cameras course web page: vision.cis.udel.edu/cv march 22, 2003 lecture 16
TRANSCRIPT
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Cameras
Course web page:vision.cis.udel.edu/cv
March 22, 2003 Lecture 16
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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
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Outline
• Lenses• Discretization effects of image
capture
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Ideal Pinhole Camera
from Forsyth & Ponce
Each point on the image plane collects light along one ray from the scene
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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
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Real pinhole camera images
from Forsyth & Ponce
Hole too small:
Diffraction
Hole too big:
Blurring
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Lenses
• Benefits: Increase light-gathering power by focusing bundles of rays from scene points onto image points
from Forsyth & Ponce
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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
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Snell’s Law
• The relationship between the angle of incidence and the angle of refraction is given by:
courtesy ofWolfram
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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
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Converging Light Rays
n1 < n2
n2n1
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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
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Focusing Light with Prisms
courtesy of S. Majewski
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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
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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
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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
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Thin Lens Image Projection
courtesy of U. Colorado
z
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Thin Lens Image Projection
z
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Thin Lens Image Projection
z
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Thin Lens Image Projection
z
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Thin Lens Model
from Forsyth & Ponce
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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
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Field of View
FOV is defined as 2Á, where Á = tan-1 d/2f
from Forsyth & Ponce
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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
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Radial Distortion
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Vignetting
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Analog Digital
• Sampling Aliasing • Quantization Banding• Limited dynamic range
Saturation • Temporal integration Motion
blur• Noise
1/30th sec.exposure
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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
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High Dynamic Range Panoramas
courtesy of D. Lischinski
HDRmosaic
Under- andover-exposed
mosaic