Abstract

Structural similarity metrics and information-theory-based metrics have been proposed as completely different alternatives to the traditional metrics based on error visibility and human vision models. Three basic criticisms were raised against the traditional error visibility approach: (1) it is based on near-threshold performance, (2) its geometric meaning may be limited, and (3) stationary pooling strategies may not be statistically justified. These criticisms and the good performance of structural and information-theory-based metrics have popularized the idea of their superiority over the error visibility approach. In this work we experimentally or analytically show that the above criticisms do not apply to error visibility metrics that use a general enough divisive normalization masking model. Therefore, the traditional divisive normalization metric [1] is not intrinsically inferior to the newer approaches. In fact, experiments on a number of databases including a wide range of distortions show that divisive normalization is fairly competitive with the newer approaches, robust, and easy to interpret in linear terms. These results suggest that, despite the criticisms of the traditional error visibility approach, divisive normalization masking models should be considered in the image quality discussion.

© 2010 Optical Society of America

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2010 (1)

V. Laparra, J. Gutiérrez, G. Camps-Valls, and J. Malo, “Denoising with kernels based on natural image relations,” J. Mach. Learn. Res. 11, 873-903 (2010).

2009 (1)

Z. Wang and A. Bovik, “Mean squared error: love it or leave it?” IEEE Signal Process. Mag. 26(1), 98-117 (2009).
[CrossRef]

2008 (1)

G. Camps, G. Gómez, J. Gutiérrez, and J. Malo, “On the suitable domain for SVM training in image coding,” J. Mach. Learn. Res. 9, 49-66 (2008).

2007 (1)

D. Chandler and S. Hemami, “VSNR: a wavelet based visual signal-to-noise ratio for natural images,” IEEE Trans. Image Process. 16, 2284-2298 (2007).
[CrossRef] [PubMed]

2006 (6)

L. Zhaoping, “Theoretical understanding of the early visual processes by data compression and data selection,” Network Comput. Neural Syst. 17, 301-334 (2006).
[CrossRef]

J. Malo, I. Epifanio, R. Navarro, and E. Simoncelli, “Non-linear image representation for efficient perceptual coding,” IEEE Trans. Image Process. 15, 68-80 (2006).
[CrossRef] [PubMed]

J. Gutiérrez, F. J. Ferri, and J. Malo, “Regularization operators for natural images based on nonlinear perception models,” IEEE Trans. Image Process. 15, 189-2000 (2006).
[CrossRef] [PubMed]

H. Sheikh, M. Sabir, and A. Bovik, “A statistical evaluation of recent full reference image quality assessment algorithms,” IEEE Trans. Image Process. 15, 3440-3451 (2006).
[CrossRef] [PubMed]

H. Sheikh and A. Bovik, “Image information and visual quality,” IEEE Trans. Image Process. 15, 430-444 (2006).
[CrossRef] [PubMed]

J. Malo and J. Gutiérrez, “V1 non-linear properties emerge from local-to-global non-linear ICA,” Network Comput. Neural Syst. 17, 85-102 (2006).
[CrossRef]

2005 (1)

H. Sheikh, A. Bovik, and G. de Veciana, “An information fidelity criterion for image quality assessment using natural scene statistics,” IEEE Trans. Image Process. 14, 2117-2128 (2005).
[CrossRef] [PubMed]

2004 (1)

Z. Wang, A. Bovik, H. Sheikh, and E. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600-612 (2004).
[CrossRef] [PubMed]

2003 (1)

I. Epifanio, J. Gutiérrez, and J. Malo, “Linear transform for simultaneous diagonalization of covariance and perceptual metric matrix in image coding,” Pattern Recogn. 36, 1799-1811 (2003).
[CrossRef]

2001 (2)

A. Watson and L. Kreslake, “Measurement of visual impairment scales for digital video,” in Proc. SPIE 4299, 79-89 (2001).
[CrossRef]

O. Schwartz and E. P. Simoncelli, “Natural signal statistics and sensory gain control,” Nat. Neurosci. 4, 819-825 (2001).
[CrossRef] [PubMed]

2000 (2)

A. Watson and C. Ramirez, “A Standard Observer for spatial vision,” Invest. Ophthalmol. Visual Sci. 41, S713 (2000).

J. Malo, R. Navarro, I. Epifanio, F. Ferri, and J. M. Artigas, “Non-linear invertible representation for joint statistical and perceptual feature representation,” Lect. Notes Comput. Sci. 1876, 658-667 (2000).
[CrossRef]

1997 (3)

J. Malo, A. M. Pons, A. Felipe, and J. Artigas, “Characterization of human visual system threshold performance by a weighting function in the Gabor domain,” J. Mod. Opt. 44, 127-148 (1997).
[CrossRef]

J. Malo, A. Pons, and J. Artigas, “Subjective image fidelity metric based on bit allocation of the human visual system in the DCT domain,” Image Vis. Comput. 15, 535-548 (1997).
[CrossRef]

A. B. Watson and J. A. Solomon, “A model of visual contrast gain control and pattern masking,” J. Opt. Soc. Am. A 14, 2379-2391 (1997).
[CrossRef]

1996 (1)

B. A. Olshausen and D. J. Field, “Emergence of simple-cell receptive field properties by learning a sparse code for natural images,” Nature 381, 607-609 (1996).
[CrossRef] [PubMed]

1994 (1)

P. Teo and D. Heeger, “Perceptual image distortion,” Proc. SPIE 2179, 127-141 (1994).
[CrossRef]

1992 (3)

E. Simoncelli, W. Freeman, E. Adelson, and D. Heeger, “Shiftable multi-scale transforms,” IEEE Trans. Inf. Theory 38, 587-607 (1992).
[CrossRef]

K. Gegenfurtner and D. Kiper, “Contrast detection in luminance and chromatic noise,” J. Opt. Soc. Am. A 9, 1880-1888 (1992).
[CrossRef] [PubMed]

D. J. Heeger, “Normalization of cell responses in cat striate cortex,” Visual Neurosci. 9, 181-198 (1992).
[CrossRef]

1990 (2)

P. Barten, “Evaluation of subjective image quality with the square root integral method,” J. Opt. Soc. Am. A 7, 2024-2031 (1990).
[CrossRef]

S. Daly, “Application of a noise-adaptive contrast sensitivity function to image data compression,” Opt. Eng. (Bellingham) 29, 977-987 (1990).
[CrossRef]

1989 (1)

L. Saghri, P. Cheatheam, and A. Habibi, “Image quality measure based on a human visual system model,” Opt. Eng. (Bellingham) 28, 813-819 (1989).

1985 (2)

N. Nill, “A visual model weighted cosine transform for image compression and quality assessment,” IEEE Trans. Commun. 33, 551-557 (1985).
[CrossRef]

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

1968 (1)

F. W. Campbell and J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. (London) 197, 551-566 (1968).

1965 (1)

J. A. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308-313 (1965).

Adelson, E.

E. Simoncelli, W. Freeman, E. Adelson, and D. Heeger, “Shiftable multi-scale transforms,” IEEE Trans. Inf. Theory 38, 587-607 (1992).
[CrossRef]

E. Simoncelli and E. Adelson, Subband Image Coding (Kluwer Academic, 1990), Chap. “Subband transforms,” pp. 143-192.

Ahumada, A.

A. Ahumada, “Computational image quality metrics: a review,” in International Symposium Digest of Technical Papers, Proceedings of the Society for Information Display, J.Morreale, ed. (SID, 1993), Vol. 24, pp. 305-308.

Artigas, J.

J. Malo, A. M. Pons, A. Felipe, and J. Artigas, “Characterization of human visual system threshold performance by a weighting function in the Gabor domain,” J. Mod. Opt. 44, 127-148 (1997).
[CrossRef]

J. Malo, A. Pons, and J. Artigas, “Subjective image fidelity metric based on bit allocation of the human visual system in the DCT domain,” Image Vis. Comput. 15, 535-548 (1997).
[CrossRef]

Artigas, J. M.

J. Malo, R. Navarro, I. Epifanio, F. Ferri, and J. M. Artigas, “Non-linear invertible representation for joint statistical and perceptual feature representation,” Lect. Notes Comput. Sci. 1876, 658-667 (2000).
[CrossRef]

Astola, J.

N. Ponomarenko, M. Carli, V. Lukin, K. Egiazarian, J. Astola, and F. Battisti, “Color image database for evaluation of image quality metrics,” in Proceedings of the International Workshop on Multi-media Signal Processing (2008), pp. 403-408.

Autrusseau, F.

P. Le Callet and F. Autrusseau, “Subjective quality assessment irccyn/ivc database,” 2005, http://www.irccyn.ec-nantes.fr/ivcdb/.

Barlow, H. B.

H. B. Barlow, “Possible principles underlying the transformation of sensory messages,” in Sensory Communication, W.Rosenblith, ed. (MIT Press, 1961), pp. 217-234.

Barten, P.

Battisti, F.

N. Ponomarenko, M. Carli, V. Lukin, K. Egiazarian, J. Astola, and F. Battisti, “Color image database for evaluation of image quality metrics,” in Proceedings of the International Workshop on Multi-media Signal Processing (2008), pp. 403-408.

Bovik, A.

Z. Wang and A. Bovik, “Mean squared error: love it or leave it?” IEEE Signal Process. Mag. 26(1), 98-117 (2009).
[CrossRef]

H. Sheikh and A. Bovik, “Image information and visual quality,” IEEE Trans. Image Process. 15, 430-444 (2006).
[CrossRef] [PubMed]

H. Sheikh, M. Sabir, and A. Bovik, “A statistical evaluation of recent full reference image quality assessment algorithms,” IEEE Trans. Image Process. 15, 3440-3451 (2006).
[CrossRef] [PubMed]

H. Sheikh, A. Bovik, and G. de Veciana, “An information fidelity criterion for image quality assessment using natural scene statistics,” IEEE Trans. Image Process. 14, 2117-2128 (2005).
[CrossRef] [PubMed]

Z. Wang, A. Bovik, H. Sheikh, and E. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600-612 (2004).
[CrossRef] [PubMed]

Z. Wang, E. Simoncelli, and A. Bovik, “Multi-scale structural similarity for image quality assessment,” in IEEE Asilomar Conference on Signals, Systems and Computers (IEEE, 2003), Vol. 37.

K. Seshadrinathan and A. Bovik, “Unifying analysis of full reference image quality assessment,” in Proceedings of the 15th IEEE International Conference on Image Processing (IEEE Signal Processing Society, 2008), pp. 1200-1203.
[CrossRef]

H. Sheikh, Z. Wang, L. Cormack, and A. Bovik, “LIVE image quality assessment database,” 2006. Available at http://live.ece.utexas.edu/research/quality.

Campbell, F. W.

F. W. Campbell and J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. (London) 197, 551-566 (1968).

Camps, G.

G. Camps, G. Gómez, J. Gutiérrez, and J. Malo, “On the suitable domain for SVM training in image coding,” J. Mach. Learn. Res. 9, 49-66 (2008).

V. Laparra, G. Camps, and J. Malo, “PCA gaussianization for image processing,” in Proceedings of the 16th IEEE International Conference on Image Processing (IEEE Signal Processing Society, 2009).

Camps-Valls, G.

V. Laparra, J. Gutiérrez, G. Camps-Valls, and J. Malo, “Denoising with kernels based on natural image relations,” J. Mach. Learn. Res. 11, 873-903 (2010).

Carli, M.

N. Ponomarenko, M. Carli, V. Lukin, K. Egiazarian, J. Astola, and F. Battisti, “Color image database for evaluation of image quality metrics,” in Proceedings of the International Workshop on Multi-media Signal Processing (2008), pp. 403-408.

Chandler, D.

D. Chandler and S. Hemami, “VSNR: a wavelet based visual signal-to-noise ratio for natural images,” IEEE Trans. Image Process. 16, 2284-2298 (2007).
[CrossRef] [PubMed]

Cheatheam, P.

L. Saghri, P. Cheatheam, and A. Habibi, “Image quality measure based on a human visual system model,” Opt. Eng. (Bellingham) 28, 813-819 (1989).

Cormack, L.

H. Sheikh, Z. Wang, L. Cormack, and A. Bovik, “LIVE image quality assessment database,” 2006. Available at http://live.ece.utexas.edu/research/quality.

Cover, T. M.

T. M. Cover and J. A. Thomas, Elements of Information Theory (Wilson, 1991).
[CrossRef]

Daly, S.

S. Daly, “Application of a noise-adaptive contrast sensitivity function to image data compression,” Opt. Eng. (Bellingham) 29, 977-987 (1990).
[CrossRef]

de Veciana, G.

H. Sheikh, A. Bovik, and G. de Veciana, “An information fidelity criterion for image quality assessment using natural scene statistics,” IEEE Trans. Image Process. 14, 2117-2128 (2005).
[CrossRef] [PubMed]

Egiazarian, K.

N. Ponomarenko, M. Carli, V. Lukin, K. Egiazarian, J. Astola, and F. Battisti, “Color image database for evaluation of image quality metrics,” in Proceedings of the International Workshop on Multi-media Signal Processing (2008), pp. 403-408.

Epifanio, I.

J. Malo, I. Epifanio, R. Navarro, and E. Simoncelli, “Non-linear image representation for efficient perceptual coding,” IEEE Trans. Image Process. 15, 68-80 (2006).
[CrossRef] [PubMed]

I. Epifanio, J. Gutiérrez, and J. Malo, “Linear transform for simultaneous diagonalization of covariance and perceptual metric matrix in image coding,” Pattern Recogn. 36, 1799-1811 (2003).
[CrossRef]

J. Malo, R. Navarro, I. Epifanio, F. Ferri, and J. M. Artigas, “Non-linear invertible representation for joint statistical and perceptual feature representation,” Lect. Notes Comput. Sci. 1876, 658-667 (2000).
[CrossRef]

Fairchild, M.

M. Fairchild, Color Appearance Models (Addison-Wesley, 1997).

Felipe, A.

J. Malo, A. M. Pons, A. Felipe, and J. Artigas, “Characterization of human visual system threshold performance by a weighting function in the Gabor domain,” J. Mod. Opt. 44, 127-148 (1997).
[CrossRef]

Ferri, F.

J. Malo, R. Navarro, I. Epifanio, F. Ferri, and J. M. Artigas, “Non-linear invertible representation for joint statistical and perceptual feature representation,” Lect. Notes Comput. Sci. 1876, 658-667 (2000).
[CrossRef]

Ferri, F. J.

J. Gutiérrez, F. J. Ferri, and J. Malo, “Regularization operators for natural images based on nonlinear perception models,” IEEE Trans. Image Process. 15, 189-2000 (2006).
[CrossRef] [PubMed]

Field, D. J.

B. A. Olshausen and D. J. Field, “Emergence of simple-cell receptive field properties by learning a sparse code for natural images,” Nature 381, 607-609 (1996).
[CrossRef] [PubMed]

Freeman, W.

E. Simoncelli, W. Freeman, E. Adelson, and D. Heeger, “Shiftable multi-scale transforms,” IEEE Trans. Inf. Theory 38, 587-607 (1992).
[CrossRef]

Gegenfurtner, K.

Gómez, G.

G. Camps, G. Gómez, J. Gutiérrez, and J. Malo, “On the suitable domain for SVM training in image coding,” J. Mach. Learn. Res. 9, 49-66 (2008).

Gutiérrez, J.

V. Laparra, J. Gutiérrez, G. Camps-Valls, and J. Malo, “Denoising with kernels based on natural image relations,” J. Mach. Learn. Res. 11, 873-903 (2010).

G. Camps, G. Gómez, J. Gutiérrez, and J. Malo, “On the suitable domain for SVM training in image coding,” J. Mach. Learn. Res. 9, 49-66 (2008).

J. Malo and J. Gutiérrez, “V1 non-linear properties emerge from local-to-global non-linear ICA,” Network Comput. Neural Syst. 17, 85-102 (2006).
[CrossRef]

J. Gutiérrez, F. J. Ferri, and J. Malo, “Regularization operators for natural images based on nonlinear perception models,” IEEE Trans. Image Process. 15, 189-2000 (2006).
[CrossRef] [PubMed]

I. Epifanio, J. Gutiérrez, and J. Malo, “Linear transform for simultaneous diagonalization of covariance and perceptual metric matrix in image coding,” Pattern Recogn. 36, 1799-1811 (2003).
[CrossRef]

Habibi, A.

L. Saghri, P. Cheatheam, and A. Habibi, “Image quality measure based on a human visual system model,” Opt. Eng. (Bellingham) 28, 813-819 (1989).

Heeger, D.

P. Teo and D. Heeger, “Perceptual image distortion,” Proc. SPIE 2179, 127-141 (1994).
[CrossRef]

E. Simoncelli, W. Freeman, E. Adelson, and D. Heeger, “Shiftable multi-scale transforms,” IEEE Trans. Inf. Theory 38, 587-607 (1992).
[CrossRef]

Heeger, D. J.

D. J. Heeger, “Normalization of cell responses in cat striate cortex,” Visual Neurosci. 9, 181-198 (1992).
[CrossRef]

Hemami, S.

D. Chandler and S. Hemami, “VSNR: a wavelet based visual signal-to-noise ratio for natural images,” IEEE Trans. Image Process. 16, 2284-2298 (2007).
[CrossRef] [PubMed]

Kingdom, F. A. A.

A. Olmos and F. A. A. Kingdom, “Mcgill calibrated colour image database,” http://tabby.vision.mcgill.ca, 2004.

Kiper, D.

Kreslake, L.

A. Watson and L. Kreslake, “Measurement of visual impairment scales for digital video,” in Proc. SPIE 4299, 79-89 (2001).
[CrossRef]

Laparra, V.

V. Laparra, J. Gutiérrez, G. Camps-Valls, and J. Malo, “Denoising with kernels based on natural image relations,” J. Mach. Learn. Res. 11, 873-903 (2010).

V. Laparra, G. Camps, and J. Malo, “PCA gaussianization for image processing,” in Proceedings of the 16th IEEE International Conference on Image Processing (IEEE Signal Processing Society, 2009).

J. Malo and V. Laparra, “Psychophysically tuned divisive normalization approximately factorizes the PDF of natural images,” submitted to Neural Comput.

Le Callet, P.

P. Le Callet and F. Autrusseau, “Subjective quality assessment irccyn/ivc database,” 2005, http://www.irccyn.ec-nantes.fr/ivcdb/.

Lubin, J.

J. Lubin, “The use of psychophysical data and models in the analysis of display system performance,” in Digital Images and Human Vision, A.Watson, ed. (MIT Press, 1993), pp. 163-178.

Lukin, V.

N. Ponomarenko, M. Carli, V. Lukin, K. Egiazarian, J. Astola, and F. Battisti, “Color image database for evaluation of image quality metrics,” in Proceedings of the International Workshop on Multi-media Signal Processing (2008), pp. 403-408.

Lyu, S.

S. Lyu and E. P. Simoncelli, “Nonlinear image representation using divisive normalization,” in Proceedings of the Conference on Computer Vision and Pattern Recognition (IEEE Computer Society, 2008), pp. 1-8.

Malo, J.

V. Laparra, J. Gutiérrez, G. Camps-Valls, and J. Malo, “Denoising with kernels based on natural image relations,” J. Mach. Learn. Res. 11, 873-903 (2010).

G. Camps, G. Gómez, J. Gutiérrez, and J. Malo, “On the suitable domain for SVM training in image coding,” J. Mach. Learn. Res. 9, 49-66 (2008).

J. Malo, I. Epifanio, R. Navarro, and E. Simoncelli, “Non-linear image representation for efficient perceptual coding,” IEEE Trans. Image Process. 15, 68-80 (2006).
[CrossRef] [PubMed]

J. Gutiérrez, F. J. Ferri, and J. Malo, “Regularization operators for natural images based on nonlinear perception models,” IEEE Trans. Image Process. 15, 189-2000 (2006).
[CrossRef] [PubMed]

J. Malo and J. Gutiérrez, “V1 non-linear properties emerge from local-to-global non-linear ICA,” Network Comput. Neural Syst. 17, 85-102 (2006).
[CrossRef]

I. Epifanio, J. Gutiérrez, and J. Malo, “Linear transform for simultaneous diagonalization of covariance and perceptual metric matrix in image coding,” Pattern Recogn. 36, 1799-1811 (2003).
[CrossRef]

J. Malo, R. Navarro, I. Epifanio, F. Ferri, and J. M. Artigas, “Non-linear invertible representation for joint statistical and perceptual feature representation,” Lect. Notes Comput. Sci. 1876, 658-667 (2000).
[CrossRef]

J. Malo, A. Pons, and J. Artigas, “Subjective image fidelity metric based on bit allocation of the human visual system in the DCT domain,” Image Vis. Comput. 15, 535-548 (1997).
[CrossRef]

J. Malo, A. M. Pons, A. Felipe, and J. Artigas, “Characterization of human visual system threshold performance by a weighting function in the Gabor domain,” J. Mod. Opt. 44, 127-148 (1997).
[CrossRef]

J. Malo and V. Laparra, “Psychophysically tuned divisive normalization approximately factorizes the PDF of natural images,” submitted to Neural Comput.

V. Laparra, G. Camps, and J. Malo, “PCA gaussianization for image processing,” in Proceedings of the 16th IEEE International Conference on Image Processing (IEEE Signal Processing Society, 2009).

A. B. Watson and J. Malo, “Video quality measures based on the Standard Spatial Observer,” in Proceedings of the 9th IEEE International Conference on Image Processing (IEEE Signal Processing Society, 2002), pp. 41-44.

Martinez-Uriegas, E.

E. Martinez-Uriegas, “Color detection and color contrast discrimination thresholds,” in Proceedings of the OSA Annual Meeting ILS-XIII (Optical Society of America, 1997), p. 81.

Mead, R.

J. A. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308-313 (1965).

Mullen, K. T.

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

Navarro, R.

J. Malo, I. Epifanio, R. Navarro, and E. Simoncelli, “Non-linear image representation for efficient perceptual coding,” IEEE Trans. Image Process. 15, 68-80 (2006).
[CrossRef] [PubMed]

J. Malo, R. Navarro, I. Epifanio, F. Ferri, and J. M. Artigas, “Non-linear invertible representation for joint statistical and perceptual feature representation,” Lect. Notes Comput. Sci. 1876, 658-667 (2000).
[CrossRef]

Nelder, J. A.

J. A. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308-313 (1965).

Nill, N.

N. Nill, “A visual model weighted cosine transform for image compression and quality assessment,” IEEE Trans. Commun. 33, 551-557 (1985).
[CrossRef]

Olmos, A.

A. Olmos and F. A. A. Kingdom, “Mcgill calibrated colour image database,” http://tabby.vision.mcgill.ca, 2004.

Olshausen, B. A.

B. A. Olshausen and D. J. Field, “Emergence of simple-cell receptive field properties by learning a sparse code for natural images,” Nature 381, 607-609 (1996).
[CrossRef] [PubMed]

Ponomarenko, N.

N. Ponomarenko, M. Carli, V. Lukin, K. Egiazarian, J. Astola, and F. Battisti, “Color image database for evaluation of image quality metrics,” in Proceedings of the International Workshop on Multi-media Signal Processing (2008), pp. 403-408.

Pons, A.

J. Malo, A. Pons, and J. Artigas, “Subjective image fidelity metric based on bit allocation of the human visual system in the DCT domain,” Image Vis. Comput. 15, 535-548 (1997).
[CrossRef]

Pons, A. M.

J. Malo, A. M. Pons, A. Felipe, and J. Artigas, “Characterization of human visual system threshold performance by a weighting function in the Gabor domain,” J. Mod. Opt. 44, 127-148 (1997).
[CrossRef]

Pratt, W.

W. Pratt, Digital Image Processing (Wiley, 1991), Chap. 3, “Photometry and Colorimetry.”

Ramirez, C.

A. Watson and C. Ramirez, “A Standard Observer for spatial vision,” Invest. Ophthalmol. Visual Sci. 41, S713 (2000).

Robson, J. G.

F. W. Campbell and J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. (London) 197, 551-566 (1968).

Sabir, M.

H. Sheikh, M. Sabir, and A. Bovik, “A statistical evaluation of recent full reference image quality assessment algorithms,” IEEE Trans. Image Process. 15, 3440-3451 (2006).
[CrossRef] [PubMed]

Saghri, L.

L. Saghri, P. Cheatheam, and A. Habibi, “Image quality measure based on a human visual system model,” Opt. Eng. (Bellingham) 28, 813-819 (1989).

Schwartz, O.

O. Schwartz and E. P. Simoncelli, “Natural signal statistics and sensory gain control,” Nat. Neurosci. 4, 819-825 (2001).
[CrossRef] [PubMed]

Seshadrinathan, K.

K. Seshadrinathan and A. Bovik, “Unifying analysis of full reference image quality assessment,” in Proceedings of the 15th IEEE International Conference on Image Processing (IEEE Signal Processing Society, 2008), pp. 1200-1203.
[CrossRef]

Sheikh, H.

H. Sheikh, M. Sabir, and A. Bovik, “A statistical evaluation of recent full reference image quality assessment algorithms,” IEEE Trans. Image Process. 15, 3440-3451 (2006).
[CrossRef] [PubMed]

H. Sheikh and A. Bovik, “Image information and visual quality,” IEEE Trans. Image Process. 15, 430-444 (2006).
[CrossRef] [PubMed]

H. Sheikh, A. Bovik, and G. de Veciana, “An information fidelity criterion for image quality assessment using natural scene statistics,” IEEE Trans. Image Process. 14, 2117-2128 (2005).
[CrossRef] [PubMed]

Z. Wang, A. Bovik, H. Sheikh, and E. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600-612 (2004).
[CrossRef] [PubMed]

H. Sheikh, Z. Wang, L. Cormack, and A. Bovik, “LIVE image quality assessment database,” 2006. Available at http://live.ece.utexas.edu/research/quality.

Simoncelli, E.

J. Malo, I. Epifanio, R. Navarro, and E. Simoncelli, “Non-linear image representation for efficient perceptual coding,” IEEE Trans. Image Process. 15, 68-80 (2006).
[CrossRef] [PubMed]

Z. Wang, A. Bovik, H. Sheikh, and E. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600-612 (2004).
[CrossRef] [PubMed]

E. Simoncelli, W. Freeman, E. Adelson, and D. Heeger, “Shiftable multi-scale transforms,” IEEE Trans. Inf. Theory 38, 587-607 (1992).
[CrossRef]

Z. Wang and E. Simoncelli, “Translation insensitive image similarity in complex wavelet domain,” in Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE, 2005), pp. 573-576.

E. Simoncelli and E. Adelson, Subband Image Coding (Kluwer Academic, 1990), Chap. “Subband transforms,” pp. 143-192.

Z. Wang, E. Simoncelli, and A. Bovik, “Multi-scale structural similarity for image quality assessment,” in IEEE Asilomar Conference on Signals, Systems and Computers (IEEE, 2003), Vol. 37.

Simoncelli, E. P.

O. Schwartz and E. P. Simoncelli, “Natural signal statistics and sensory gain control,” Nat. Neurosci. 4, 819-825 (2001).
[CrossRef] [PubMed]

Z. Wang and E. P. Simoncelli, “An adaptive linear system framework for image distortion analysis,” in Proceedings of the 12th IEEE International Conference on Image Processing (IEEE Computer Society, 2005), Vol. III, pp. 1160-1163.

S. Lyu and E. P. Simoncelli, “Nonlinear image representation using divisive normalization,” in Proceedings of the Conference on Computer Vision and Pattern Recognition (IEEE Computer Society, 2008), pp. 1-8.

Solomon, J. A.

Teo, P.

P. Teo and D. Heeger, “Perceptual image distortion,” Proc. SPIE 2179, 127-141 (1994).
[CrossRef]

Thomas, J. A.

T. M. Cover and J. A. Thomas, Elements of Information Theory (Wilson, 1991).
[CrossRef]

Wandell, B. A.

X. Zhang and B. A. Wandell, “A spatial extension to CIELAB for digital color image reproduction,” in Society for Information Display Symposium Technical Digest (SID, 1996), Vol. 27, pp. 731-734.

Wang, Z.

Z. Wang and A. Bovik, “Mean squared error: love it or leave it?” IEEE Signal Process. Mag. 26(1), 98-117 (2009).
[CrossRef]

Z. Wang, A. Bovik, H. Sheikh, and E. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600-612 (2004).
[CrossRef] [PubMed]

Z. Wang and E. P. Simoncelli, “An adaptive linear system framework for image distortion analysis,” in Proceedings of the 12th IEEE International Conference on Image Processing (IEEE Computer Society, 2005), Vol. III, pp. 1160-1163.

Z. Wang, E. Simoncelli, and A. Bovik, “Multi-scale structural similarity for image quality assessment,” in IEEE Asilomar Conference on Signals, Systems and Computers (IEEE, 2003), Vol. 37.

Z. Wang and E. Simoncelli, “Translation insensitive image similarity in complex wavelet domain,” in Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE, 2005), pp. 573-576.

H. Sheikh, Z. Wang, L. Cormack, and A. Bovik, “LIVE image quality assessment database,” 2006. Available at http://live.ece.utexas.edu/research/quality.

Watson, A.

A. Watson and L. Kreslake, “Measurement of visual impairment scales for digital video,” in Proc. SPIE 4299, 79-89 (2001).
[CrossRef]

A. Watson and C. Ramirez, “A Standard Observer for spatial vision,” Invest. Ophthalmol. Visual Sci. 41, S713 (2000).

Watson, A. B.

A. B. Watson and J. A. Solomon, “A model of visual contrast gain control and pattern masking,” J. Opt. Soc. Am. A 14, 2379-2391 (1997).
[CrossRef]

A. B. Watson, Digital Images and Human Vision (MIT Press, 1993).

A. B. Watson and J. Malo, “Video quality measures based on the Standard Spatial Observer,” in Proceedings of the 9th IEEE International Conference on Image Processing (IEEE Signal Processing Society, 2002), pp. 41-44.

Zhang, X.

X. Zhang and B. A. Wandell, “A spatial extension to CIELAB for digital color image reproduction,” in Society for Information Display Symposium Technical Digest (SID, 1996), Vol. 27, pp. 731-734.

Zhaoping, L.

L. Zhaoping, “Theoretical understanding of the early visual processes by data compression and data selection,” Network Comput. Neural Syst. 17, 301-334 (2006).
[CrossRef]

Comput. J. (1)

J. A. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308-313 (1965).

IEEE Signal Process. Mag. (1)

Z. Wang and A. Bovik, “Mean squared error: love it or leave it?” IEEE Signal Process. Mag. 26(1), 98-117 (2009).
[CrossRef]

IEEE Trans. Commun. (1)

N. Nill, “A visual model weighted cosine transform for image compression and quality assessment,” IEEE Trans. Commun. 33, 551-557 (1985).
[CrossRef]

IEEE Trans. Image Process. (7)

J. Malo, I. Epifanio, R. Navarro, and E. Simoncelli, “Non-linear image representation for efficient perceptual coding,” IEEE Trans. Image Process. 15, 68-80 (2006).
[CrossRef] [PubMed]

D. Chandler and S. Hemami, “VSNR: a wavelet based visual signal-to-noise ratio for natural images,” IEEE Trans. Image Process. 16, 2284-2298 (2007).
[CrossRef] [PubMed]

Z. Wang, A. Bovik, H. Sheikh, and E. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600-612 (2004).
[CrossRef] [PubMed]

H. Sheikh, A. Bovik, and G. de Veciana, “An information fidelity criterion for image quality assessment using natural scene statistics,” IEEE Trans. Image Process. 14, 2117-2128 (2005).
[CrossRef] [PubMed]

H. Sheikh and A. Bovik, “Image information and visual quality,” IEEE Trans. Image Process. 15, 430-444 (2006).
[CrossRef] [PubMed]

J. Gutiérrez, F. J. Ferri, and J. Malo, “Regularization operators for natural images based on nonlinear perception models,” IEEE Trans. Image Process. 15, 189-2000 (2006).
[CrossRef] [PubMed]

H. Sheikh, M. Sabir, and A. Bovik, “A statistical evaluation of recent full reference image quality assessment algorithms,” IEEE Trans. Image Process. 15, 3440-3451 (2006).
[CrossRef] [PubMed]

IEEE Trans. Inf. Theory (1)

E. Simoncelli, W. Freeman, E. Adelson, and D. Heeger, “Shiftable multi-scale transforms,” IEEE Trans. Inf. Theory 38, 587-607 (1992).
[CrossRef]

Image Vis. Comput. (1)

J. Malo, A. Pons, and J. Artigas, “Subjective image fidelity metric based on bit allocation of the human visual system in the DCT domain,” Image Vis. Comput. 15, 535-548 (1997).
[CrossRef]

Invest. Ophthalmol. Visual Sci. (1)

A. Watson and C. Ramirez, “A Standard Observer for spatial vision,” Invest. Ophthalmol. Visual Sci. 41, S713 (2000).

J. Mach. Learn. Res. (2)

G. Camps, G. Gómez, J. Gutiérrez, and J. Malo, “On the suitable domain for SVM training in image coding,” J. Mach. Learn. Res. 9, 49-66 (2008).

V. Laparra, J. Gutiérrez, G. Camps-Valls, and J. Malo, “Denoising with kernels based on natural image relations,” J. Mach. Learn. Res. 11, 873-903 (2010).

J. Mod. Opt. (1)

J. Malo, A. M. Pons, A. Felipe, and J. Artigas, “Characterization of human visual system threshold performance by a weighting function in the Gabor domain,” J. Mod. Opt. 44, 127-148 (1997).
[CrossRef]

J. Opt. Soc. Am. A (3)

J. Physiol. (London) (2)

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

F. W. Campbell and J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. (London) 197, 551-566 (1968).

Lect. Notes Comput. Sci. (1)

J. Malo, R. Navarro, I. Epifanio, F. Ferri, and J. M. Artigas, “Non-linear invertible representation for joint statistical and perceptual feature representation,” Lect. Notes Comput. Sci. 1876, 658-667 (2000).
[CrossRef]

Nat. Neurosci. (1)

O. Schwartz and E. P. Simoncelli, “Natural signal statistics and sensory gain control,” Nat. Neurosci. 4, 819-825 (2001).
[CrossRef] [PubMed]

Nature (1)

B. A. Olshausen and D. J. Field, “Emergence of simple-cell receptive field properties by learning a sparse code for natural images,” Nature 381, 607-609 (1996).
[CrossRef] [PubMed]

Network Comput. Neural Syst. (2)

J. Malo and J. Gutiérrez, “V1 non-linear properties emerge from local-to-global non-linear ICA,” Network Comput. Neural Syst. 17, 85-102 (2006).
[CrossRef]

L. Zhaoping, “Theoretical understanding of the early visual processes by data compression and data selection,” Network Comput. Neural Syst. 17, 301-334 (2006).
[CrossRef]

Opt. Eng. (Bellingham) (2)

S. Daly, “Application of a noise-adaptive contrast sensitivity function to image data compression,” Opt. Eng. (Bellingham) 29, 977-987 (1990).
[CrossRef]

L. Saghri, P. Cheatheam, and A. Habibi, “Image quality measure based on a human visual system model,” Opt. Eng. (Bellingham) 28, 813-819 (1989).

Pattern Recogn. (1)

I. Epifanio, J. Gutiérrez, and J. Malo, “Linear transform for simultaneous diagonalization of covariance and perceptual metric matrix in image coding,” Pattern Recogn. 36, 1799-1811 (2003).
[CrossRef]

Proc. SPIE (2)

P. Teo and D. Heeger, “Perceptual image distortion,” Proc. SPIE 2179, 127-141 (1994).
[CrossRef]

A. Watson and L. Kreslake, “Measurement of visual impairment scales for digital video,” in Proc. SPIE 4299, 79-89 (2001).
[CrossRef]

Visual Neurosci. (1)

D. J. Heeger, “Normalization of cell responses in cat striate cortex,” Visual Neurosci. 9, 181-198 (1992).
[CrossRef]

Other (29)

E. Simoncelli and E. Adelson, Subband Image Coding (Kluwer Academic, 1990), Chap. “Subband transforms,” pp. 143-192.

T. M. Cover and J. A. Thomas, Elements of Information Theory (Wilson, 1991).
[CrossRef]

V. Laparra, G. Camps, and J. Malo, “PCA gaussianization for image processing,” in Proceedings of the 16th IEEE International Conference on Image Processing (IEEE Signal Processing Society, 2009).

Personal communication by Z. Wang (Z.Wang@ece.uwaterloo.ca, October 2010).

SSIM available at http://www.ece.uwaterloo.ca/~z70wang/research/ssim/.

MSSIM and VIF available at: http://live.ece.utexas.edu/research/quality/.

Video Quality Experts Group, “Final report from the video quality experts group on the validation of objective models of multimedia quality assessment, phase I,” VQEG Tech. Rep. 2.6, 2008. [Online]. Available at http://www.its.bldrdoc.gov/vqeg/projects/multimedia/.

The software implementations of commonly used metrics do not come with this non-linearity.

M. Fairchild, Color Appearance Models (Addison-Wesley, 1997).

J. Malo and V. Laparra, “Psychophysically tuned divisive normalization approximately factorizes the PDF of natural images,” submitted to Neural Comput.

Divisive Normalization metric code and additional results available at http://www.uv.es/vista/vistavalencia/div_norm_metric/div_norm.html.

S. Lyu and E. P. Simoncelli, “Nonlinear image representation using divisive normalization,” in Proceedings of the Conference on Computer Vision and Pattern Recognition (IEEE Computer Society, 2008), pp. 1-8.

X. Zhang and B. A. Wandell, “A spatial extension to CIELAB for digital color image reproduction,” in Society for Information Display Symposium Technical Digest (SID, 1996), Vol. 27, pp. 731-734.

A. Ahumada, “Computational image quality metrics: a review,” in International Symposium Digest of Technical Papers, Proceedings of the Society for Information Display, J.Morreale, ed. (SID, 1993), Vol. 24, pp. 305-308.

A. B. Watson, Digital Images and Human Vision (MIT Press, 1993).

J. Lubin, “The use of psychophysical data and models in the analysis of display system performance,” in Digital Images and Human Vision, A.Watson, ed. (MIT Press, 1993), pp. 163-178.

Z. Wang, E. Simoncelli, and A. Bovik, “Multi-scale structural similarity for image quality assessment,” in IEEE Asilomar Conference on Signals, Systems and Computers (IEEE, 2003), Vol. 37.

Z. Wang and E. P. Simoncelli, “An adaptive linear system framework for image distortion analysis,” in Proceedings of the 12th IEEE International Conference on Image Processing (IEEE Computer Society, 2005), Vol. III, pp. 1160-1163.

K. Seshadrinathan and A. Bovik, “Unifying analysis of full reference image quality assessment,” in Proceedings of the 15th IEEE International Conference on Image Processing (IEEE Signal Processing Society, 2008), pp. 1200-1203.
[CrossRef]

H. B. Barlow, “Possible principles underlying the transformation of sensory messages,” in Sensory Communication, W.Rosenblith, ed. (MIT Press, 1961), pp. 217-234.

Z. Wang and E. Simoncelli, “Translation insensitive image similarity in complex wavelet domain,” in Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE, 2005), pp. 573-576.

H. Sheikh, Z. Wang, L. Cormack, and A. Bovik, “LIVE image quality assessment database,” 2006. Available at http://live.ece.utexas.edu/research/quality.

N. Ponomarenko, M. Carli, V. Lukin, K. Egiazarian, J. Astola, and F. Battisti, “Color image database for evaluation of image quality metrics,” in Proceedings of the International Workshop on Multi-media Signal Processing (2008), pp. 403-408.

P. Le Callet and F. Autrusseau, “Subjective quality assessment irccyn/ivc database,” 2005, http://www.irccyn.ec-nantes.fr/ivcdb/.

Available at http://foulard.ece.cornell.edu/dmc27/vsnr/vsnr.html.

A. Olmos and F. A. A. Kingdom, “Mcgill calibrated colour image database,” http://tabby.vision.mcgill.ca, 2004.

A. B. Watson and J. Malo, “Video quality measures based on the Standard Spatial Observer,” in Proceedings of the 9th IEEE International Conference on Image Processing (IEEE Signal Processing Society, 2002), pp. 41-44.

E. Martinez-Uriegas, “Color detection and color contrast discrimination thresholds,” in Proceedings of the OSA Annual Meeting ILS-XIII (Optical Society of America, 1997), p. 81.

W. Pratt, Digital Image Processing (Wiley, 1991), Chap. 3, “Photometry and Colorimetry.”

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Figures (9)

Fig. 1
Fig. 1

Linear gains S (left), regularization constants β γ (center), and interaction kernel H (right).

Fig. 2
Fig. 2

Frequency sensitivity prediction for achromatic sinusoids (left) and the corresponding CSF of the Standard Spatial Observer (right).

Fig. 3
Fig. 3

Gabor patch of 6 cyc deg (test) on top of sinusoids of the same frequency and orientation (background). In each row the contrast of the Gabor patch is increased from 0 to 0.6. The contrast of the background is 0 (top row), 0.1 (middle row), and 0.2 (bottom row).

Fig. 4
Fig. 4

Gabor patch of 6 cyc deg (test) on top of sinusoids of the same frequency and different orientation (background). The visibility of the test on top of non-zero backgrounds is reduced but not as much as in Fig. 3.

Fig. 5
Fig. 5

Response predictions for masks of the same orientation (left) and orthogonal orientation (right). Different curves represent different background (mask) contrast. The three curves of each plot correspond to the visibility of the three rows in Figs. 3, 4.

Fig. 6
Fig. 6

Scatter plots, fitted functions, and correlation coefficients for the considered metrics on the LIVE database. The legend shows the symbols representing each distortion in the LIVE database. The solid line represents the linear fitting. The dashed curve represents the four-parameter sigmoid function used in [14], and the dash-dot line represents the five-parameter sigmoid used in [20, 49]. The dotted curve stands for the fourth-order polynomial used in [53].

Fig. 7
Fig. 7

Scatter plots, fitted functions, and correlation coefficients for the considered metrics on the TID database (excluding LIVE-like distortions). The legend represents the symbols corresponding to the distortions that are not present in the LIVE database. Line styles for the calibration functions have the same meaning as in Fig. 6.

Fig. 8
Fig. 8

Scatter plots, fitted functions, and correlation coefficients for the considered metrics on the IVC database (excluding LIVE-like distortions). The only non-LIVE distortion in the IVC database is what they call LAR distortion (see [41] for details). Line styles for the calibration functions have the same meaning as in Fig. 6.

Fig. 9
Fig. 9

Scatter plots, fitted functions, and correlation coefficients for the considered metrics on the Cornell database. The legend represents the symbols corresponding to the distortions that are not present in the LIVE database (no Cornell distortion is present in LIVE since Cornell is an achromatic database). Line styles for the calibration functions have the same meaning as in Fig. 6.

Tables (6)

Tables Icon

Table 1 Parameter Space, Optimal Values Found, and Improvement of the Pearson Correlation in the Progressive Stages of the Optimization

Tables Icon

Table 2 MI Measures in Bits a

Tables Icon

Table 3 Quality of Metrics on the LIVE Database (F-test): Probability That the Model in The Row is Better Than the Model in the Column for the Linear and Several Non-Linear Fits a

Tables Icon

Table 4 Quality of Metrics on the TID Database (Excluding LIVE-like Distortion) a

Tables Icon

Table 5 Quality of Metrics on the IVC Database (Excluding LIVE-like Distortion) a

Tables Icon

Table 6 Quality of Metrics on the (Achromatic) Cornell Database a

Equations (12)

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

x T w S w R r .
S i = S ( e , o , p ) = A o exp ( ( 4 e ) θ s o θ ) ,
R ( w ) i = r i = sign ( w i ) | S i w i | γ β i γ + k = 1 n H i k | S k w k | γ ,
H i k = H ( e , o , p ) , ( e , o , p ) = K exp ( ( ( e e ) 2 σ e 2 + ( o o ) 2 σ o 2 + ( p p ) 2 σ p 2 ) ) ,
d p f ( x , x ) = 1 n [ f [ [ p Δ r f p q p ] 1 q p ] q f ] 1 q f ,
d f p ( x , x ) = 1 n [ p [ [ f Δ r f p q f ] 1 q f ] q p ] 1 q p ,
Ω { A 1 Y , d , A 1 U V , s Y , s U V , θ , γ , b , σ e , σ o , σ p , q p , q f } .
d ( x , x + Δ x ) 2 = Δ x T M ( x ) Δ x = Δ w T M ( w ) Δ w = Δ r T I Δ r .
Δ r = R ( w ) S T Δ x .
M ( x ) = T T S R ( w ) T R ( w ) S T ,
M ( w ) = S R ( w ) T R ( w ) S .
R ( w ) i j = R i w j = γ ( | w i | γ 1 β i + k H i k | w k | γ δ i j | w i | γ | w j | γ 1 ( β i + k H i k | w k | γ ) 2 H i j ) .

Metrics