. What is a (regular)camera? x c ξ r y x

5. (Veblen & Young, 1910; Pottman and Wallner, 2001). Illustrations © H. Havlicek, VUT. x ξ y r x y r ξ © E. Molzcan © Leica ?? © T. Pajdla, CTU Nondegenerate linear congruences

6. x c ξ r y c

7. x c ξ r y x c ξ

8. x c ξ r y x c ξ ξ

9. x c ξ r y x ξ r y Linear family of lines x ξ x c ξ ξ ξ

10. Rank-3 reguli © H. Havlicek, VUT

11. Rank-4 (nondegenerate) linear congruences © H. Havlicek, VUT

12. x ξ y r x y r ξ Hyperbolic linear congruences

13. © H. Havlicek, VUT © E. Molzcan © Leica Hyperbolic linear congruences

14. © H. Havlicek, VUT © T. Pajdla, CTU Elliptic linear congruences

15. © H. Havlicek, VUT y ≈ P x ξ ≈ Q y B ( y 1, y 2 ) = 0 T ( y 1, y 2, y 3 ) = 0 Rank-4 (nondegenerate) linear congruences

16. x ξ x Ax ξ The Essential Map (Pajdla, 2002) x ! » = x Ç Ax

17. x ξ p1p1 ±1±1 ±2±2 a1a1 b1b1 a2a2 b2b2 z1z1 z2z2 p2p2 Hyperbolic linear congruences

18. x ξ ± a2a2 p1p1 z p2p2 p a1a1 Parabolic linear congruences ± s ° T

19. TO DO… “Regular” construction of parabolic congruences A 4 £ 4 fundamental matrix for these? Understanding the interplay between cameras and the essential map A Understanding the interplay between lines common to two cameras and epipolar loci Intrinsic parameters, natural retinal parameterizations, and calibration What about non-linear essential maps? What about the light field? Implementation