Abstract

We present a tone mapping algorithm that is derived from a model of retinal processing. Our approach has two major improvements over existing methods. First, tone mapping is applied directly on the mosaic image captured by the sensor, analogous to the human visual system that applies a nonlinearity to the chromatic responses captured by the cone mosaic. This reduces the number of necessary operations by a factor 3. Second, we introduce a variation of the center/surround class of local tone mapping algorithms, which are known to increase the local contrast of images but tend to create artifacts. Our method gives a good improvement in contrast while avoiding halos and maintaining good global appearance. Like traditional center/surround algorithms, our method uses a weighted average of surrounding pixel values. Instead of being used directly, the weighted average serves as a variable in the Naka–Rushton equation, which models the photoreceptors’ nonlinearity. Our algorithm provides pleasing results on various images with different scene content and dynamic range.

© 2007 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
  21. D. Alleysson, S. Süsstrunk, and J. Herault, "Linear demosaicing inspired by the human visual system," IEEE Trans. Image Process. 14, 439-449 (2005).
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    [CrossRef] [PubMed]
  30. Z.-U. Rahman, D. J. Jobson, and G. A. Woodell, "Retinex processing for automatic image enhancement," J. Electron. Imaging 13, 100-110 (2004).
    [CrossRef]
  31. R. Fattal, D. Lischinski, and M. Werman, "Gradient domain high dynamic range compression," in Proceedings of ACM SIGGRAPH 2002, Annual Conference on Computer Graphics (ACM, 2002), pp. 249-256.
  32. F. Durand and J. Dorsey, "Fast bilateral filtering for the display of high-dynamic-range images," in Proceedings of ACM SIGGRAPH 2002, Annual Conference on Computer Graphics (ACM, 2002), pp. 257-266.
  33. K. Barnard and B. Funt, "Investigations into multi-scale Retinex," in Colour Imaging: Vision and Technology, (Wiley, 1999), pp. 9-17.
  34. K. T. Mullen, "The contrast sensitivity of human colour vision to red/green and blue/yellow chromatic gratings," J. Physiol. (London) 359, 381-400 (1985).
  35. D. Coffin, http://cybercom.net/~dcoffin/dcraw/.
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  39. J. Kuang, H. Yamaguchi, G. M. Johnson, and M. D. Fairchild, "Testing HDR image rendering algorithms," in Proceedings of IS&T/SID Twelfth Color Imaging Conference: Color Science, Systems, and Application, (IS&T, 2004), pp. 315-320.
  40. D. Alleysson, L. Meylan and S. Süsstrunk, "HDR CFA image rendering," in Proceedings of EURASIP 14th European Signal Processing Conference (European Association for Signal Processing, 2006).
  41. Supplementary material available at http://ivrg.epfl.ch/supplementarylowbarmaterial/index.html.
  42. M. Schwab, M. Karrenbach, and J. Claerbout, "Making scientific computations reproducible," Comput. Sci. Eng. 2, 61-67 (2000).
    [CrossRef]

2006 (2)

J. H. Van Hateren, "Encoding of high dynamic range video with a model of human cones," ACM Trans. Graphics 25, 1380-1399 (2006).
[CrossRef]

L. Meylan and S. Süsstrunk, "High dynamic range image rendering with a Retinex-based adaptive filter," IEEE Trans. Image Process. 15, 2820-2830 (2006).
[CrossRef] [PubMed]

2005 (2)

D. Alleysson, S. Süsstrunk, and J. Herault, "Linear demosaicing inspired by the human visual system," IEEE Trans. Image Process. 14, 439-449 (2005).
[CrossRef] [PubMed]

E. Dubois, "Frequency-domain methods for demosaicing of Bayer-sampled color images," IEEE Signal Process. Lett. 12, 847-850 (2005).
[CrossRef]

2004 (1)

Z.-U. Rahman, D. J. Jobson, and G. A. Woodell, "Retinex processing for automatic image enhancement," J. Electron. Imaging 13, 100-110 (2004).
[CrossRef]

2002 (1)

H. Spitzer and S. Semo, "Color constancy: a biological model and its application for still and video images," Pattern Recogn. 35, 1645-1659 (2002).
[CrossRef]

2001 (1)

A. Roorda, A. B. Mehta, P. Lennie, and D. R. Williams, "Packing arrangement of the three cone classes in primate retina," Vision Res. 41, 1291-1306 (2001).
[CrossRef] [PubMed]

2000 (1)

M. Schwab, M. Karrenbach, and J. Claerbout, "Making scientific computations reproducible," Comput. Sci. Eng. 2, 61-67 (2000).
[CrossRef]

1999 (3)

G. J. Braun and M. D. Fairchild, "Image lightness rescaling using sigmoidal contrast enhancement functions," J. Electron. Imaging 8, 380-393 (1999).
[CrossRef]

A. Roorda and D. R. Williams, "The arrangement of the three cone classes in the living human eye," Nature 397, 520-522 (1999).
[CrossRef] [PubMed]

M. Kamermans and H. Spekreijse, "The feedback pathway from horizontal cells to cones. A mini review with a look ahead," Vision Res. 39, 2449-2468 (1999).
[CrossRef] [PubMed]

1998 (1)

D. C. Hood, "Lower-level visual processing and models of light adaptation," Annu. Rev. Psychol. 49, 503-535 (1998).
[CrossRef] [PubMed]

1997 (1)

G. Ward, H. Rushmeier, and C. Piatko, "A visibility matching tone reproduction operator for high dynamic range scenes," IEEE Trans. Vis. Comput. Graph. 3, 291-306 (1997).
[CrossRef]

1993 (1)

T. Yeh, J. Pokorny, and V. C. Smith, "Chromatic discrimination with variation in chromaticity and luminance: data and theory," Vision Res. 33, 1835-1845 (1993).
[CrossRef] [PubMed]

1991 (1)

M. A. Webster and J. Mollon, "Changes in colour appearance following post-receptoral adaptation," Nature (London) 349, 235-238 (1991).
[CrossRef]

1985 (2)

C. R. Ingling and E. Martinez-Uriegas, "The spatiotemporal properties of the r-g x-cell channel," Vision Res. 25, 33-38 (1985).
[CrossRef] [PubMed]

K. T. Mullen, "The contrast sensitivity of human colour vision to red/green and blue/yellow chromatic gratings," J. Physiol. (London) 359, 381-400 (1985).

1966 (1)

K.-I. Naka and W. A. H. Rushton, "S-potentials from luminosity units in the retina of fish (Cyprinidae)," J. Physiol. (London) 185, 587-599 (1966).

Alleysson, D.

D. Alleysson, S. Süsstrunk, and J. Herault, "Linear demosaicing inspired by the human visual system," IEEE Trans. Image Process. 14, 439-449 (2005).
[CrossRef] [PubMed]

D. Alleysson, L. Meylan and S. Süsstrunk, "HDR CFA image rendering," in Proceedings of EURASIP 14th European Signal Processing Conference (European Association for Signal Processing, 2006).

Ashikhmin, M.

M. Ashikhmin, "A tone mapping algorithm for high contrast images," in Proceedings of Eurographics Workshop on Rendering Techniques (Eurographics Association, 2002), pp. 145-155.

Barnard, K.

K. Barnard and B. Funt, "Investigations into multi-scale Retinex," in Colour Imaging: Vision and Technology, (Wiley, 1999), pp. 9-17.

Bayer, B. E.

B. E. Bayer, "Color imaging array," U.S. patent 3,971,065 (March 3, 1976).

Braun, G. J.

G. J. Braun and M. D. Fairchild, "Image lightness rescaling using sigmoidal contrast enhancement functions," J. Electron. Imaging 8, 380-393 (1999).
[CrossRef]

Chalmers, A.

P. Ledda, A. Chalmers, T. Troscianko, and H. Seetzen, "Evaluation of tone mapping operators using a high dynamic range display," in Proceedings of ACM SIGGRAPH 2005, Annual Conference on Computer Graphics (ACM, 2005), pp. 640-648.

Chang, L.

N. Lian, L. Chang, and Y. Tan, "Improved color filter array demosaicing by accurate luminance estimation," in Proceedings of IEEE Conference on Image Processing (IEEE, 2005), pp. I-41-44.

Claerbout, J.

M. Schwab, M. Karrenbach, and J. Claerbout, "Making scientific computations reproducible," Comput. Sci. Eng. 2, 61-67 (2000).
[CrossRef]

Coffin, D.

D. Coffin, http://cybercom.net/~dcoffin/dcraw/.

De Valois, K. K.

R. L. De Valois and K. K. De Valois, Spatial Vision, Oxford Psychology Series 14, (Oxford U. Press, 1990).

De Valois, R. L.

R. L. De Valois and K. K. De Valois, Spatial Vision, Oxford Psychology Series 14, (Oxford U. Press, 1990).

Debevec, P.

E. Reinhard, G. Ward, S. Pattanaik, and P. Debevec, High Dynamic Range Imaging. Acquisition, Display, and Image-Based Lighting, (Morgan Kaufmann, 2005).

Devlin, K.

K. Devlin, "A review of tone reproduction techniques," Technical Rep. CSTR-02-005 (Department of Computer Science, University of Bristol, 2002).

Dorsey, J.

F. Durand and J. Dorsey, "Fast bilateral filtering for the display of high-dynamic-range images," in Proceedings of ACM SIGGRAPH 2002, Annual Conference on Computer Graphics (ACM, 2002), pp. 257-266.

Dubois, E.

E. Dubois, "Frequency-domain methods for demosaicing of Bayer-sampled color images," IEEE Signal Process. Lett. 12, 847-850 (2005).
[CrossRef]

Durand, F.

F. Durand and J. Dorsey, "Fast bilateral filtering for the display of high-dynamic-range images," in Proceedings of ACM SIGGRAPH 2002, Annual Conference on Computer Graphics (ACM, 2002), pp. 257-266.

Enroth-Cugell, C.

R. Shapley and C. Enroth-Cugell, "Visual adaptation and retinal gain controls," in Progress in Retinal Research (Pergamon, 1984), pp. 263-346.
[CrossRef]

Fairchild, M. D.

G. J. Braun and M. D. Fairchild, "Image lightness rescaling using sigmoidal contrast enhancement functions," J. Electron. Imaging 8, 380-393 (1999).
[CrossRef]

J. Kuang, H. Yamaguchi, G. M. Johnson, and M. D. Fairchild, "Testing HDR image rendering algorithms," in Proceedings of IS&T/SID Twelfth Color Imaging Conference: Color Science, Systems, and Application, (IS&T, 2004), pp. 315-320.

Fattal, R.

R. Fattal, D. Lischinski, and M. Werman, "Gradient domain high dynamic range compression," in Proceedings of ACM SIGGRAPH 2002, Annual Conference on Computer Graphics (ACM, 2002), pp. 249-256.

Ferwerda, J.

E. Reinhard, M. Stark, P. Shirley, and J. Ferwerda, "Photographic tone reproduction for digital images," in Proceedings of ACM SIGGRAPH 2002, Annual Conference on Computer Graphics (ACM, 2002), pp. 267-276.

Funt, B.

K. Barnard and B. Funt, "Investigations into multi-scale Retinex," in Colour Imaging: Vision and Technology, (Wiley, 1999), pp. 9-17.

Graham, N. V. S.

N. V. S. Graham, Visual Pattern Analysers, Oxford Psychology Series 16 (Oxford U. Press, 1989).
[CrossRef]

Hanlon, L.

J. Holm, I. Tastl, L. Hanlon, and P. Hubel, "Color processing for digital photography," in Colour Engineering: Achieving Device Independent Colour, P.Green and L.MacDonald eds. (Wiley, 2002), pp. 179-220.

Haralick, R. M.

R. M. Haralick and L. G. Shapiro, Computer and Robot Vision, 1st ed. (Addison-Wesley, 1993).

Herault, J.

D. Alleysson, S. Süsstrunk, and J. Herault, "Linear demosaicing inspired by the human visual system," IEEE Trans. Image Process. 14, 439-449 (2005).
[CrossRef] [PubMed]

Holm, J.

J. Holm, I. Tastl, L. Hanlon, and P. Hubel, "Color processing for digital photography," in Colour Engineering: Achieving Device Independent Colour, P.Green and L.MacDonald eds. (Wiley, 2002), pp. 179-220.

J. Holm, "Photographic tone and colour reproduction goals," in Proceedings of CIE Expert Symposium'96 on Colour Standards for Image Technology, (CIE, 1996), pp. 51-56.

Hood, D. C.

D. C. Hood, "Lower-level visual processing and models of light adaptation," Annu. Rev. Psychol. 49, 503-535 (1998).
[CrossRef] [PubMed]

Hubel, P.

J. Holm, I. Tastl, L. Hanlon, and P. Hubel, "Color processing for digital photography," in Colour Engineering: Achieving Device Independent Colour, P.Green and L.MacDonald eds. (Wiley, 2002), pp. 179-220.

Ingling, C. R.

C. R. Ingling and E. Martinez-Uriegas, "The spatiotemporal properties of the r-g x-cell channel," Vision Res. 25, 33-38 (1985).
[CrossRef] [PubMed]

Jobson, D. J.

Z.-U. Rahman, D. J. Jobson, and G. A. Woodell, "Retinex processing for automatic image enhancement," J. Electron. Imaging 13, 100-110 (2004).
[CrossRef]

Johnson, G. M.

J. Kuang, H. Yamaguchi, G. M. Johnson, and M. D. Fairchild, "Testing HDR image rendering algorithms," in Proceedings of IS&T/SID Twelfth Color Imaging Conference: Color Science, Systems, and Application, (IS&T, 2004), pp. 315-320.

Kamermans, M.

M. Kamermans and H. Spekreijse, "The feedback pathway from horizontal cells to cones. A mini review with a look ahead," Vision Res. 39, 2449-2468 (1999).
[CrossRef] [PubMed]

Karrenbach, M.

M. Schwab, M. Karrenbach, and J. Claerbout, "Making scientific computations reproducible," Comput. Sci. Eng. 2, 61-67 (2000).
[CrossRef]

Kuang, J.

J. Kuang, H. Yamaguchi, G. M. Johnson, and M. D. Fairchild, "Testing HDR image rendering algorithms," in Proceedings of IS&T/SID Twelfth Color Imaging Conference: Color Science, Systems, and Application, (IS&T, 2004), pp. 315-320.

Ledda, P.

P. Ledda, A. Chalmers, T. Troscianko, and H. Seetzen, "Evaluation of tone mapping operators using a high dynamic range display," in Proceedings of ACM SIGGRAPH 2005, Annual Conference on Computer Graphics (ACM, 2005), pp. 640-648.

Lennie, P.

A. Roorda, A. B. Mehta, P. Lennie, and D. R. Williams, "Packing arrangement of the three cone classes in primate retina," Vision Res. 41, 1291-1306 (2001).
[CrossRef] [PubMed]

Lian, N.

N. Lian, L. Chang, and Y. Tan, "Improved color filter array demosaicing by accurate luminance estimation," in Proceedings of IEEE Conference on Image Processing (IEEE, 2005), pp. I-41-44.

Lischinski, D.

R. Fattal, D. Lischinski, and M. Werman, "Gradient domain high dynamic range compression," in Proceedings of ACM SIGGRAPH 2002, Annual Conference on Computer Graphics (ACM, 2002), pp. 249-256.

Martinez-Uriegas, E.

C. R. Ingling and E. Martinez-Uriegas, "The spatiotemporal properties of the r-g x-cell channel," Vision Res. 25, 33-38 (1985).
[CrossRef] [PubMed]

Mehta, A. B.

A. Roorda, A. B. Mehta, P. Lennie, and D. R. Williams, "Packing arrangement of the three cone classes in primate retina," Vision Res. 41, 1291-1306 (2001).
[CrossRef] [PubMed]

Meylan, L.

L. Meylan and S. Süsstrunk, "High dynamic range image rendering with a Retinex-based adaptive filter," IEEE Trans. Image Process. 15, 2820-2830 (2006).
[CrossRef] [PubMed]

D. Alleysson, L. Meylan and S. Süsstrunk, "HDR CFA image rendering," in Proceedings of EURASIP 14th European Signal Processing Conference (European Association for Signal Processing, 2006).

Mollon, J.

M. A. Webster and J. Mollon, "Changes in colour appearance following post-receptoral adaptation," Nature (London) 349, 235-238 (1991).
[CrossRef]

Mullen, K. T.

K. T. Mullen, "The contrast sensitivity of human colour vision to red/green and blue/yellow chromatic gratings," J. Physiol. (London) 359, 381-400 (1985).

Naka, K.-I.

K.-I. Naka and W. A. H. Rushton, "S-potentials from luminosity units in the retina of fish (Cyprinidae)," J. Physiol. (London) 185, 587-599 (1966).

Pattanaik, S.

E. Reinhard, G. Ward, S. Pattanaik, and P. Debevec, High Dynamic Range Imaging. Acquisition, Display, and Image-Based Lighting, (Morgan Kaufmann, 2005).

Piatko, C.

G. Ward, H. Rushmeier, and C. Piatko, "A visibility matching tone reproduction operator for high dynamic range scenes," IEEE Trans. Vis. Comput. Graph. 3, 291-306 (1997).
[CrossRef]

Pokorny, J.

T. Yeh, J. Pokorny, and V. C. Smith, "Chromatic discrimination with variation in chromaticity and luminance: data and theory," Vision Res. 33, 1835-1845 (1993).
[CrossRef] [PubMed]

Pratt, W. K.

W. K. Pratt, Digital Image Processing (Wiley, 1991).

Rahman, Z.-U.

Z.-U. Rahman, D. J. Jobson, and G. A. Woodell, "Retinex processing for automatic image enhancement," J. Electron. Imaging 13, 100-110 (2004).
[CrossRef]

Reinhard, E.

E. Reinhard, G. Ward, S. Pattanaik, and P. Debevec, High Dynamic Range Imaging. Acquisition, Display, and Image-Based Lighting, (Morgan Kaufmann, 2005).

E. Reinhard, M. Stark, P. Shirley, and J. Ferwerda, "Photographic tone reproduction for digital images," in Proceedings of ACM SIGGRAPH 2002, Annual Conference on Computer Graphics (ACM, 2002), pp. 267-276.

Roorda, A.

A. Roorda, A. B. Mehta, P. Lennie, and D. R. Williams, "Packing arrangement of the three cone classes in primate retina," Vision Res. 41, 1291-1306 (2001).
[CrossRef] [PubMed]

A. Roorda and D. R. Williams, "The arrangement of the three cone classes in the living human eye," Nature 397, 520-522 (1999).
[CrossRef] [PubMed]

Rushmeier, H.

G. Ward, H. Rushmeier, and C. Piatko, "A visibility matching tone reproduction operator for high dynamic range scenes," IEEE Trans. Vis. Comput. Graph. 3, 291-306 (1997).
[CrossRef]

Rushton, W. A. H.

K.-I. Naka and W. A. H. Rushton, "S-potentials from luminosity units in the retina of fish (Cyprinidae)," J. Physiol. (London) 185, 587-599 (1966).

Schwab, M.

M. Schwab, M. Karrenbach, and J. Claerbout, "Making scientific computations reproducible," Comput. Sci. Eng. 2, 61-67 (2000).
[CrossRef]

Seetzen, H.

P. Ledda, A. Chalmers, T. Troscianko, and H. Seetzen, "Evaluation of tone mapping operators using a high dynamic range display," in Proceedings of ACM SIGGRAPH 2005, Annual Conference on Computer Graphics (ACM, 2005), pp. 640-648.

Semo, S.

H. Spitzer and S. Semo, "Color constancy: a biological model and its application for still and video images," Pattern Recogn. 35, 1645-1659 (2002).
[CrossRef]

Shapiro, L. G.

R. M. Haralick and L. G. Shapiro, Computer and Robot Vision, 1st ed. (Addison-Wesley, 1993).

Shapley, R.

R. Shapley and C. Enroth-Cugell, "Visual adaptation and retinal gain controls," in Progress in Retinal Research (Pergamon, 1984), pp. 263-346.
[CrossRef]

Shirley, P.

E. Reinhard, M. Stark, P. Shirley, and J. Ferwerda, "Photographic tone reproduction for digital images," in Proceedings of ACM SIGGRAPH 2002, Annual Conference on Computer Graphics (ACM, 2002), pp. 267-276.

Smith, V. C.

T. Yeh, J. Pokorny, and V. C. Smith, "Chromatic discrimination with variation in chromaticity and luminance: data and theory," Vision Res. 33, 1835-1845 (1993).
[CrossRef] [PubMed]

Spekreijse, H.

M. Kamermans and H. Spekreijse, "The feedback pathway from horizontal cells to cones. A mini review with a look ahead," Vision Res. 39, 2449-2468 (1999).
[CrossRef] [PubMed]

Spitzer, H.

H. Spitzer and S. Semo, "Color constancy: a biological model and its application for still and video images," Pattern Recogn. 35, 1645-1659 (2002).
[CrossRef]

Stark, M.

E. Reinhard, M. Stark, P. Shirley, and J. Ferwerda, "Photographic tone reproduction for digital images," in Proceedings of ACM SIGGRAPH 2002, Annual Conference on Computer Graphics (ACM, 2002), pp. 267-276.

Süsstrunk, S.

L. Meylan and S. Süsstrunk, "High dynamic range image rendering with a Retinex-based adaptive filter," IEEE Trans. Image Process. 15, 2820-2830 (2006).
[CrossRef] [PubMed]

D. Alleysson, S. Süsstrunk, and J. Herault, "Linear demosaicing inspired by the human visual system," IEEE Trans. Image Process. 14, 439-449 (2005).
[CrossRef] [PubMed]

D. Alleysson, L. Meylan and S. Süsstrunk, "HDR CFA image rendering," in Proceedings of EURASIP 14th European Signal Processing Conference (European Association for Signal Processing, 2006).

Tan, Y.

N. Lian, L. Chang, and Y. Tan, "Improved color filter array demosaicing by accurate luminance estimation," in Proceedings of IEEE Conference on Image Processing (IEEE, 2005), pp. I-41-44.

Tastl, I.

J. Holm, I. Tastl, L. Hanlon, and P. Hubel, "Color processing for digital photography," in Colour Engineering: Achieving Device Independent Colour, P.Green and L.MacDonald eds. (Wiley, 2002), pp. 179-220.

Troscianko, T.

P. Ledda, A. Chalmers, T. Troscianko, and H. Seetzen, "Evaluation of tone mapping operators using a high dynamic range display," in Proceedings of ACM SIGGRAPH 2005, Annual Conference on Computer Graphics (ACM, 2005), pp. 640-648.

Van Hateren, J. H.

J. H. Van Hateren, "Encoding of high dynamic range video with a model of human cones," ACM Trans. Graphics 25, 1380-1399 (2006).
[CrossRef]

Ward, G.

G. Ward, H. Rushmeier, and C. Piatko, "A visibility matching tone reproduction operator for high dynamic range scenes," IEEE Trans. Vis. Comput. Graph. 3, 291-306 (1997).
[CrossRef]

E. Reinhard, G. Ward, S. Pattanaik, and P. Debevec, High Dynamic Range Imaging. Acquisition, Display, and Image-Based Lighting, (Morgan Kaufmann, 2005).

Webster, M. A.

M. A. Webster and J. Mollon, "Changes in colour appearance following post-receptoral adaptation," Nature (London) 349, 235-238 (1991).
[CrossRef]

Werman, M.

R. Fattal, D. Lischinski, and M. Werman, "Gradient domain high dynamic range compression," in Proceedings of ACM SIGGRAPH 2002, Annual Conference on Computer Graphics (ACM, 2002), pp. 249-256.

Williams, D. R.

A. Roorda, A. B. Mehta, P. Lennie, and D. R. Williams, "Packing arrangement of the three cone classes in primate retina," Vision Res. 41, 1291-1306 (2001).
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Figures (8)

Fig. 1
Fig. 1

Bayer CFA (left) and the spatiochromatic sampling of the cone mosaic (right) (Inspired from Roorda et al. [1]).

Fig. 2
Fig. 2

(a) Traditional image processing workflow. (b) Our proposed workflow. (c) Image rendered with a global tone mapping operator (gamma). (d) Image rendered according to our method.

Fig. 3
Fig. 3

Simplified model of the retina.

Fig. 4
Fig. 4

Naka–Rushton function with different adaptation factors X 0 .

Fig. 5
Fig. 5

Simulation of the OPL adaptive nonlinear processing. The input signal is processed by the Naka–Rushton equation, whose adaptation factors are given by filtering the CFA image with a low-pass filter. The second nonlinearity that models the IPL layer works similarly.

Fig. 6
Fig. 6

Chrominance channels are separated before interpolation.

Fig. 7
Fig. 7

Comparison of our algorithm with other tone mapping operators. Left column: Low-dynamic-range scene. Middle column: Medium-to high-dynamic-range scene. Right column: High-dynamic-range scene. First row: Global tone mapping with camera default setting. Second row: Images processed with MSRCR [30]. Third row: Images processed with the Retinex-based adaptive filter method [29]. Fourth row: Images processed with our proposed algorithm.

Fig. 8
Fig. 8

Example of our method applied with different filter sizes. Left: Small filters ( σ H = 1 and σ A = 1 ). Right: Large filter ( σ H = 3 and σ A = 5 ).

Equations (20)

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

Y = X X + X 0 ,
I ( p ) = log ( I ( p ) ) log ( I ( p ) G ) ,
H ( p ) = I CFA ( p ) G H + I CFA ¯ 2 ,
G H ( x , y ) = e [ ( x 2 + y 2 ) 2 σ H 2 ] ,
I bip ( p ) = ( I CFA ( max ) + H ( p ) ) I CFA ( p ) I CFA ( p ) + H ( p ) ,
I ga ( p ) = ( I bip ( max ) + A ( p ) ) I bip ( p ) I bip ( p ) + A ( p ) ,
A ( p ) = I bip ( p ) G A + I bip ¯ 2 ,
G A ( x , y ) = e [ ( x 2 + y 2 ) 2 σ A 2 ] ,
F dem = 1 256 [ 1 4 6 4 1 4 16 24 16 4 6 24 36 24 6 4 16 24 16 4 1 4 6 4 1 ] .
L ( p ) = I ga ( p ) F dem ,
C ( p ) = I ga ( p ) L ( p ) ,
m R ( x , y ) = ( 1 + cos ( π x ) ) ( 1 + cos ( π y ) ) 4 ,
m G ( x , y ) = ( 1 cos ( π x ) cos ( π y ) ) 2 ,
m B ( x , y ) = ( 1 cos ( π x ) ) ( 1 cos ( π y ) ) 4 ,
C 1 ( x , y ) = C ( x , y ) m R ( x , y ) ,
C 2 ( x , y ) = C ( x , y ) m G ( x , y ) ,
C 3 ( x , y ) = C ( x , y ) m B ( x , y ) .
R ( p ) = L ( p ) + C 1 ( p ) ,
G ( p ) = L ( p ) + C 2 ( p ) ,
B ( p ) = L ( p ) + C 3 ( p ) ,

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