Stanford CS223B Computer Vision, Winter 2006 Lecture 2: Lenses and Vision Software

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Stanford CS223B Computer Vision, Winter
2006Lecture 2 Lenses and Vision Software

• Professors Sebastian Thrun and Jana Kosecka
• CAs Vaibhav Vaish and David Stavens

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Todays Goals

• Thin Lens
• Aberrations
• Vision Software

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Pinhole Camera (last Wednesday)
-- Brunelleschi, XVth Century
Marc Pollefeys comp256, Lect 2
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Snells Law
Snells law n1 sin a1 n2 sin a2
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Thin Lens Definition
Spherical lense surface Parallel rays are
refracted to single point
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Thin Lens Projection
optical axis
Image plane
z
f
Spherical lense surface Parallel rays are
refracted to single point
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Thin Lens Projection
optical axis
Image plane
z
f
f
Spherical lense surface Parallel rays are
refracted to single point
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Thin Lens Properties

1. Any ray entering a thin lens parallel to the
   optical axis must go through the focus on other
   side
2. Any ray entering through the focus on one side
   will be parallel to the optical axis on the other
   side

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Thin Lens Model
Q
P
O
Fr
Fl
p
R
Z
f
f
z
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Thin Lens Model
Q
P
O
Fr
Fl
p
R
Z
f
f
z
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A Transformation
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The Thin Lens Law
Q
P
O
Fr
Fl
p
R
Z
f
f
z
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The Thin Lens Law
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Limits of the Thin Lens Model
3 assumptions

• all rays from a point are focused onto 1 image
  point
• Remember thin lens small angle assumption

2. all image points in a single plane
3. magnification is constant
Deviations from this ideal are aberrations
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Todays Goals

• Thin Lens
• Aberrations
• Vision Software

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Aberrations
2 types
geometrical geometry of the lense, small for
paraxial rays
chromatic refractive index function of
wavelength
Marc Pollefeys
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Geometrical Aberrations

• spherical aberration
• astigmatism
• distortion
• coma

aberrations are reduced by combining lenses
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Astigmatism

• Different focal length for inclined rays

Marc Pollefeys
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Astigmatism

• Different focal length for inclined rays

Marc Pollefeys
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Spherical Aberration
rays parallel to the axis do not converge outer
portions of the lens yield smaller focal lenghts
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Distortion

• magnification/focal length different
• for different angles of inclination

pincushion (tele-photo)
barrel (wide-angle)
Can be corrected! (if parameters are know)
Marc Pollefeys
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Coma

• point off the axis depicted as comet shaped blob

Marc Pollefeys
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Chromatic Aberration
rays of different wavelengths focused in
different planes cannot be removed
completely
Marc Pollefeys
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Vignetting
Effect Darkens pixels near the image boundary
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Vignetting
Effect Darkens pixels near the image boundary
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CCD vs. CMOS

• Mature technology
• Specific technology
• High production cost
• High power consumption
• Higher fill rate
• Blooming
• Sequential readout

• Recent technology
• Standard IC technology
• Cheap
• Low power
• Less sensitive
• Per pixel amplification
• Random pixel access
• Smart pixels
• On chip integration with other components

Marc Pollefeys
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Todays Goals

• Thin Lens
• Aberrations
• Vision Software