the plenoptic function

19
The Plenoptic Function Lázaro Hermoso Beltrán

Upload: min

Post on 13-Jan-2016

67 views

Category:

Documents


0 download

DESCRIPTION

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

TRANSCRIPT

Page 1: The Plenoptic Function

The Plenoptic Function

Lázaro Hermoso Beltrán

Page 2: The Plenoptic Function

2

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

Page 3: The Plenoptic Function

3

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

Page 4: The Plenoptic Function

4

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

Page 5: The Plenoptic Function

5

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

Page 6: The Plenoptic Function

6

The Holographic Movie Example

• Black and white photo

• Color photograph

• Color movie

• Color holographic movie

)( P

),( P

),,,,,( tEEEP zyxvv

),( tP vv

Page 7: The Plenoptic Function

7

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

Page 8: The Plenoptic Function

8

P.M. in Human Vision

•Measurements has limitedresolution and number ofSamples

•Space and time the more importants

Page 10: The Plenoptic Function

10

P.M. in Human Vision

Page 11: The Plenoptic Function

11

Plenoptic Measurements: Red Bar Example

(Vx, Vy, Vz)

Page 12: The Plenoptic Function

12

P.M. in Machine Vision

•Develop a taxonomy of derivative types

•“Periodic Table”of visual elements

•Constraints Available information (PF)

Page 13: The Plenoptic Function

13

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

Page 14: The Plenoptic Function

14

RGB – Representation

• Three 5-D functions

),,,,( EzEyExvvPG

),,,,( EzEyExvvPR ),,,,( EzEyExvvPB

Page 15: The Plenoptic Function

15

Plenoptic Modelling

• Without time and wavelength

• Taking samples with cameras in enough close positions

• We can reconstruct PF interpolating the samples

),,,,( EzEyExvvP

Page 16: The Plenoptic Function

16

Light Field

• Assumption that that rays does not change intensity along direction

• Parametrization rays with 2 parallel planes

Page 17: The Plenoptic Function

17

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

Page 18: The Plenoptic Function

18

Interpolate Views

Page 19: The Plenoptic Function

19

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”