Cameras
Course web page:vision.cis.udel.edu/cv
March 22, 2003 Lecture 16
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
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 nair < nwater < nglass
µ1: Angle of incidence
µ2: Angle of refraction
courtesy ofWolfram
Snell’s Law
• The relationship between the angle of incidence and the angle of refraction is given by:
courtesy ofWolfram
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:
n1 < n2 ) µ2 < µ1 and n1 > n2 ) µ2 > µ1
courtesy ofWolfram
So n1 < n2
in this image
divergence
convergence
Converging Light Rays
n1 < n2
n2n1
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 locationshave different angles of incidence and thus wind up withdifferent focal points
courtesy of S. Majewski
Lenses as Compound Prisms
We can get the light rays to have a common focus bygradually widening the effective apex angle as we getfarther 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 focuscourtesy of MTSU
Thin Lens Image Projection
courtesy of U. Colorado
z
Thin Lens Image Projection
z
Thin Lens Image Projection
z
Thin Lens Image Projection
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
1/30th 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
HDRmosaic
Under- andover-exposed
mosaic