General linear cameras with finite aperture
Download
1 / 68

General Linear Cameras with Finite Aperture - PowerPoint PPT Presentation


  • 104 Views
  • Uploaded on

General Linear Cameras with Finite Aperture. Andrew Adams and Marc Levoy Stanford University. Ray Space. Slices of Ray Space. Pushbroom Cross Slit General Linear Cameras. Yu and McMillan ‘04. Román et al. ‘04. Projections of Ray Space. Plenoptic Cameras Camera Arrays

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'General Linear Cameras with Finite Aperture' - tannar


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
General linear cameras with finite aperture l.jpg

General Linear Cameras with Finite Aperture

Andrew Adams and Marc Levoy

Stanford University



Slices of ray space l.jpg
Slices of Ray Space

  • Pushbroom

  • Cross Slit

  • General Linear

    Cameras

Yu and McMillan ‘04

Román et al. ‘04


Projections of ray space l.jpg
Projections of Ray Space

  • Plenoptic Cameras

  • Camera Arrays

  • Regular Cameras

Ng et al. ‘04

Leica Apo-Summicron-M

Wilburn et al. ‘05



What is this paper6 l.jpg
What is this paper?

  • An intuitive reformulation of general linear cameras in terms of eigenvectors


What is this paper7 l.jpg
What is this paper?

  • An intuitive reformulation of general linear cameras in terms of eigenvectors

  • An analogous description of focus


What is this paper8 l.jpg
What is this paper?

  • An intuitive reformulation of general linear cameras in terms of eigenvectors

  • An analogous description of focus

  • A theoretical framework for understanding and characterizing linear slices and integral projections of ray space


Slices of ray space9 l.jpg
Slices of Ray Space

  • Perspective View

  • Image(x, y) = L(x, y, 0, 0)


Slices of ray space10 l.jpg
Slices of Ray Space

  • Orthographic View

  • Image(x, y) = L(x, y, x, y)


Slices of ray space11 l.jpg
Slices of Ray Space

  • Image(x, y) = L(x, y, P(x, y))

  • P determines perspective

  • Let’s assume P is linear




Slices of ray space14 l.jpg
Slices of Ray Space

  • Rays meet when:

    ((1-z)P + zI) is low rank

  • Substitute b = z/(z-1):

    ((1-z)P + zI) = (1-z)(P – bI)

  • Rays meet when:

    (P – bI) is low rank


Slices of ray space15 l.jpg
Slices of Ray Space

  • 0 < b1 = b2 < 1


Slices of ray space16 l.jpg
Slices of Ray Space

  • b1 = b2 < 0


Slices of ray space17 l.jpg
Slices of Ray Space

  • b1 = b2 = 1


Slices of ray space18 l.jpg
Slices of Ray Space

  • b1 = b2 > 1



Slices of ray space20 l.jpg
Slices of Ray Space

  • b1 != b2 = 1


Slices of ray space21 l.jpg
Slices of Ray Space

  • b1 = b2 != 1, deficient eigenspace


Slices of ray space22 l.jpg
Slices of Ray Space

  • b1 = b2 = 1, deficient eigenspace


Slices of ray space23 l.jpg
Slices of Ray Space

  • b1, b2 complex



Slices of ray space25 l.jpg
Slices of Ray Space

Real Eigenvalues

Complex Conjugate Eigenvalues


Slices of ray space26 l.jpg
Slices of Ray Space

Real Eigenvalues

Equal Eigenvalues

Complex Conjugate Eigenvalues


Slices of ray space27 l.jpg
Slices of Ray Space

Real Eigenvalues

Equal Eigenvalues

Equal Eigenvalues,

2D Eigenspace

Complex Conjugate Eigenvalues


Slices of ray space28 l.jpg
Slices of Ray Space

One slit at infinity

Real Eigenvalues

Equal Eigenvalues

Equal Eigenvalues,

2D Eigenspace

Complex Conjugate Eigenvalues





Projections of ray space32 l.jpg
Projections of Ray Space

  • Rays Integrated at (x, y) = (0, 0):

F


Projections of ray space33 l.jpg
Projections of Ray Space

  • Rays meet when:

    ((1-z)I + zF) is low rank

  • Substitute b = (z-1)/z:

    ((1-z)I + zF) = z(F – bI)

  • Rays meet when:

    (F – bI) is low rank


Projections of ray space34 l.jpg
Projections of Ray Space

  • 0 < b1 = b2 < 1


Projections of ray space35 l.jpg
Projections of Ray Space

  • 0 < b1 = b2 < 1













Projections of ray space47 l.jpg
Projections of Ray Space

  • b1 = b2 != 1, deficient eigenspace


Projections of ray space48 l.jpg
Projections of Ray Space

  • b1 = b2 != 1, deficient eigenspace


Projections of ray space49 l.jpg
Projections of Ray Space

  • b1 = b2 = 1, deficient eigenspace


Projections of ray space50 l.jpg
Projections of Ray Space

  • b1 = b2 = 1, deficient eigenspace


Projections of ray space51 l.jpg
Projections of Ray Space

  • b1, b2 complex



Slices of ray space53 l.jpg
Slices of Ray Space

Real Eigenvalues

Complex Conjugate Eigenvalues


Slices of ray space54 l.jpg
Slices of Ray Space

Real Eigenvalues

Equal Eigenvalues

Complex Conjugate Eigenvalues


Slices of ray space55 l.jpg
Slices of Ray Space

Real Eigenvalues

Equal Eigenvalues

Equal Eigenvalues,

2D Eigenspace

Complex Conjugate Eigenvalues


Slices of ray space56 l.jpg
Slices of Ray Space

One focal slit at infinity

Real Eigenvalues

Equal Eigenvalues

Equal Eigenvalues,

2D Eigenspace

Complex Conjugate Eigenvalues


Projections of ray space57 l.jpg
Projections of Ray Space

  • Let’s generalize:


Projections of ray space58 l.jpg
Projections of Ray Space

  • Let’s generalize:


Projections of ray space59 l.jpg
Projections of Ray Space

  • Let’s generalize:


Projections of ray space60 l.jpg
Projections of Ray Space

  • Let’s generalize:



Projections of ray space62 l.jpg
Projections of Ray Space

  • Factor Q as:

  • M warps lightfield in (x, y)

    • warps final image


Projections of ray space63 l.jpg
Projections of Ray Space

  • Factor Q as:

  • M warps lightfield in (x, y)

    • warps final image

  • A warps lightfield in (u, v)

    • shapes domain of integration (bokeh, aperture size)



Conclusion65 l.jpg
Conclusion

  • General Linear Cameras can be characterized by the eigenvalues of a 2x2 matrix.


Conclusion66 l.jpg
Conclusion

  • General Linear Cameras can be characterized by the eigenvalues of a 2x2 matrix.

  • Focus can be described in the same fashion.


Conclusion67 l.jpg
Conclusion

  • General Linear Cameras can be characterized by the eigenvalues of a 2x2 matrix.

  • Focus can be described in the same fashion.

  • These matrices are a good way to analyze and specify linear integral projections of ray space.



ad