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

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

Outline Lenses Discretization effects of image capture

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

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

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

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

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

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

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

Converging Light Rays n1 < n2n1 < n2 n2n2 n1n1

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

Focusing Light with Prisms courtesy of S. Majewski

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

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

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

Thin Lens Image Projection courtesy of U. Colorado z

Thin Lens Image Projection z

z

z

Thin Lens Model from Forsyth & Ponce

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

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

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

Radial Distortion

Vignetting

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

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

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