CS 44957495 Computer Vision

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CS 4495/7495Computer Vision

• Cameras and Geometric Camera Models
• Jim Rehg
• (Borrowed liberally from Frank Dellaert and
  Forsyth Ponce)

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Outline

• Pinhole Cameras
• Cameras with Lenses
• Research Highlight Perspective cues for scene
  understanding
• Next lecture Camera Calibration

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Cameras

• First photograph due to Niepce
• Basic abstraction is the pinhole camera
• lenses required to ensure image is not too dark
• various other abstractions can be applied

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Pinhole cameras

• Abstract camera model - box with a small hole in
  it

• Pinhole cameras work in practice

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The equation of projection
Weird and difficult diagram in the book
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Pinhole Camera Model
Image plane
Focal length f
Center of projection
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Pinhole Camera Model
Image plane
Virtual Image
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Pinhole Camera Model
Image plane
Virtual Image
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Distant objects are smaller
C
B
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Pinhole Camera Summary
k
P
p
i
C
Q
f
q
O
j
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Parallel lines meet
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Vanishing points

• each set of parallel lines (direction) meets at
  a different point
• The vanishing point for this direction
• Sets of parallel lines on the same plane lead to
  collinear vanishing points.
• The line is called the horizon for that plane

• Good ways to spot faked images
• scale and perspective dont work
• vanishing points behave badly
• supermarket tabloids are a great source.

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Geometric properties of projection

• Points go to points
• Lines go to lines
• Planes go to whole image
• Polygons go to polygons
• Degenerate cases
• line through focal point to point
• plane through focal point to line

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Weak perspective

• perspective effects, but not over the scale of
  individual objects
• collect points into a group at about the same
  depth, then divide each point by the depth of its
  group
• easy
• - wrong

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Orthographic projection
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• Cameras with Lenses

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Pinhole too big - many directions are
averaged, blurring the image Pinhole too
small- diffraction effects blur the
image Generally, pinhole cameras are dark,
because a very small set of rays from a
particular point hits the screen.
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The reason for lenses
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The thin lens
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Focussing
http//www.theimagingsource.com
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Spherical aberration
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Vignetting
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Other annoying phenomena

• Chromatic aberration
• Light at different wavelengths follows different
  paths hence, some wavelengths are defocussed
• Machines coat the lens
• Humans live with it
• Geometric phenomena
• Radial Distortion
• Barrel distortion

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Geometric Context from a Single Image
Hoiem, Efros, Hebert
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Automatic Pop-up
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Putting Objects in Perspective
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Other stuff in Chapter 1

• Background reading
• Human eye
• Sensing
• CCD Cameras
• Sensor Models