Abstract

We present a method for measurement and reconstruction of light fields in finite spaces. Using a custom-made device called a plenopter, we can measure spatially and directionally varying radiance distribution functions from a real-world scene up to their second-order spherical harmonics approximations. Interpolating between measurement points, we can recover this function for arbitrary points of a scene. We visualized the global structure of the light field using light tubes, which gives an intuitive description of the flux propagation throughout three-dimensional scenes and provides information about the quality of light in the scenes. Our second-order reconstructions are sufficient to render convex matte objects and therefore have a direct interest for computer graphics applications.

© 2009 Optical Society of America

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  1. A. Gershun, “The light field,” Moscow (1936), translated by P. Moon and G. Tinoshenko in J. Math. Phys. 18, 51-151 (1939).
  2. P. Moon and D. E. Spencer, The Photic Field (MIT, 1981).
  3. P. R. Boyce, Human Factors in Lighting (Macmillan, 1981).
  4. C. Cuttle, Lighting by Design (Architectural, 2003).
  5. C. Cuttle, “Cubic illumination,” Light. Res. Technol. 29, 1-14(1997).
    [CrossRef]
  6. http://www.megatron.co.uk/cim/index.html.
  7. A. A. Mury, S. C. Pont, and J. J. Koenderink, “Light field constancy within natural scenes,” Appl. Opt. 46, 7308-7316(2007).
    [CrossRef] [PubMed]
  8. E. H. Adelson and J. Bergen, “The plenoptic function and the elements of early vision,” in Computational Models of Visual Processing, M. Landy and J. Movshon, eds. (MIT, 1991), pp. 3-20.
  9. S. J. Gortler, R. Grzeszczuk, R. Szeliski, and M. F. Cohen, “The lumigraph,” in Computer Graphics, Proc. SIGGRAPH 96 (1996), pp. 43-54.
  10. M. Levoy and P. Hanrahan, “Light field rendering,” in Proc. SIGGRAPH 96 (1996), pp. 31-42.
    [CrossRef]
  11. http://www.debevec.org/Probes/.
  12. P. Debevec, “Rendering synthetic objects into real scenes: bridging traditional and image-based graphics with global illumination and high dynamic range photography,” in Proc. SIGGRAPH 98 (1998), pp. 189-198.
    [CrossRef]
  13. J. Unger, A. Wenger, T. Hawkins, A. Gardner, and P. Debevec, “Capturing and rendering with incident light fields,” in Proc. of the 14th Eurographics Workshop on Rendering (2003).
  14. R. Epstein, P. Hallinan, and A. Yuille, “5 plus or minus 2 eigenimages suffice: an empirical investigation of low-dimensional lighting models,” in Proc. IEEE Workshop Physics-Based Modeling in Computer Vision (1995), pp. 108-116.
    [CrossRef]
  15. P. W. Hallinan, “A low-dimensional representation of human faces for arbitrary lighting conditions,” in Proc. IEEE Conference on Computer Vision and Pattern Recognition (1994), pp. 995-999.
    [CrossRef]
  16. R. Ramamoorthi and P. Hanrahan, “On the relationship between radiance and irradiance: determining the illumination from images of a convex Lambertian object,” J. Opt. Soc. Am. A 18, 2448-2459 (2001).
    [CrossRef]
  17. R. Basri and D. Jacobs, “Lambertian reflectance and linear subspaces,” Proc. 8th IEEE Int. Conf. Computer Vision (2001), pp. 383-390.
  18. A. A. Mury, S. C. Pont, and J. J. Koenderink, “Spatial properties of light fields in natural scenes,” in Proc. APGV 2007, ACM SIGGRAPH, S. N. Spencer, ed. (2007), p. 140.
  19. J. J. Koenderink, S. C. Pont, A. J. van Doorn, A. M. L. Kappers, and J. T. Todd, “The visual light field,” Perception 36, 1595-1610 (2007).
    [CrossRef]
  20. G. W. Larson and R. A. Shakespeare, Rendering with Radiance: the Art and Science of Lighting Visualization (Morgan Kaufmann, 1997).
  21. A. Jacobs, MSc in Energy, Architecture and Sustainability: European Masters in the Integration of Renewable Energies into Buildings, RADIANCE Course (Advanced) (London Metropolitan University, 2004).
    [PubMed]
  22. G. Greger, P. Shirley, P. Hubbard, and D. Greenberg, “The irradiance volume,” IEEE Comput. Graph. Appl. 18, 32-43(1998).
    [CrossRef]
  23. V. Verma, D. Kao, and A. Pang, “A flow-guided streamlines seeding strategy,” Proc. IEEE Visualization (2000), pp. 163-170.
  24. C. Cuttle, “Lighting patterns and the flow of light,” Light. Res. Technol. 3, 171-189 (1971).

2007 (2)

A. A. Mury, S. C. Pont, and J. J. Koenderink, “Light field constancy within natural scenes,” Appl. Opt. 46, 7308-7316(2007).
[CrossRef] [PubMed]

J. J. Koenderink, S. C. Pont, A. J. van Doorn, A. M. L. Kappers, and J. T. Todd, “The visual light field,” Perception 36, 1595-1610 (2007).
[CrossRef]

2001 (1)

1998 (1)

G. Greger, P. Shirley, P. Hubbard, and D. Greenberg, “The irradiance volume,” IEEE Comput. Graph. Appl. 18, 32-43(1998).
[CrossRef]

1997 (1)

C. Cuttle, “Cubic illumination,” Light. Res. Technol. 29, 1-14(1997).
[CrossRef]

1971 (1)

C. Cuttle, “Lighting patterns and the flow of light,” Light. Res. Technol. 3, 171-189 (1971).

1939 (1)

A. Gershun, “The light field,” Moscow (1936), translated by P. Moon and G. Tinoshenko in J. Math. Phys. 18, 51-151 (1939).

Adelson, E. H.

E. H. Adelson and J. Bergen, “The plenoptic function and the elements of early vision,” in Computational Models of Visual Processing, M. Landy and J. Movshon, eds. (MIT, 1991), pp. 3-20.

Basri, R.

R. Basri and D. Jacobs, “Lambertian reflectance and linear subspaces,” Proc. 8th IEEE Int. Conf. Computer Vision (2001), pp. 383-390.

Bergen, J.

E. H. Adelson and J. Bergen, “The plenoptic function and the elements of early vision,” in Computational Models of Visual Processing, M. Landy and J. Movshon, eds. (MIT, 1991), pp. 3-20.

Boyce, P. R.

P. R. Boyce, Human Factors in Lighting (Macmillan, 1981).

Cohen, M. F.

S. J. Gortler, R. Grzeszczuk, R. Szeliski, and M. F. Cohen, “The lumigraph,” in Computer Graphics, Proc. SIGGRAPH 96 (1996), pp. 43-54.

Cuttle, C.

C. Cuttle, “Cubic illumination,” Light. Res. Technol. 29, 1-14(1997).
[CrossRef]

C. Cuttle, “Lighting patterns and the flow of light,” Light. Res. Technol. 3, 171-189 (1971).

C. Cuttle, Lighting by Design (Architectural, 2003).

Debevec, P.

P. Debevec, “Rendering synthetic objects into real scenes: bridging traditional and image-based graphics with global illumination and high dynamic range photography,” in Proc. SIGGRAPH 98 (1998), pp. 189-198.
[CrossRef]

J. Unger, A. Wenger, T. Hawkins, A. Gardner, and P. Debevec, “Capturing and rendering with incident light fields,” in Proc. of the 14th Eurographics Workshop on Rendering (2003).

Epstein, R.

R. Epstein, P. Hallinan, and A. Yuille, “5 plus or minus 2 eigenimages suffice: an empirical investigation of low-dimensional lighting models,” in Proc. IEEE Workshop Physics-Based Modeling in Computer Vision (1995), pp. 108-116.
[CrossRef]

Gardner, A.

J. Unger, A. Wenger, T. Hawkins, A. Gardner, and P. Debevec, “Capturing and rendering with incident light fields,” in Proc. of the 14th Eurographics Workshop on Rendering (2003).

Gershun, A.

A. Gershun, “The light field,” Moscow (1936), translated by P. Moon and G. Tinoshenko in J. Math. Phys. 18, 51-151 (1939).

Gortler, S. J.

S. J. Gortler, R. Grzeszczuk, R. Szeliski, and M. F. Cohen, “The lumigraph,” in Computer Graphics, Proc. SIGGRAPH 96 (1996), pp. 43-54.

Greenberg, D.

G. Greger, P. Shirley, P. Hubbard, and D. Greenberg, “The irradiance volume,” IEEE Comput. Graph. Appl. 18, 32-43(1998).
[CrossRef]

Greger, G.

G. Greger, P. Shirley, P. Hubbard, and D. Greenberg, “The irradiance volume,” IEEE Comput. Graph. Appl. 18, 32-43(1998).
[CrossRef]

Grzeszczuk, R.

S. J. Gortler, R. Grzeszczuk, R. Szeliski, and M. F. Cohen, “The lumigraph,” in Computer Graphics, Proc. SIGGRAPH 96 (1996), pp. 43-54.

Hallinan, P.

R. Epstein, P. Hallinan, and A. Yuille, “5 plus or minus 2 eigenimages suffice: an empirical investigation of low-dimensional lighting models,” in Proc. IEEE Workshop Physics-Based Modeling in Computer Vision (1995), pp. 108-116.
[CrossRef]

Hallinan, P. W.

P. W. Hallinan, “A low-dimensional representation of human faces for arbitrary lighting conditions,” in Proc. IEEE Conference on Computer Vision and Pattern Recognition (1994), pp. 995-999.
[CrossRef]

Hanrahan, P.

Hawkins, T.

J. Unger, A. Wenger, T. Hawkins, A. Gardner, and P. Debevec, “Capturing and rendering with incident light fields,” in Proc. of the 14th Eurographics Workshop on Rendering (2003).

Hubbard, P.

G. Greger, P. Shirley, P. Hubbard, and D. Greenberg, “The irradiance volume,” IEEE Comput. Graph. Appl. 18, 32-43(1998).
[CrossRef]

Jacobs, A.

A. Jacobs, MSc in Energy, Architecture and Sustainability: European Masters in the Integration of Renewable Energies into Buildings, RADIANCE Course (Advanced) (London Metropolitan University, 2004).
[PubMed]

Jacobs, D.

R. Basri and D. Jacobs, “Lambertian reflectance and linear subspaces,” Proc. 8th IEEE Int. Conf. Computer Vision (2001), pp. 383-390.

Kao, D.

V. Verma, D. Kao, and A. Pang, “A flow-guided streamlines seeding strategy,” Proc. IEEE Visualization (2000), pp. 163-170.

Kappers, A. M. L.

J. J. Koenderink, S. C. Pont, A. J. van Doorn, A. M. L. Kappers, and J. T. Todd, “The visual light field,” Perception 36, 1595-1610 (2007).
[CrossRef]

Koenderink, J. J.

J. J. Koenderink, S. C. Pont, A. J. van Doorn, A. M. L. Kappers, and J. T. Todd, “The visual light field,” Perception 36, 1595-1610 (2007).
[CrossRef]

A. A. Mury, S. C. Pont, and J. J. Koenderink, “Light field constancy within natural scenes,” Appl. Opt. 46, 7308-7316(2007).
[CrossRef] [PubMed]

A. A. Mury, S. C. Pont, and J. J. Koenderink, “Spatial properties of light fields in natural scenes,” in Proc. APGV 2007, ACM SIGGRAPH, S. N. Spencer, ed. (2007), p. 140.

Larson, G. W.

G. W. Larson and R. A. Shakespeare, Rendering with Radiance: the Art and Science of Lighting Visualization (Morgan Kaufmann, 1997).

Levoy, M.

M. Levoy and P. Hanrahan, “Light field rendering,” in Proc. SIGGRAPH 96 (1996), pp. 31-42.
[CrossRef]

Moon, P.

P. Moon and D. E. Spencer, The Photic Field (MIT, 1981).

Mury, A. A.

A. A. Mury, S. C. Pont, and J. J. Koenderink, “Light field constancy within natural scenes,” Appl. Opt. 46, 7308-7316(2007).
[CrossRef] [PubMed]

A. A. Mury, S. C. Pont, and J. J. Koenderink, “Spatial properties of light fields in natural scenes,” in Proc. APGV 2007, ACM SIGGRAPH, S. N. Spencer, ed. (2007), p. 140.

Pang, A.

V. Verma, D. Kao, and A. Pang, “A flow-guided streamlines seeding strategy,” Proc. IEEE Visualization (2000), pp. 163-170.

Pont, S. C.

J. J. Koenderink, S. C. Pont, A. J. van Doorn, A. M. L. Kappers, and J. T. Todd, “The visual light field,” Perception 36, 1595-1610 (2007).
[CrossRef]

A. A. Mury, S. C. Pont, and J. J. Koenderink, “Light field constancy within natural scenes,” Appl. Opt. 46, 7308-7316(2007).
[CrossRef] [PubMed]

A. A. Mury, S. C. Pont, and J. J. Koenderink, “Spatial properties of light fields in natural scenes,” in Proc. APGV 2007, ACM SIGGRAPH, S. N. Spencer, ed. (2007), p. 140.

Ramamoorthi, R.

Shakespeare, R. A.

G. W. Larson and R. A. Shakespeare, Rendering with Radiance: the Art and Science of Lighting Visualization (Morgan Kaufmann, 1997).

Shirley, P.

G. Greger, P. Shirley, P. Hubbard, and D. Greenberg, “The irradiance volume,” IEEE Comput. Graph. Appl. 18, 32-43(1998).
[CrossRef]

Spencer, D. E.

P. Moon and D. E. Spencer, The Photic Field (MIT, 1981).

Szeliski, R.

S. J. Gortler, R. Grzeszczuk, R. Szeliski, and M. F. Cohen, “The lumigraph,” in Computer Graphics, Proc. SIGGRAPH 96 (1996), pp. 43-54.

Todd, J. T.

J. J. Koenderink, S. C. Pont, A. J. van Doorn, A. M. L. Kappers, and J. T. Todd, “The visual light field,” Perception 36, 1595-1610 (2007).
[CrossRef]

Unger, J.

J. Unger, A. Wenger, T. Hawkins, A. Gardner, and P. Debevec, “Capturing and rendering with incident light fields,” in Proc. of the 14th Eurographics Workshop on Rendering (2003).

van Doorn, A. J.

J. J. Koenderink, S. C. Pont, A. J. van Doorn, A. M. L. Kappers, and J. T. Todd, “The visual light field,” Perception 36, 1595-1610 (2007).
[CrossRef]

Verma, V.

V. Verma, D. Kao, and A. Pang, “A flow-guided streamlines seeding strategy,” Proc. IEEE Visualization (2000), pp. 163-170.

Wenger, A.

J. Unger, A. Wenger, T. Hawkins, A. Gardner, and P. Debevec, “Capturing and rendering with incident light fields,” in Proc. of the 14th Eurographics Workshop on Rendering (2003).

Yuille, A.

R. Epstein, P. Hallinan, and A. Yuille, “5 plus or minus 2 eigenimages suffice: an empirical investigation of low-dimensional lighting models,” in Proc. IEEE Workshop Physics-Based Modeling in Computer Vision (1995), pp. 108-116.
[CrossRef]

Appl. Opt. (1)

IEEE Comput. Graph. Appl. (1)

G. Greger, P. Shirley, P. Hubbard, and D. Greenberg, “The irradiance volume,” IEEE Comput. Graph. Appl. 18, 32-43(1998).
[CrossRef]

J. Math. Phys. (1)

A. Gershun, “The light field,” Moscow (1936), translated by P. Moon and G. Tinoshenko in J. Math. Phys. 18, 51-151 (1939).

J. Opt. Soc. Am. A (1)

Light. Res. Technol. (2)

C. Cuttle, “Cubic illumination,” Light. Res. Technol. 29, 1-14(1997).
[CrossRef]

C. Cuttle, “Lighting patterns and the flow of light,” Light. Res. Technol. 3, 171-189 (1971).

Perception (1)

J. J. Koenderink, S. C. Pont, A. J. van Doorn, A. M. L. Kappers, and J. T. Todd, “The visual light field,” Perception 36, 1595-1610 (2007).
[CrossRef]

Other (17)

G. W. Larson and R. A. Shakespeare, Rendering with Radiance: the Art and Science of Lighting Visualization (Morgan Kaufmann, 1997).

A. Jacobs, MSc in Energy, Architecture and Sustainability: European Masters in the Integration of Renewable Energies into Buildings, RADIANCE Course (Advanced) (London Metropolitan University, 2004).
[PubMed]

V. Verma, D. Kao, and A. Pang, “A flow-guided streamlines seeding strategy,” Proc. IEEE Visualization (2000), pp. 163-170.

http://www.megatron.co.uk/cim/index.html.

R. Basri and D. Jacobs, “Lambertian reflectance and linear subspaces,” Proc. 8th IEEE Int. Conf. Computer Vision (2001), pp. 383-390.

A. A. Mury, S. C. Pont, and J. J. Koenderink, “Spatial properties of light fields in natural scenes,” in Proc. APGV 2007, ACM SIGGRAPH, S. N. Spencer, ed. (2007), p. 140.

P. Moon and D. E. Spencer, The Photic Field (MIT, 1981).

P. R. Boyce, Human Factors in Lighting (Macmillan, 1981).

C. Cuttle, Lighting by Design (Architectural, 2003).

E. H. Adelson and J. Bergen, “The plenoptic function and the elements of early vision,” in Computational Models of Visual Processing, M. Landy and J. Movshon, eds. (MIT, 1991), pp. 3-20.

S. J. Gortler, R. Grzeszczuk, R. Szeliski, and M. F. Cohen, “The lumigraph,” in Computer Graphics, Proc. SIGGRAPH 96 (1996), pp. 43-54.

M. Levoy and P. Hanrahan, “Light field rendering,” in Proc. SIGGRAPH 96 (1996), pp. 31-42.
[CrossRef]

http://www.debevec.org/Probes/.

P. Debevec, “Rendering synthetic objects into real scenes: bridging traditional and image-based graphics with global illumination and high dynamic range photography,” in Proc. SIGGRAPH 98 (1998), pp. 189-198.
[CrossRef]

J. Unger, A. Wenger, T. Hawkins, A. Gardner, and P. Debevec, “Capturing and rendering with incident light fields,” in Proc. of the 14th Eurographics Workshop on Rendering (2003).

R. Epstein, P. Hallinan, and A. Yuille, “5 plus or minus 2 eigenimages suffice: an empirical investigation of low-dimensional lighting models,” in Proc. IEEE Workshop Physics-Based Modeling in Computer Vision (1995), pp. 108-116.
[CrossRef]

P. W. Hallinan, “A low-dimensional representation of human faces for arbitrary lighting conditions,” in Proc. IEEE Conference on Computer Vision and Pattern Recognition (1994), pp. 995-999.
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Example of flux lines—the distribution of the flux lines inside two three-story buildings opposite each other (shown as cross sections) under an overcast sky. The flux lines start at the overcast sky and enter the buildings through the windows. The interreflections are taken into account.

Fig. 2
Fig. 2

First nine spherical harmonics basis functions.

Fig. 3
Fig. 3

Plenopter: a light-measuring device capable of capturing local light fields up to the second order. Twelve photocells with wide apertures of 74 ° cover the entire sphere capturing light from all directions.

Fig. 4
Fig. 4

Schematic description of the light sources (view from above) and panoramic photographs of the Light Lab for different lighting installations. (a) Three diffuse area light sources on the ceiling along the left wall. (b) Large circular diffuse area light source in the middle of the ceiling. (c) Four small spotlights (close to collimated) at the corners on the ceiling directed straight downward. (d) Three diffuse area light sources on the ceiling in a triangular configuration.

Fig. 5
Fig. 5

Logarithmic contour plots representing the magnitudes of space illumination (left), light vector (middle), and squash tensor (right) over the middle level ( 155 cm ) for scenes depicted in Fig. 4. The magnitudes were scaled individually such that the maximum range of gray values is used. White crosses indicate the measurement points used for interpolation; black crosses indicate the extra measurements taken in Scenes A and D.

Fig. 6
Fig. 6

Spherical harmonics coefficients calculated in Scenes A (left) and D (right) at extra points indicated by crosses on Fig. 5. Light gray bars represent spherical harmonics calculated from real measurements and dark gray from interpolated values.

Fig. 7
Fig. 7

Panoramic 180 ° × 360 ° plots representing second-order approximations of the light fields corresponding to the coefficients in Fig. 6 (left, real measurements; right, interpolated) for Scenes A and D.

Fig. 8
Fig. 8

Light tubes for the scenes schematically depicted in Fig. 4. The light sources are indicated by squares and circles. The tubes describe radiant flux transfer. Flux through any section of any light tube within a scene is constant. The light vectors are tangential to the tubes, and their magnitudes are counter proportional to the square areas of tubes sections.

Fig. 9
Fig. 9

Object’s appearance along a light tube. (a) One of the light tubes selected from Scene C. (b) Pictures of Lambertian 3D object (Stanford Bunny) rendered using light fields at points indicated on the tube. The contour plots represent 180 ° × 360 ° panoramic images of the second-order light fields at those points.

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