Abstract

Estimation of camera response function (CRF) has become important in the field of computer graphics and radiance measurement to achieve accurate modeling and high dynamic range imaging. A method is proposed to provide accurate radiance for direct measurement of the CRF in this paper by using a polariscope. The experimental results indicate that the accuracy of the estimated CRF obtained by the new approach is about 5% better than that of the previous method.

© 2013 Optical Society of America

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  1. Y. Yu, P. E. Debevec, J. Malik, and T. Hawkins, “Inverse global illumination: recovering reflectance models of real scenes from photographs,” in Proceedings of the 26th Annual ACM SIGGRAPH Conference on Computer Graphics and Interactive Techniques (1999), pp. 215–224.
  2. P. E. Debevec, “Rendering synthetic objects into real scenes,” in Proceedings of the 25th Annual ACM SIGGRAPH Conference on Computer Graphics and Interactive Techniques (1998), pp. 189–198.
  3. S. Marschner, S. Westin, E. Lafortune, and K. Torrance, “Image-based BRDF measurement,” Appl. Opt. 39, 2592–2600 (2000).
    [CrossRef]
  4. Q. T. Luong, P. Fua, and Y. Leclerc, “The radiometry of multiple images,” IEEE Trans. Pattern Anal. Mach. Intell. 24, 19–33 (2002).
    [CrossRef]
  5. A. D. Nurse, “Full-field automated photoelasticity by use of a three wavelength approach to phase stepping,” Appl. Opt. 36, 5781–5786 (1997).
    [CrossRef]
  6. L. Zhenkun, Y. Dazhen, and Y. Wanming, “Whole-field determination of isoclinic parameter by five-step color phase shifting and its error analysis,” Opt. Lasers Eng. 40, 189–200 (2003).
    [CrossRef]
  7. H. P. Wu, Y. P. Lee, and S. H. Chang, “Fast measurement of automotive headlamp based on high dynamic range imaging,” Appl. Opt. 51, 6870–6880 (2012).
    [CrossRef]
  8. P. E. Debevec and J. Malik, “Recovering high dynamic range radiance maps from photographs,” in Proceedings of the 24th Annual ACM SIGGRAPH Conference on Computer Graphics and Interactive Techniques (1997), pp. 369–378.
  9. A. R. Varkonyi-Koczy and A. Rovid, “High-dynamic-range image reproduction methods,” IEEE Trans. Instrum. Meas. 56, 1465–1472 (2007).
    [CrossRef]
  10. T. Mitsunaga and S. K. Nayar, “High dynamic range imaging: spatially varying pixel exposures,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (2000), pp. 472–479.
  11. M. D. Grossberg and S. K. Nayar, “Modeling the space of camera response functions,” IEEE Trans. Pattern Anal. Mach. Intell. 26, 1272–1282 (2004).
    [CrossRef]
  12. Y. Tsin, V. Ramesh, and T. Kanade, “Statistical calibration of CCD imaging process,” in Proceedings of the IEEE International Conference on Computer Vision (2001), pp. 480–487.
  13. S. Mann, “Comparametric equations with practical applications in quantigraphic image processing,” IEEE Trans. Image Process. 9, 1389–1406 (2000).
    [CrossRef]
  14. S. Mann and R. Mann, “Quantigraphic imaging: estimating the camera response and exposures from differently exposed images,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (2001), pp. 842–849.
  15. F. M. Candocia and D. A. Mandarino, “A semiparametric model for accurate camera response function modeling and exposure estimation from comparametric data,” IEEE Trans. Image Process 14, 1138–1150 (2005).
    [CrossRef]
  16. C. Manders, C. Aimone, and S. Mum, “Camera response function recovery from different illuminations of identical subject matter,” in IEEE International Conference on Image Processing (2004), pp. 2965–2968.
  17. G. Healey and R. Kondepudy, “Radiometric CCD camera calibration and noise estimation,” IEEE Trans. Pattern Anal. Mach. Intell. 16, 267–276 (1994).
    [CrossRef]
  18. A. Bevilacqua, A. Gherardi, and L. Carozza, “A robust approach to reconstruct experimentally the camera response function,” in First Workshops on Image Processing Theory, Tools and Applications (2008), pp. 1–6.
  19. B. Wilburn, H. Xu, and Y. Matsushita, “Radiometric calibration using temporal irradiance mixtures,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (2008), pp. 1–7.
  20. J. M. Bennett, “Polarization,” in Handbook of Optics, M. Bass and E. W. Van Stryland, eds. (McGraw-Hill, 1995), Vol. 1, pp. 5.12–5.13.
  21. D. A. Forsyth and J. Ponce, Computer Vision A Modern Approach (Prentice-Hall, 2003), pp. 62–63.
  22. C. Kolb, D. Mitchell, and P. Hanrahan, “A realistic camera model for computer graphics,” in Proceedings of the 22nd Annual ACM SIGGRAPH Conference on Computer Graphics and Interactive Techniques (1995), pp. 317–324.

2012 (1)

2007 (1)

A. R. Varkonyi-Koczy and A. Rovid, “High-dynamic-range image reproduction methods,” IEEE Trans. Instrum. Meas. 56, 1465–1472 (2007).
[CrossRef]

2005 (1)

F. M. Candocia and D. A. Mandarino, “A semiparametric model for accurate camera response function modeling and exposure estimation from comparametric data,” IEEE Trans. Image Process 14, 1138–1150 (2005).
[CrossRef]

2004 (1)

M. D. Grossberg and S. K. Nayar, “Modeling the space of camera response functions,” IEEE Trans. Pattern Anal. Mach. Intell. 26, 1272–1282 (2004).
[CrossRef]

2003 (1)

L. Zhenkun, Y. Dazhen, and Y. Wanming, “Whole-field determination of isoclinic parameter by five-step color phase shifting and its error analysis,” Opt. Lasers Eng. 40, 189–200 (2003).
[CrossRef]

2002 (1)

Q. T. Luong, P. Fua, and Y. Leclerc, “The radiometry of multiple images,” IEEE Trans. Pattern Anal. Mach. Intell. 24, 19–33 (2002).
[CrossRef]

2000 (2)

S. Mann, “Comparametric equations with practical applications in quantigraphic image processing,” IEEE Trans. Image Process. 9, 1389–1406 (2000).
[CrossRef]

S. Marschner, S. Westin, E. Lafortune, and K. Torrance, “Image-based BRDF measurement,” Appl. Opt. 39, 2592–2600 (2000).
[CrossRef]

1997 (1)

1994 (1)

G. Healey and R. Kondepudy, “Radiometric CCD camera calibration and noise estimation,” IEEE Trans. Pattern Anal. Mach. Intell. 16, 267–276 (1994).
[CrossRef]

Aimone, C.

C. Manders, C. Aimone, and S. Mum, “Camera response function recovery from different illuminations of identical subject matter,” in IEEE International Conference on Image Processing (2004), pp. 2965–2968.

Bennett, J. M.

J. M. Bennett, “Polarization,” in Handbook of Optics, M. Bass and E. W. Van Stryland, eds. (McGraw-Hill, 1995), Vol. 1, pp. 5.12–5.13.

Bevilacqua, A.

A. Bevilacqua, A. Gherardi, and L. Carozza, “A robust approach to reconstruct experimentally the camera response function,” in First Workshops on Image Processing Theory, Tools and Applications (2008), pp. 1–6.

Candocia, F. M.

F. M. Candocia and D. A. Mandarino, “A semiparametric model for accurate camera response function modeling and exposure estimation from comparametric data,” IEEE Trans. Image Process 14, 1138–1150 (2005).
[CrossRef]

Carozza, L.

A. Bevilacqua, A. Gherardi, and L. Carozza, “A robust approach to reconstruct experimentally the camera response function,” in First Workshops on Image Processing Theory, Tools and Applications (2008), pp. 1–6.

Chang, S. H.

Dazhen, Y.

L. Zhenkun, Y. Dazhen, and Y. Wanming, “Whole-field determination of isoclinic parameter by five-step color phase shifting and its error analysis,” Opt. Lasers Eng. 40, 189–200 (2003).
[CrossRef]

Debevec, P. E.

P. E. Debevec, “Rendering synthetic objects into real scenes,” in Proceedings of the 25th Annual ACM SIGGRAPH Conference on Computer Graphics and Interactive Techniques (1998), pp. 189–198.

Y. Yu, P. E. Debevec, J. Malik, and T. Hawkins, “Inverse global illumination: recovering reflectance models of real scenes from photographs,” in Proceedings of the 26th Annual ACM SIGGRAPH Conference on Computer Graphics and Interactive Techniques (1999), pp. 215–224.

P. E. Debevec and J. Malik, “Recovering high dynamic range radiance maps from photographs,” in Proceedings of the 24th Annual ACM SIGGRAPH Conference on Computer Graphics and Interactive Techniques (1997), pp. 369–378.

Forsyth, D. A.

D. A. Forsyth and J. Ponce, Computer Vision A Modern Approach (Prentice-Hall, 2003), pp. 62–63.

Fua, P.

Q. T. Luong, P. Fua, and Y. Leclerc, “The radiometry of multiple images,” IEEE Trans. Pattern Anal. Mach. Intell. 24, 19–33 (2002).
[CrossRef]

Gherardi, A.

A. Bevilacqua, A. Gherardi, and L. Carozza, “A robust approach to reconstruct experimentally the camera response function,” in First Workshops on Image Processing Theory, Tools and Applications (2008), pp. 1–6.

Grossberg, M. D.

M. D. Grossberg and S. K. Nayar, “Modeling the space of camera response functions,” IEEE Trans. Pattern Anal. Mach. Intell. 26, 1272–1282 (2004).
[CrossRef]

Hanrahan, P.

C. Kolb, D. Mitchell, and P. Hanrahan, “A realistic camera model for computer graphics,” in Proceedings of the 22nd Annual ACM SIGGRAPH Conference on Computer Graphics and Interactive Techniques (1995), pp. 317–324.

Hawkins, T.

Y. Yu, P. E. Debevec, J. Malik, and T. Hawkins, “Inverse global illumination: recovering reflectance models of real scenes from photographs,” in Proceedings of the 26th Annual ACM SIGGRAPH Conference on Computer Graphics and Interactive Techniques (1999), pp. 215–224.

Healey, G.

G. Healey and R. Kondepudy, “Radiometric CCD camera calibration and noise estimation,” IEEE Trans. Pattern Anal. Mach. Intell. 16, 267–276 (1994).
[CrossRef]

Kanade, T.

Y. Tsin, V. Ramesh, and T. Kanade, “Statistical calibration of CCD imaging process,” in Proceedings of the IEEE International Conference on Computer Vision (2001), pp. 480–487.

Kolb, C.

C. Kolb, D. Mitchell, and P. Hanrahan, “A realistic camera model for computer graphics,” in Proceedings of the 22nd Annual ACM SIGGRAPH Conference on Computer Graphics and Interactive Techniques (1995), pp. 317–324.

Kondepudy, R.

G. Healey and R. Kondepudy, “Radiometric CCD camera calibration and noise estimation,” IEEE Trans. Pattern Anal. Mach. Intell. 16, 267–276 (1994).
[CrossRef]

Lafortune, E.

Leclerc, Y.

Q. T. Luong, P. Fua, and Y. Leclerc, “The radiometry of multiple images,” IEEE Trans. Pattern Anal. Mach. Intell. 24, 19–33 (2002).
[CrossRef]

Lee, Y. P.

Luong, Q. T.

Q. T. Luong, P. Fua, and Y. Leclerc, “The radiometry of multiple images,” IEEE Trans. Pattern Anal. Mach. Intell. 24, 19–33 (2002).
[CrossRef]

Malik, J.

Y. Yu, P. E. Debevec, J. Malik, and T. Hawkins, “Inverse global illumination: recovering reflectance models of real scenes from photographs,” in Proceedings of the 26th Annual ACM SIGGRAPH Conference on Computer Graphics and Interactive Techniques (1999), pp. 215–224.

P. E. Debevec and J. Malik, “Recovering high dynamic range radiance maps from photographs,” in Proceedings of the 24th Annual ACM SIGGRAPH Conference on Computer Graphics and Interactive Techniques (1997), pp. 369–378.

Mandarino, D. A.

F. M. Candocia and D. A. Mandarino, “A semiparametric model for accurate camera response function modeling and exposure estimation from comparametric data,” IEEE Trans. Image Process 14, 1138–1150 (2005).
[CrossRef]

Manders, C.

C. Manders, C. Aimone, and S. Mum, “Camera response function recovery from different illuminations of identical subject matter,” in IEEE International Conference on Image Processing (2004), pp. 2965–2968.

Mann, R.

S. Mann and R. Mann, “Quantigraphic imaging: estimating the camera response and exposures from differently exposed images,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (2001), pp. 842–849.

Mann, S.

S. Mann, “Comparametric equations with practical applications in quantigraphic image processing,” IEEE Trans. Image Process. 9, 1389–1406 (2000).
[CrossRef]

S. Mann and R. Mann, “Quantigraphic imaging: estimating the camera response and exposures from differently exposed images,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (2001), pp. 842–849.

Marschner, S.

Matsushita, Y.

B. Wilburn, H. Xu, and Y. Matsushita, “Radiometric calibration using temporal irradiance mixtures,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (2008), pp. 1–7.

Mitchell, D.

C. Kolb, D. Mitchell, and P. Hanrahan, “A realistic camera model for computer graphics,” in Proceedings of the 22nd Annual ACM SIGGRAPH Conference on Computer Graphics and Interactive Techniques (1995), pp. 317–324.

Mitsunaga, T.

T. Mitsunaga and S. K. Nayar, “High dynamic range imaging: spatially varying pixel exposures,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (2000), pp. 472–479.

Mum, S.

C. Manders, C. Aimone, and S. Mum, “Camera response function recovery from different illuminations of identical subject matter,” in IEEE International Conference on Image Processing (2004), pp. 2965–2968.

Nayar, S. K.

M. D. Grossberg and S. K. Nayar, “Modeling the space of camera response functions,” IEEE Trans. Pattern Anal. Mach. Intell. 26, 1272–1282 (2004).
[CrossRef]

T. Mitsunaga and S. K. Nayar, “High dynamic range imaging: spatially varying pixel exposures,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (2000), pp. 472–479.

Nurse, A. D.

Ponce, J.

D. A. Forsyth and J. Ponce, Computer Vision A Modern Approach (Prentice-Hall, 2003), pp. 62–63.

Ramesh, V.

Y. Tsin, V. Ramesh, and T. Kanade, “Statistical calibration of CCD imaging process,” in Proceedings of the IEEE International Conference on Computer Vision (2001), pp. 480–487.

Rovid, A.

A. R. Varkonyi-Koczy and A. Rovid, “High-dynamic-range image reproduction methods,” IEEE Trans. Instrum. Meas. 56, 1465–1472 (2007).
[CrossRef]

Torrance, K.

Tsin, Y.

Y. Tsin, V. Ramesh, and T. Kanade, “Statistical calibration of CCD imaging process,” in Proceedings of the IEEE International Conference on Computer Vision (2001), pp. 480–487.

Varkonyi-Koczy, A. R.

A. R. Varkonyi-Koczy and A. Rovid, “High-dynamic-range image reproduction methods,” IEEE Trans. Instrum. Meas. 56, 1465–1472 (2007).
[CrossRef]

Wanming, Y.

L. Zhenkun, Y. Dazhen, and Y. Wanming, “Whole-field determination of isoclinic parameter by five-step color phase shifting and its error analysis,” Opt. Lasers Eng. 40, 189–200 (2003).
[CrossRef]

Westin, S.

Wilburn, B.

B. Wilburn, H. Xu, and Y. Matsushita, “Radiometric calibration using temporal irradiance mixtures,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (2008), pp. 1–7.

Wu, H. P.

Xu, H.

B. Wilburn, H. Xu, and Y. Matsushita, “Radiometric calibration using temporal irradiance mixtures,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (2008), pp. 1–7.

Yu, Y.

Y. Yu, P. E. Debevec, J. Malik, and T. Hawkins, “Inverse global illumination: recovering reflectance models of real scenes from photographs,” in Proceedings of the 26th Annual ACM SIGGRAPH Conference on Computer Graphics and Interactive Techniques (1999), pp. 215–224.

Zhenkun, L.

L. Zhenkun, Y. Dazhen, and Y. Wanming, “Whole-field determination of isoclinic parameter by five-step color phase shifting and its error analysis,” Opt. Lasers Eng. 40, 189–200 (2003).
[CrossRef]

Appl. Opt. (3)

IEEE Trans. Image Process (1)

F. M. Candocia and D. A. Mandarino, “A semiparametric model for accurate camera response function modeling and exposure estimation from comparametric data,” IEEE Trans. Image Process 14, 1138–1150 (2005).
[CrossRef]

IEEE Trans. Image Process. (1)

S. Mann, “Comparametric equations with practical applications in quantigraphic image processing,” IEEE Trans. Image Process. 9, 1389–1406 (2000).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

A. R. Varkonyi-Koczy and A. Rovid, “High-dynamic-range image reproduction methods,” IEEE Trans. Instrum. Meas. 56, 1465–1472 (2007).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (3)

M. D. Grossberg and S. K. Nayar, “Modeling the space of camera response functions,” IEEE Trans. Pattern Anal. Mach. Intell. 26, 1272–1282 (2004).
[CrossRef]

Q. T. Luong, P. Fua, and Y. Leclerc, “The radiometry of multiple images,” IEEE Trans. Pattern Anal. Mach. Intell. 24, 19–33 (2002).
[CrossRef]

G. Healey and R. Kondepudy, “Radiometric CCD camera calibration and noise estimation,” IEEE Trans. Pattern Anal. Mach. Intell. 16, 267–276 (1994).
[CrossRef]

Opt. Lasers Eng. (1)

L. Zhenkun, Y. Dazhen, and Y. Wanming, “Whole-field determination of isoclinic parameter by five-step color phase shifting and its error analysis,” Opt. Lasers Eng. 40, 189–200 (2003).
[CrossRef]

Other (12)

P. E. Debevec and J. Malik, “Recovering high dynamic range radiance maps from photographs,” in Proceedings of the 24th Annual ACM SIGGRAPH Conference on Computer Graphics and Interactive Techniques (1997), pp. 369–378.

Y. Yu, P. E. Debevec, J. Malik, and T. Hawkins, “Inverse global illumination: recovering reflectance models of real scenes from photographs,” in Proceedings of the 26th Annual ACM SIGGRAPH Conference on Computer Graphics and Interactive Techniques (1999), pp. 215–224.

P. E. Debevec, “Rendering synthetic objects into real scenes,” in Proceedings of the 25th Annual ACM SIGGRAPH Conference on Computer Graphics and Interactive Techniques (1998), pp. 189–198.

Y. Tsin, V. Ramesh, and T. Kanade, “Statistical calibration of CCD imaging process,” in Proceedings of the IEEE International Conference on Computer Vision (2001), pp. 480–487.

T. Mitsunaga and S. K. Nayar, “High dynamic range imaging: spatially varying pixel exposures,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (2000), pp. 472–479.

S. Mann and R. Mann, “Quantigraphic imaging: estimating the camera response and exposures from differently exposed images,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (2001), pp. 842–849.

C. Manders, C. Aimone, and S. Mum, “Camera response function recovery from different illuminations of identical subject matter,” in IEEE International Conference on Image Processing (2004), pp. 2965–2968.

A. Bevilacqua, A. Gherardi, and L. Carozza, “A robust approach to reconstruct experimentally the camera response function,” in First Workshops on Image Processing Theory, Tools and Applications (2008), pp. 1–6.

B. Wilburn, H. Xu, and Y. Matsushita, “Radiometric calibration using temporal irradiance mixtures,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (2008), pp. 1–7.

J. M. Bennett, “Polarization,” in Handbook of Optics, M. Bass and E. W. Van Stryland, eds. (McGraw-Hill, 1995), Vol. 1, pp. 5.12–5.13.

D. A. Forsyth and J. Ponce, Computer Vision A Modern Approach (Prentice-Hall, 2003), pp. 62–63.

C. Kolb, D. Mitchell, and P. Hanrahan, “A realistic camera model for computer graphics,” in Proceedings of the 22nd Annual ACM SIGGRAPH Conference on Computer Graphics and Interactive Techniques (1995), pp. 317–324.

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Figures (11)

Fig. 1.
Fig. 1.

Plane polariscope which is composed of one polarizer and one analyzer.

Fig. 2.
Fig. 2.

Image of the analyzer output taken at the rotation angle of 20°, 40°, 60°, and 80°, respectively.

Fig. 3.
Fig. 3.

Irradiance measured by the photometer (dot) and predicted by the formula (curve), respectively, for each angle.

Fig. 4.
Fig. 4.

Pixel value acquired and its corresponding normalized exposure value computed by using Eq. (9). These points were then fitted to form the CRF curve.

Fig. 5.
Fig. 5.

Seven images captured with different exposure times were used for the CRF estimation based on the DM method.

Fig. 6.
Fig. 6.

Comparison of the estimated CRF’s based on the proposed method and the DM method.

Fig. 7.
Fig. 7.

Patterns of the headlamp light were used in the performance evaluation for the estimated CRF. They were acquired under different exposures: (a) 1/4s and (b) 1/2s.

Fig. 8.
Fig. 8.

Rms errors defined for homogeneity test were computed in each given region for both methods.

Fig. 9.
Fig. 9.

Effect of the extinction ratio on radiation accuracy.

Fig. 10.
Fig. 10.

Effect of the mechanical rotation error on radiation accuracy.

Fig. 11.
Fig. 11.

Overall radiation accuracy of the experimental setup.

Equations (16)

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ρp=TeTt=IminImax,
T(θ)=(TtTe)cos2θ+Te,
I(θ)=I0[(TtTe)cos2θ+Te].
E=Lπ4(df)2cos4α,
X=Ets=kI(θ)[π4(df)2cos4α]ts=sI(θ)ts,
X2X1=Ets2Ets1=ts2ts1=r.
e=rX1X21=rϕ1(Z1)ϕ1(Z2)1,
δ=1Ni=1N(rϕ1(Z1i)ϕ1(Z2i)1)2×100%.
Xij=sI(θi)tsj[(TtTe)cos2θi+Te]tsj,
ε=i=146j=18(k=0nakXijkZij)2.
T(θ)=(TtTe)cos2θ+Te
T(θ)=Tt[(1ρp)cos2θ+ρp].
Tideal(θ)=Ttcos2θ.
ERρ=T(θ)Tideal(θ)Tideal(θ)=(1ρp)cos2θ+ρpcos2θcos2θ=ρp+ρpcos2θ.
T˜(θ)=(TtTe)cos2(θΔθ)+Te.
ERθ=T˜(θ)T(θ)T(θ)=(1ρp)cos2(θΔθ)+ρp(1ρp)cos2θ+ρp1cos2(θΔθ)+ρpcos2θ+ρp1=1+cos(θΔθ)+2ρp1+cosθ+2ρp1=cos(θΔθ)cosθ1+cosθ+2ρp.

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