1. Cameras Course web page: vision.cis.udel.edu/cv March 22, 2003  Lecture 16

2. Announcements Read Forsyth & Ponce, Chapter 3-3.3 on camera calibration for Monday HW3: Some image sizes have been reduced and you don’t have to try as many window sizes

3. Outline Lenses Discretization effects of image capture

4. Ideal Pinhole Camera from Forsyth & Ponce Each point on the image plane collects light along one ray from the scene

5. Real Pinhole Cameras Problems –Pinholes don’t let through much light ! Dimness/exposure time trade-off –A bigger hole (aka aperture) means that each image point sees a disk of scene points, whose contributions are averaged ! Blurring –Very small apertures introduce diffraction effects from Forsyth & Ponce

6. Real pinhole camera images from Forsyth & Ponce Hole too small: Diffraction Hole too big: Blurring

7. Lenses Benefits: Increase light-gathering power by focusing bundles of rays from scene points onto image points from Forsyth & Ponce

8. Refraction Definition: Bending of light ray as it crosses interface between media (e.g., air ! glass or vice versa) Index of refraction (IOR) n for a medium: Ratio of speed of light in vacuum to that in medium –By definition, n ¸ 1 –Examples: 1 ¼ n air < n water < n glass µ 1 : Angle of incidence µ 2 : Angle of refraction courtesy of Wolfram

9. Snell’s Law The relationship between the angle of incidence and the angle of refraction is given by: courtesy of Wolfram

10. Snell’s Law: Implications Since µ / sin µ over the range [0, ¼/2] and the angle of refraction is given by we can infer the following from their IORs: n 1 n 2 ) µ 2 > µ 1 courtesy of Wolfram So n 1 < n 2 in this image divergence convergence

11. Converging Light Rays n1 < n2n1 < n2 n2n2 n1n1

12. Redirecting Light Prisms: Light traveling from a low IOR medium to a high IOR medium and back again is bent by an amount proportional to the apex angle courtesy of Prentice-Hall

13. Focusing Light with Prisms courtesy of S. Majewski

14. Focusing Light with Prisms: Many Beams Light rays intersecting the prisms at different locations have different angles of incidence and thus wind up with different focal points courtesy of S. Majewski

15. Lenses as Compound Prisms We can get the light rays to have a common focus by gradually widening the effective apex angle as we get farther from the center of the lens courtesy of S. Majewski

16. Thin Lenses Properties –A ray entering the lens parallel to the optical axis goes through the focus on the other side –A ray entering the lens from the focus on one side emerges parallel to the axis on the other side optical axis focus courtesy of MTSU

17. Thin Lens Image Projection courtesy of U. Colorado z

18. Thin Lens Image Projection z

19. z

20. z

21. Thin Lens Model from Forsyth & Ponce

22. Depth of Field The thin lens equation implies that scene points at different distances from the lens are in focus at different image distances Only a given range of object distances produce acceptable sharpness

23. Field of View FOV is defined as 2Á, where Á = tan -1 d/2f from Forsyth & Ponce

24. Lens Problems Limited depth of field Radial, tangential distortion: Straight lines curved Vignetting: Image darker at edges Spherical aberration Chromatic aberration: Focal length function of wavelength

25. Radial Distortion

26. Vignetting

27. Analog  Digital Sampling  Aliasing Quantization  Banding Limited dynamic range  Saturation Temporal integration  Motion blur Noise 1/30 th sec. exposure

28. Sampling Limited spatial resolution of capture devices results in visual artifacts (i.e., aliasing) –Nyquist theorem: Must sample 2x highest frequency component of signal to reconstruct adequately

29. High Dynamic Range Panoramas courtesy of D. Lischinski HDR mosaic Under- and over-exposed mosaic