the plenoptic function lázaro hermoso beltrán. 2 previous concepts “the body of the air is full...
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The Plenoptic Function
Lázaro Hermoso Beltrán
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Previous Concepts“The body of the air is full of an infinite number of radiant pyramids caused by the objects located in it”
Leonardo Da Vinci
• Pencil of rays: The set of light rays passing through any point in space
• Plenoptic function • Plenus : complete or full• Optic
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Definition (I)“Radiance received along any direction V arriving at any point
E in space, at any time ‘t’ and over any range of wavelength”
• 7-Dimensional function
),,,,,,( tEzEyExvvPI
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Geometric Components of the pencil of ray lights
ANGULAR COORDINATES
– E = (Ex, Ey, Ez) • Viewpoint
– . • Direction of the ray light passin trough the
Viewpoint
CARTESIAN COORDINATES
– Comonly used in machine vision
)( , vvV
),,,,,,( tEzEyExvvPI
),,,,,,( tEzEyExyxPI
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How would obtain plenoptic function
1. Placing an imaginary eye at every position2. Record the intensity of light at every angle3. For every wavelength4. At every time t
It does not need specify the direction of gaze!!
)( , vv
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The Holographic Movie Example
• Black and white photo
• Color photograph
• Color movie
• Color holographic movie
)( P
),( P
),,,,,( tEEEP zyxvv
),( tP vv
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Plenoptic Measurements in Human Vision
• PF potential iformation available
• Observer takes samples from PF
• Not all the information is usefull. Enviroment has determined what is usefull (movements predators). Enviroment constraints
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P.M. in Human Vision
•Measurements has limitedresolution and number ofSamples
•Space and time the more importants
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P.M. in Human Vision
• An example of what we can not measure
http://web.mit.edu/persci/demos/Lightness/gaz-teaching/flash/koffka-movie.swf
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P.M. in Human Vision
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Plenoptic Measurements: Red Bar Example
(Vx, Vy, Vz)
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P.M. in Machine Vision
•Develop a taxonomy of derivative types
•“Periodic Table”of visual elements
•Constraints Available information (PF)
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Aplications: Image Based Rendering
• IBR : Sampling and Rendering• Problem, PF is 7D function.We need reduce it!
• RGB representation
• Plenoptic modelling
• Light Field/Lumigraph P(s, t, u, v)
• 2D-Image Mosaicing
),,,,( EzEyExvvP
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RGB – Representation
• Three 5-D functions
),,,,( EzEyExvvPG
),,,,( EzEyExvvPR ),,,,( EzEyExvvPB
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Plenoptic Modelling
• Without time and wavelength
• Taking samples with cameras in enough close positions
• We can reconstruct PF interpolating the samples
),,,,( EzEyExvvP
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Light Field
• Assumption that that rays does not change intensity along direction
• Parametrization rays with 2 parallel planes
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2D-Image Mosacing•To paste serial 2D images to obtain a wider image. The images share the same proyection point
•Panoramic mosaic or Panorama
•We reconstruct a 2D Plenoptic function
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Interpolate Views
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References
• E.H. Adelson and J. Bergen, “The plenoptic function andthe elements of early vision” In Computational Models ofVisual Processing, pages 3-20. MIT Press, 1991
• The Plenoptic Illumination Function Tien-TsinWong1 Chi-Wing Fu2 Pheng-Ann Heng1 Chi-Sing Leung3
• McMillan, Bishop. “Plenotic Modeling: An Image-Based Rendering System”
• Shum, Kang. “A Review of Image-based Rendering Techniques”