Caustics of Catadioptric Cameras

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Caustics of Catadioptric Cameras

• Rahul Swaminathan,
• Michael D. Grossberg and Shree K. Nayar
• CAVE Lab, Columbia University
• ICCV Conference
• Vancouver, July 2001

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Imaging Systems.
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The Single Viewpoint
All incoming rays of light meet at a point.
Camera
Detector
Incoming light rays
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Catadioptric Systems Single Viewpoint.
(Nayar , Baker Peri )
Only combinations of conic reflectors produce
single viewpoint systems.
Parabolic mirror
Telecentric lens.
Parashot 360
Acquired image.
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What about such systems?
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Non-Single Viewpoint Cameras.

• No single viewpoint. Locus of Viewpoints
  formed.
• Can we elegantly describe the geometry of
  viewpoints?
• Effect of new geometry on imaging
  characteristics.
• Is there a simple technique to calibrate such
  systems?

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Locus of Viewpoints Caustics.
Adapted from Jensen, 1997
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How is a Caustic formed?
Incoming light rays
Reflector
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Computing the Caustic.
Burkhard Shealy, 1973
Entry Pupil
At the caustic, there exists a singularity
r
Reflector
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Jacobian Method.
Burkhard, 1973
At the caustic, moving along Vr is the same as
moving along the reflector.
Entry pupil
Reflector
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Conic Catadioptrics
Imaging plane
d
?(t)
O
p
Reflector
z(t)
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Conic Catadioptric Cameras
Imaging plane
d ??
O
O
p
p
Reflector
Reflector
Perspective lens based
Telecentric lens based
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Some Caustics.
Pinhole
Elliptical Reflector e .75 , p 1.0 , d 0.5
d
p
Caustic
Reflector
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Some Caustics.
Pinhole
Parabolic Reflector e 1.0 , p 1.0 , d 1.0
d
Reflector
p
Caustic
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Some Caustics.
Reflector
Elliptical Reflector e .75 , p 1.0 , d ?
Caustic
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Some Caustics.
Reflector
Elliptical Reflector e .75 , p 1.0 , d ?
Caustic
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Some Caustics.
Lens pinhole
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3D Caustic Surfaces.
Caustic for a parabola, source outside the
reflector and along the axis of symmetry.
Caustic surface for a source placed off-axis with
respect to the reflector.
All caustics are computed in closed form, then
plotted.
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3D Caustic Surfaces.
Caustic for a parabola, source outside the
reflector and along the axis of symmetry.
Caustic surface for a source placed off-axis with
respect to the reflector.
All caustics are computed in closed form, then
plotted.
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Geometric Properties.
Reflector
Caustic
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Deriving Resolution Characteristics.
f
Reflector
Z
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Deriving Resolution Characteristics.
Caustic
Reflector
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Resolution Characteristics.
?(t)
O
p
Reflector
z(t)
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Resolution Characteristics.
?(t)
O
p
Reflector
z(t)
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Calibration.
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Calibration.
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Calibration.
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Calibration.
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Importance of Caustics to Graphics.
Caustics formed by the refracting water
surface,lead to such exotic light patterns.
Realistic reproduction, requires modeling of
caustics