# the plenoptic function

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The Plenoptic Function Lázaro Hermoso Beltrán

Post on 13-Jan-2016

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The Plenoptic Function. Lázaro Hermoso Beltrán. 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 - PowerPoint PPT Presentation

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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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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

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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”