Plenoptic Imaging
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Plenoptic Imaging. Chong Chen Dan Schonfeld Department of Electrical and Computer Engineering University of Illinois at Chicago May 7 2009. Plenoptic Function (1). From plenus (complete or full) and optic .

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Chong Chen Dan Schonfeld Department of Electrical and Computer Engineering

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Chong chen dan schonfeld department of electrical and computer engineering

Plenoptic Imaging

Chong Chen

Dan Schonfeld

Department of Electrical and Computer Engineering

University of Illinois at Chicago

May 7 2009


Plenoptic function 1

Plenoptic Function (1)

  • From plenus (complete or full) and optic.

  • An idealized function to express the image of a scene from any possible viewing position at any viewing angle at any point in time.


Plenoptic function 2

Plenoptic Function (2)


Plenoptic camera 1

R. Ng et al., Stanford University 2005

Plenoptic Camera (1)


Plenoptic camera 2

R. Ng et al., Stanford University 2005

Plenoptic Camera (2)


Image base rendering

Image-Base Rendering

L. McMillan and G. Bishop, SIGGRAPH 1995


Lightfield

M. Levoy and P. Hanrahan, SIGGRAPH 1996

Lightfield

The lightfield data is composed of six 4D functions, where the plane of the inner box is indexed with coordinate (u, v) and that of the outer box with coordinate (s, t).


Sampling and reconstruction

Sampling and Reconstruction

  • The lightfield reconstruction is computed as

  • The sampled lightfield ls(u,v,s,t) is represented by

H.Y. Shum et al., SIGGRAPH 2000


Plenoptic sampling 1

Plenoptic Sampling (1)

Assumptions: Lambertian surfaces and no occlusion.

H.Y. Shum et al., SIGGRAPH 2000


Plenoptic sampling 2

Plenoptic Sampling (2)

where L’ is the 2D Fourier transform of l(x,y,0,0)

The spectral support of a lightfield signal is bounded by the minimum and maximum depths only, no matter how complicated the spectral support might be because of depth variations in the scene.

H.Y. Shum et al., SIGGRAPH 2000


Unstructured lumigraph

Unstructured Lumigraph

M. Cohen et al., SIGGRAPH 2001


Parallel cameras

Parallel Cameras

Plenoptic signals taken by parallel cameras will be bandlimited, and their spectral support is bounded by the minimum and maximum depths.


Unstructured cameras 1

Unstructured Cameras (1)

Plenoptic signals taken by unparallel cameras will not be bandlimited.

is the Bessel Function.


Unstructured cameras 2

Unstructured Cameras (2)

Assuming

Plenoptic signals taken by unparallel cameras with limited FOV and rotations can be approximated to be bandlimited


Concentric mosaic 1

Concentric Mosaic (1)

After linearization

  • for the constant depth concentric mosaic, the spectrum lies on a line with slope

C. Zhang and T. Chen, Carnegie Mellon University 2001


Concentric mosaic 2

Concentric Mosaic (2)

Before linearization

Bernstein's inequality: if is a bounded function on with supported in the ball . Then for all multi-indices , there exist constants (depending only on and on the dimension n) such that


Unoccluded image constraints

Unoccluded Image Constraints

If any point (f(x), g(x)) on the surface of the scene is differentiable, there is no occlusion with the surface if and only if

which can be proved by Cauchy's Mean-Value Theorem.


Conclusions and future work

Plenoptic signals taken by unparallel cameras will not be bandlimited.

Plenoptic signals taken by unparallel cameras with limited FOV and rotations can be approximated to be bandlimited.

Sampling (light conditions, surface luminance)

Reconstruction (integral imaging)

Conclusions and Future Work


Thank you

Thank you !


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