Stanford CS223B Computer Vision, Winter 200809 Lecture 2 Image Formation

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Stanford CS223B Computer Vision, Winter
2008/09Lecture 2 Image Formation

• Professor Sebastian Thrun
• CAs Ethan Dreyfuss, Young Min Kim, Alex Teichman
  

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Topics

• Cameras and Projections
• Pinhole Camera, vanishing points
• Orthographic Projection
• Perspective Camera Model
• Weak-Perspective Camera Model
• The Thin Lens
• Aberrations

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Pinhole Camera
-- Brunelleschi, XVth Century
many slides in this lecture from Marc Pollefeys
comp256, Lect 2
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Perspective Projection
A similar triangles approach to vision.
Marc Pollefeys
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Implications For Perception
Same size things get smaller, we hardly notice
Parallel lines meet at a point
A Cartoon Epistemology http//cns-alumni.bu.edu
/slehar/cartoonepist/cartoonepist.html
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Perspective Projection
O
X
-x
f
f
Z
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Consequences Parallel lines meet

• There exist vanishing points

Marc Pollefeys
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The Effect of Perspective
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Vanishing points
VPL
H
VPR
VP2
VP1
Different directions correspond to different
vanishing points
VP3
Marc Pollefeys
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Question

• How many vanishing points may there be in an
  image?

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Perspective Projection
O
X
-x
f
Z
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Weak Perspective Projection
Z
O
-x
Z
f
Z
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Generalization of Orthographic Projection
When the camera is at a (roughly constant)
distance from the scene, take m1.
Marc Pollefeys
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Pictorial Comparison
Weak perspective
Perspective
?
Marc Pollefeys
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Summary Perspective Laws

• Perspective
• Weak perspective
• Orthographic

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So why not always use very tiny pinholes?

• Might require long exposure, may lead to motion
  blur
• Diffraction

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Limits for pinhole cameras
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Topics

• Cameras and Projections
• Pinhole Camera, vanishing points
• Orthographic Projection
• Perspective Camera Model
• Weak-Perspective Camera Model
• The Thin Lens
• Aberrations

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Human Eyes Use Lenses
(Theodore D. Ruche and Harry C. Patton,
Physiology and Biophysics, 19th ed. Saunders,
Philadelphia,1965)
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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

• Any ray entering a thin lens parallel to the
  optical axis must go through the focus on other
  side
• 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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Thin Lens Depth of Field
P
optical axis
Image plane
p
z
f
f
Spherical lense surface Parallel rays are
refracted to single point
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Depth of Field
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Depth of Field
Source wikipedia.org
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Depth of Field
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To Ways to Change the Depth of Field

• Change z (distance of image plane to lens)
• Deform lens

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Thin Lens Depth of Field
P
optical axis
Image plane
p
z
f
f
Spherical lense surface Parallel rays are
refracted to single point
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Human Eye
(Theodore D. Ruche and Harry C. Patton,
Physiology and Biophysics, 19th ed. Saunders,
Philadelphia,1965)
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Focusing Through Lens Deformation
(Theodore D. Ruche and Harry C. Patton,
Physiology and Biophysics, 19th ed. Saunders,
Philadelphia,1965)
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Thin Lens Aperture
P
optical axis
Image plane
p
z
f
f
Spherical lense surface Parallel rays are
refracted to single point
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Aperture
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Large Aperture

• Reduces necessary exposure time
• Decreases depth of field (sometimes desired
  most pronounced with telephoto lenses (large
  focal length))

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Our Aperture Iris
Source www.cl.cam.ac.uk
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Topics

• Cameras and Projections
• Pinhole Camera, vanishing points
• Orthographic Projection
• Perspective Camera Model
• Weak-Perspective Camera Model
• The Thin Lens
• Aberrations

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Limits of the Thin Lens ModelAberrations
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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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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Summary

• Cameras and Projections
• Pinhole Camera, vanishing points
• Orthographic Projection
• Perspective Camera Model
• Weak-Perspective Camera Model
• The Thin Lens
• Aberrations