Abstract

We introduce a novel imaging technique called light field moment imaging (LMI) that uses the continuity equation to extract the first angular moments of a light field. We use these moments to construct perspective views of a scene. Examples of LMI in photography and microscopy are presented.

© 2013 Optical Society of America

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References

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  1. T. Kanade, A. Yoshida, K. Oda, H. Kano, and M. Tanaka, in IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1996. Proceedings CVPR’96, 1996 (IEEE, 1996), p. 196.
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    [CrossRef]
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  7. M. Levoy, Z. Zhang, and I. McDowall, J. Microsc. 235, 144 (2009).
    [CrossRef]
  8. F. A. Jenkins and H. A. White, Fundamentals of Optics, 3rd ed. (McGraw-Hill, 1957).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  12. D. Paganin, D. Barty, P. J. McMahon, and K. A. Nugent, J. Microsc. 214, 51 (2004).
    [CrossRef]
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    [CrossRef]

2013 (1)

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. Beausoleil, Nature 495, 348 (2013).
[CrossRef]

2010 (1)

2009 (1)

M. Levoy, Z. Zhang, and I. McDowall, J. Microsc. 235, 144 (2009).
[CrossRef]

2008 (1)

J. W. Nadler, D. E. Angelaki, and G. C. DeAngelis, Nature 452, 642 (2008).
[CrossRef]

2007 (1)

A. Veeraraghavan, R. Raskar, A. Agrawal, A. Mohan, and J. Tumblin, ACM Trans. Graph. 26, 69 (2007).
[CrossRef]

2005 (1)

R. Ng, ACM Trans. Graph. 24, 735 (2005).
[CrossRef]

2004 (1)

D. Paganin, D. Barty, P. J. McMahon, and K. A. Nugent, J. Microsc. 214, 51 (2004).
[CrossRef]

1992 (1)

E. H. Adelson and J. Y. Wang, IEEE Trans. Pattern Anal. Mach. Intell. 14, 99 (1992).
[CrossRef]

Adelson, E. H.

E. H. Adelson and J. Y. Wang, IEEE Trans. Pattern Anal. Mach. Intell. 14, 99 (1992).
[CrossRef]

Agrawal, A.

A. Veeraraghavan, R. Raskar, A. Agrawal, A. Mohan, and J. Tumblin, ACM Trans. Graph. 26, 69 (2007).
[CrossRef]

Angelaki, D. E.

J. W. Nadler, D. E. Angelaki, and G. C. DeAngelis, Nature 452, 642 (2008).
[CrossRef]

Barbastathis, G.

Barty, D.

D. Paganin, D. Barty, P. J. McMahon, and K. A. Nugent, J. Microsc. 214, 51 (2004).
[CrossRef]

Beausoleil, R.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. Beausoleil, Nature 495, 348 (2013).
[CrossRef]

Brug, J.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. Beausoleil, Nature 495, 348 (2013).
[CrossRef]

DeAngelis, G. C.

J. W. Nadler, D. E. Angelaki, and G. C. DeAngelis, Nature 452, 642 (2008).
[CrossRef]

Fattal, D.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. Beausoleil, Nature 495, 348 (2013).
[CrossRef]

Fiorentino, M.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. Beausoleil, Nature 495, 348 (2013).
[CrossRef]

Jenkins, F. A.

F. A. Jenkins and H. A. White, Fundamentals of Optics, 3rd ed. (McGraw-Hill, 1957).

Kanade, T.

T. Kanade, A. Yoshida, K. Oda, H. Kano, and M. Tanaka, in IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1996. Proceedings CVPR’96, 1996 (IEEE, 1996), p. 196.

Kano, H.

T. Kanade, A. Yoshida, K. Oda, H. Kano, and M. Tanaka, in IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1996. Proceedings CVPR’96, 1996 (IEEE, 1996), p. 196.

Levoy, M.

M. Levoy, Z. Zhang, and I. McDowall, J. Microsc. 235, 144 (2009).
[CrossRef]

McDowall, I.

M. Levoy, Z. Zhang, and I. McDowall, J. Microsc. 235, 144 (2009).
[CrossRef]

McMahon, P. J.

D. Paganin, D. Barty, P. J. McMahon, and K. A. Nugent, J. Microsc. 214, 51 (2004).
[CrossRef]

Mohan, A.

A. Veeraraghavan, R. Raskar, A. Agrawal, A. Mohan, and J. Tumblin, ACM Trans. Graph. 26, 69 (2007).
[CrossRef]

Nadler, J. W.

J. W. Nadler, D. E. Angelaki, and G. C. DeAngelis, Nature 452, 642 (2008).
[CrossRef]

Nakagawa, Y.

S. K. Nayar and Y. Nakagawa, in 1990 IEEE International Conference on Robotics and Automation, 1990. Proceedings (IEEE, 1990), p. 218.

Nayar, S. K.

S. K. Nayar and Y. Nakagawa, in 1990 IEEE International Conference on Robotics and Automation, 1990. Proceedings (IEEE, 1990), p. 218.

M. Noguchi and S. K. Nayar, in Proceedings of the 12th IAPR International Conference on Pattern Recognition, 1994, Vol. 1 (IEEE, 1994), p. 147.

Ng, R.

R. Ng, ACM Trans. Graph. 24, 735 (2005).
[CrossRef]

Noguchi, M.

M. Noguchi and S. K. Nayar, in Proceedings of the 12th IAPR International Conference on Pattern Recognition, 1994, Vol. 1 (IEEE, 1994), p. 147.

Nugent, K. A.

D. Paganin, D. Barty, P. J. McMahon, and K. A. Nugent, J. Microsc. 214, 51 (2004).
[CrossRef]

Oda, K.

T. Kanade, A. Yoshida, K. Oda, H. Kano, and M. Tanaka, in IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1996. Proceedings CVPR’96, 1996 (IEEE, 1996), p. 196.

Paganin, D.

D. Paganin, D. Barty, P. J. McMahon, and K. A. Nugent, J. Microsc. 214, 51 (2004).
[CrossRef]

Peng, Z.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. Beausoleil, Nature 495, 348 (2013).
[CrossRef]

Raskar, R.

A. Veeraraghavan, R. Raskar, A. Agrawal, A. Mohan, and J. Tumblin, ACM Trans. Graph. 26, 69 (2007).
[CrossRef]

Scharstein, D.

D. Scharstein and R. Szeliski, in IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings, Vol. 1 (IEEE, 2003), p. 195.

Szeliski, R.

D. Scharstein and R. Szeliski, in IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings, Vol. 1 (IEEE, 2003), p. 195.

Tanaka, M.

T. Kanade, A. Yoshida, K. Oda, H. Kano, and M. Tanaka, in IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1996. Proceedings CVPR’96, 1996 (IEEE, 1996), p. 196.

Tian, L.

Tran, T.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. Beausoleil, Nature 495, 348 (2013).
[CrossRef]

Tumblin, J.

A. Veeraraghavan, R. Raskar, A. Agrawal, A. Mohan, and J. Tumblin, ACM Trans. Graph. 26, 69 (2007).
[CrossRef]

Veeraraghavan, A.

A. Veeraraghavan, R. Raskar, A. Agrawal, A. Mohan, and J. Tumblin, ACM Trans. Graph. 26, 69 (2007).
[CrossRef]

Vo, S.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. Beausoleil, Nature 495, 348 (2013).
[CrossRef]

Waller, L.

Wang, J. Y.

E. H. Adelson and J. Y. Wang, IEEE Trans. Pattern Anal. Mach. Intell. 14, 99 (1992).
[CrossRef]

White, H. A.

F. A. Jenkins and H. A. White, Fundamentals of Optics, 3rd ed. (McGraw-Hill, 1957).

Yoshida, A.

T. Kanade, A. Yoshida, K. Oda, H. Kano, and M. Tanaka, in IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1996. Proceedings CVPR’96, 1996 (IEEE, 1996), p. 196.

Zhang, Z.

M. Levoy, Z. Zhang, and I. McDowall, J. Microsc. 235, 144 (2009).
[CrossRef]

ACM Trans. Graph. (2)

R. Ng, ACM Trans. Graph. 24, 735 (2005).
[CrossRef]

A. Veeraraghavan, R. Raskar, A. Agrawal, A. Mohan, and J. Tumblin, ACM Trans. Graph. 26, 69 (2007).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

E. H. Adelson and J. Y. Wang, IEEE Trans. Pattern Anal. Mach. Intell. 14, 99 (1992).
[CrossRef]

J. Microsc. (2)

D. Paganin, D. Barty, P. J. McMahon, and K. A. Nugent, J. Microsc. 214, 51 (2004).
[CrossRef]

M. Levoy, Z. Zhang, and I. McDowall, J. Microsc. 235, 144 (2009).
[CrossRef]

Nature (2)

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. Beausoleil, Nature 495, 348 (2013).
[CrossRef]

J. W. Nadler, D. E. Angelaki, and G. C. DeAngelis, Nature 452, 642 (2008).
[CrossRef]

Opt. Express (1)

Other (5)

F. A. Jenkins and H. A. White, Fundamentals of Optics, 3rd ed. (McGraw-Hill, 1957).

T. Kanade, A. Yoshida, K. Oda, H. Kano, and M. Tanaka, in IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1996. Proceedings CVPR’96, 1996 (IEEE, 1996), p. 196.

S. K. Nayar and Y. Nakagawa, in 1990 IEEE International Conference on Robotics and Automation, 1990. Proceedings (IEEE, 1990), p. 218.

D. Scharstein and R. Szeliski, in IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings, Vol. 1 (IEEE, 2003), p. 195.

M. Noguchi and S. K. Nayar, in Proceedings of the 12th IAPR International Conference on Pattern Recognition, 1994, Vol. 1 (IEEE, 1994), p. 147.

Supplementary Material (4)

» Media 1: MPG (1552 KB)     
» Media 2: MPG (1706 KB)     
» Media 3: MPG (1692 KB)     
» Media 4: MPG (1520 KB)     

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Figures (2)

Fig. 1.
Fig. 1.

(a) Schematic of the light field parameterization used. θX and θY are defined by the projections of a ray onto the xz and yz planes, respectively. (b) A photograph of a bent sheet of paper. A video showing two images at different focal planes, followed by an animation of the viewpoint traveling horizontally is shown as Media 1. (c) Normalized depth map of the sheet with gray-scale bar indicating depth. Normalized depth ranges from 0 (closest to camera) to 1 (farthest from camera).

Fig. 2.
Fig. 2.

(a) Micrograph of a folded tissue slice. Scale bar is 200 μm. The two input images and a perspective-shifting animation of the tissue slice are shown as Media 2. (b) Micrograph of the head of a wood tick. Scale bar is 200 μm. The two input images and a perspective-shifting animation of the wood tick head are shown as Media 3. (c) Gray-scale plot of the magnitude of the moment vector field M for the tissue sample in (a). The gray-scale bar shows the dimensionless value of |M|. (d) Micrograph of a pile of 5 μm fluorescent beads. Scale bar is 25 μm. The two input images and a perspective-shifting animation of this sample are shown as Media 4.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

·(L¯V)=0,
L¯/z=·L¯[tanθX,tanθY].
I(x,y;z)z=2U(x,y;z).
[s,t]=L[tanθX,tanθY]dtanθXdtanθYLdtanθXdtanθY.
H(fx,fy)=[4π2(fx2+fy2)]1for(fx2+fy2)0,
H(fx,fy)=1for(fx2+fy2)=0,
U=IFT[H×FT{(I1I2)/Δz}],
L(x,y,tanθX,tanθY)=I2(x,y)×exp{[tanθXs(x,y)]2/σ2[tanθYt(x,y)]2/σ2}.

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