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Caustics of Catadioptric Cameras

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Catadioptric Systems: Single Viewpoint. ... Hyperbola : e 1. Conic Catadioptric Cameras. Imaging plane. Reflector. O. p. Reflector ... – PowerPoint PPT presentation

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Title: Caustics of Catadioptric Cameras


1
Caustics of Catadioptric Cameras
  • Rahul Swaminathan,
  • Michael D. Grossberg and Shree K. Nayar
  • CAVE Lab, Columbia University
  • ICCV Conference
  • Vancouver, July 2001

2
Imaging Systems.
3
The Single Viewpoint
All incoming rays of light meet at a point.
Camera
Detector
Incoming light rays
4
Catadioptric Systems Single Viewpoint.
(Nayar , Baker Peri )
Only combinations of conic reflectors produce
single viewpoint systems.
Parabolic mirror
Telecentric lens.
Parashot 360
Acquired image.
5
What about such systems?
6
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?

7
Locus of Viewpoints Caustics.
Adapted from Jensen, 1997
8
How is a Caustic formed?
Incoming light rays
Reflector
9
Computing the Caustic.
Burkhard Shealy, 1973
Entry Pupil
At the caustic, there exists a singularity
r
Reflector
10
Jacobian Method.
Burkhard, 1973
At the caustic, moving along Vr is the same as
moving along the reflector.
Entry pupil
Reflector
11
Conic Catadioptrics
Imaging plane
d
?(t)
O
p
Reflector
z(t)
12
Conic Catadioptric Cameras
Imaging plane
d ??
O
O
p
p
Reflector
Reflector
Perspective lens based
Telecentric lens based
13
Some Caustics.
Pinhole
Elliptical Reflector e .75 , p 1.0 , d 0.5
d
p
Caustic
Reflector
14
Some Caustics.
Pinhole
Parabolic Reflector e 1.0 , p 1.0 , d 1.0
d
Reflector
p
Caustic
15
Some Caustics.
Reflector
Elliptical Reflector e .75 , p 1.0 , d ?
Caustic
16
Some Caustics.
Reflector
Elliptical Reflector e .75 , p 1.0 , d ?
Caustic
17
Some Caustics.
Lens pinhole
18
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.
19
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.
20
Geometric Properties.
Reflector
Caustic
21
Deriving Resolution Characteristics.
f
Reflector
Z
22
Deriving Resolution Characteristics.
Caustic
Reflector
23
Resolution Characteristics.
?(t)
O
p
Reflector
z(t)
24
Resolution Characteristics.
?(t)
O
p
Reflector
z(t)
25
Calibration.
26
Calibration.
27
Calibration.
28
Calibration.
29
Importance of Caustics to Graphics.
Caustics formed by the refracting water
surface,lead to such exotic light patterns.
Realistic reproduction, requires modeling of
caustics
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