3. The 5D Plenoptic Function
P(q, f, l, t)
Q: What is the set of all things that one can ever see?
A: The Plenoptic Function [Adelson and Bergen 1991]
(from plenus, complete or full, and optic)
4. The 5D Plenoptic Function
P(q, f, l, t)
Q: What is the set of all things that one can ever see?
A: The Plenoptic Function [Adelson and Bergen 1991]
(from plenus, complete or full, and optic)
5. The 5D Plenoptic Function
P(q, f, l, t, px, py, pz )
P(q, f, l, t, px, py, pz ) defines the intensity of light:
• as a function of viewpoint
• as a function of time
• as a function of wavelength
6. The 5D Plenoptic Function
P(q, f, l, t, px, py, pz )
P(q, f, l, t, px, py, pz ) defines the intensity of light:
• as a function of viewpoint
• as a function of time
• as a function of wavelength
7. The 5D Plenoptic Function
Let’s ignore color and time (i.e., these are attributes of rays)…
P(q, f, px, py, pz)
The plenoptic function is 5D:
• 3D position
• 2D direction
Require 5D to represent attributes across occlusions
8. The 4D Light Field
Consider a region free of occluding objects…
P(q, f, px, py, pz)
The plenoptic function (light field) is 4D
• 2D position
• 2D direction
The space of all lines in a 3D space is 4D
[Levoy and Hanrahan 1996; Gortler et al. 1996]
11. Alternative Parameterizations
Left: Points on a plane or curved surface and directions leaving each point
Center: Pairs of points on the surface of a sphere
Right: Pair of points on two different (typically parallel) planes
16. Static Camera Arrays
Stanford Multi-Camera Array Distributed Light Field Camera
125 cameras using custom hardware 64 cameras with distributed rendering
[Wilburn et al. 2002, Wilburn et al. 2005] [Yang et al. 2002]
18. Controlled Camera or Object Motion
Stanford Spherical Gantry Relighting with 4D Incident Light Fields
[Levoy and Hanrahan 1996] [Masselus et al. 2003]
19. Uncontrolled Camera or Object Motion
Unstructured Lumigraph Rendering
[Gortler et al. 1996; Buehler et al. 2001]
21. Parallax Barriers (Pinhole Arrays)
barrier
sensor
Spatially-multiplexed light field capture using masks (i.e., barriers):
• Cause severe attenuation long exposures or lower SNR
• Impose fixed trade-off between spatial and angular resolution
(unless implemented with programmable masks, e.g. LCDs)
[Ives 1903]
23. Light Field Photograph (Decoded)
looking to the right
looking up
Sample Image
[The (New) Stanford Light Field Archive]
24. Integral Imaging (“Fly’s Eye” Lenslets)
lenslet
f
sensor
Spatially-multiplexed light field capture using lenslets:
• Impose fixed trade-off between spatial and angular resolution
[Lippmann 1908]
25. Modern, Digital Implementations
Digital Light Field Photography
• Hand-held plenoptic camera [Ng et al. 2005]
• Heterodyne light field camera [Veeraraghavan et al. 2007]