Abstract

Quantization of the coefficients within a discrete wavelet transform subband gives rise to distortions in the reconstructed image that are localized in spatial frequency and orientation and are spatially correlated with the image. We investigated the detectability of these distortions: Contrast thresholds were measured for both simple and compound distortions presented in the unmasked paradigm and against two natural-image maskers. Simple and compound distortions were generated through uniform scalar quantization of one or two subbands. Unmasked detection thresholds for simple distortions yielded contrast sensitivity functions similar to those reported for 1-octave Gabor patches. Detection thresholds for simple distortions presented against two natural-image backgrounds revealed that thresholds were elevated across the frequency range of 1.15–18.4 cycles per degree with the greatest elevation for low-frequency distortions. Unmasked thresholds for compound distortions revealed relative sensitivities of 1.1–1.2, suggesting that summation of responses to wavelet distortions is similar to summation of responses to gratings. Masked thresholds for compound distortions revealed relative sensitivities of 1.5–1.7, suggesting greater summation when distortions are masked by natural images.

© 2003 Optical Society of America

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  1. R. L. DeValois, K. K. Devalois, Spatial Vision (Oxford U. Press, New York, 1990).
  2. D. Regan, Human Perception of Objects: Early Visual Processing of Spatial Form Defined by Luminance, Color, Texture, Motion, and Binocular Disparity (Sinauer, Sunderland, Mass., 2000).
  3. I. J. Cox, M. L. Miller, “A review of watermarking and the importance of perceptual modeling,” in Human Vision and Electronic Imaging II, B. Rogowitz, T. Pappas, eds., Proc. SPIE3016, 92–99 (1997).
    [CrossRef]
  4. D. J. Heeger, J. R. Bergen, “Pyramid-based texture analysis/synthesis,” in Proceedings of SIGGRAPH 95 (Association for Computing Machinery, Los Angeles, Calif., 1995), pp. 229–238.
  5. D. J. Jobson, Z. Rahman, G. A. Woodell, “A multi-scale Retinex for bridging the gap between color images and the human observation of scenes,” IEEE Trans. Image Process. 6, 965–976 (1997).
    [CrossRef]
  6. “Information technology–JPEG 2000 image coding system: core coding system,” (International Organization for Standardization, Geneva, Switzerland, 2000).
  7. T. Caelli, G. Moraglia, “On the detection of signals embedded in natural scenes,” Percept. Psychophys. 39, 87–95 (1986).
    [CrossRef] [PubMed]
  8. D. J. Field, “Relations between the statistics of natural images and the response properties of cortical cells,” J. Opt. Soc. Am. A 4, 2379–2394 (1987).
    [CrossRef] [PubMed]
  9. D. C. Knill, D. J. Field, D. Kersten, “Human discrimination of fractal images,” J. Opt. Soc. Am. A 7, 1113–1123 (1990).
    [CrossRef] [PubMed]
  10. E. P. Simoncelli, B. A. Olshausen, “Natural image statistics and neural representation,” Annu. Rev. Neurosci. 24, 1193–1216 (2001).
    [CrossRef] [PubMed]
  11. C. A. Parraga, T. Troscianko, D. J. Tolhurst, “The human visual system is optimised for processing the spatial information in natural visual images,” Curr. Biol. 10, 35–38 (2000).
    [CrossRef] [PubMed]
  12. M. A. Webster, E. Miyahara, “Contrast adaptation and the spatial structure of natural image,” J. Opt. Soc. Am. A 14, 2355–2366 (1997).
    [CrossRef]
  13. A. V. Oppenheim, J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529–541 (1981).
    [CrossRef]
  14. M. G. A. Thomson, D. H. Foster, R. J. Summers, “Human sensitivity to phase perturbations in natural images: a statistical framework,” Perception 29, 1057–1069 (2000).
    [CrossRef]
  15. P. J. Bex, W. Makous, “Spatial frequency, phase, and the contrast of natural images,” J. Opt. Soc. Am. A 19, 1096–1106 (2002).
    [CrossRef]
  16. W. S. Geisler, J. S. Perry, B. J. Super, D. P. Gallogly, “Edge co-occurrence in natural images predicts contour grouping performance,” Vision Res. 41, 711–724 (2001).
    [CrossRef] [PubMed]
  17. J. J. Atick, “Could information theory provide an ecological theory of sensory processing?” Network 3, 213–251 (1992).
    [CrossRef]
  18. B. A. Olshausen, D. J. Field, “Sparse coding with an overcomplete basis set: a strategy employed by V1?” Vision Res. 37, 3311–3325 (1997).
    [CrossRef]
  19. A. Hyvärinen, P. O. Hoyer, “A two-layer sparse coding model learns simple and complex cell receptive fields and topography from natural images,” Vision Res. 41, 2413–2423 (2001).
    [CrossRef] [PubMed]
  20. A. Hyvärinen, P. O. Hoyer, “Emergence of phase and shift invariant features by decomposition of natural images into independent feature subspaces,” Neural Comput. 12, 1705–1720 (2000).
    [CrossRef]
  21. P. O. Hoyer, A. Hyvärinen, “A multi-layer sparse coding network learns contour coding from natural images,” Vision Res. 42, 1593–1605 (2002).
    [CrossRef] [PubMed]
  22. G. E. Legge, J. M. Foley, “Contrast masking in human vision,” J. Opt. Soc. Am. 70, 1458–1470 (1980).
    [CrossRef] [PubMed]
  23. P. C. Teo, D. J. Heeger, “Perceptual image distortion,” in Human Vision, Visual Processing, and Digital Display V, B. Rogowitz, J. Allebach, eds., Proc. SPIE2179, 127–141 (1994).
    [CrossRef]
  24. J. M. Foley, “Human luminance pattern mechanisms: masking experiments require a new model,” J. Opt. Soc. Am. A 11, 1710–1719 (1994).
    [CrossRef]
  25. J. M. Foley, C. C. Chen, “Pattern detection in the presence of maskers that differ in spatial phase and temporal offset: threshold measurements and a model,” Vision Res. 39, 3855–3872 (1999).
    [CrossRef]
  26. A. B. Watson, J. A. Solomon, “A model of visual contrast gain control and pattern masking,” J. Opt. Soc. Am. A 14, 2379–2390 (1997).
    [CrossRef]
  27. T. S. Meese, D. J. Holmes, “Adaptation and gain pool summation: alternative models and masking data,” Vision Res. 42, 1113–1125 (2002).
    [CrossRef] [PubMed]
  28. D. G. Albrecht, W. S. Geisler, “Motion selectivity and the contrast-response function of simple cells in the visual cortex,” Visual Neurosci. 7, 531–546 (1991).
    [CrossRef]
  29. D. J. Heeger, “Normalization of cell responses in cat striate cortex,” Visual Neurosci 9, 181–197 (1992).
    [CrossRef]
  30. S. Daly, “Visible differences predictor: an algorithm for the assessment of image fidelity,” in Digital Images and Human Vision, A. B. Watson, ed. (MIT Press, Cambridge, Mass., 1993), pp. 179–206.
  31. P. W. Jones, S. Daly, R. S. Gaborsky, M. Rabbani, “Comparative study of wavelet and DCT decompositions with equivalent quantization and encoding strategies for medical images,” in Medical Imaging, Y. Kim, ed., Proc. SPIE2431, 571–582 (1995).
    [CrossRef]
  32. W. Zeng, S. Daly, S. Lei, “An overview of the visual optimization tools in JPEG 2000,” Signal Process. Image Commun. 17, 85–104 (2002).
    [CrossRef]
  33. W. Zeng, S. Daly, S. Lei, “Point-wise extended visual masking for JPEG-2000 image compression,” in Proceedings of the IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 2000), pp. 657–660.
  34. E. Peli, “Contrast in complex images,” J. Opt. Soc. Am. A 7, 2032–2040 (1990).
    [CrossRef] [PubMed]
  35. F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. (London) 197, 551–566 (1968).
  36. N. Graham, Visual Pattern Analyzers (Oxford U. Press, New York, 1989).
  37. V. Manahilov, W. A. Simpson, “Energy model for contrast detection: spatial-frequency and orientation selectivity in grating summation,” Vision Res. 41, 1547–1560 (2001).
    [CrossRef] [PubMed]
  38. A. B. Watson, “Summation of grating patches indicates many types of detector at one retinal location,” Vision Res. 22, 17–25 (1982).
    [CrossRef] [PubMed]
  39. R. F. Quick, “A vector magnitude model of contrast detection,” Kybernetik 16, 65–67 (1974).
    [CrossRef]
  40. Y. Bonneh, D. Sagi, “Effects of spatial configuration on contrast detection,” Vision Res. 38, 3541–3553 (1998).
    [CrossRef]
  41. C. R. Carlson, R. W. Cohen, I. Gorog, “Visual processing of simple two-dimensional sine-wave luminance gratings,” Vision Res. 17, 351–358 (1977).
    [CrossRef] [PubMed]
  42. N. Graham, J. Nachmias, “Detection of grating patterns containing two spatial frequencies: a comparison of single-channel and multiple-channels models,” Vision Res. 11, 251–259 (1971).
    [CrossRef] [PubMed]
  43. M. B. Sachs, J. Nachmias, J. G. Robson, “Spatial-frequency channels in human vision,” J. Opt. Soc. Am. 61, 1176–1186 (1971).
    [CrossRef] [PubMed]
  44. G. Meinhardt, “Evidence for different nonlinear summation schemes for lines and gratings at threshold,” Biol. Cybern. 81, 263–277 (1999).
    [CrossRef] [PubMed]
  45. A. B. Watson, G. Y. Yang, J. A. Solomon, J. Villasenor, “Visibility of wavelet quantization noise,” IEEE Trans. Image Process. 6, 1164–1175 (1997).
    [CrossRef] [PubMed]
  46. A. B. Watson, “The cortex transform: rapid computation of simulated neural images,” Comput. Vision Graph. Image Process. 39, 311–327 (1987).
    [CrossRef]
  47. J. Villasenor, B. Belzer, J. Liao, “Wavelet filter evaluation for image compression,” IEEE Trans. Image Process. 4, 1053–1060 (1995).
    [CrossRef] [PubMed]
  48. M. G. Ramos, S. S. Hemami, “Suprathreshold wavelet coefficient quantization in complex stimuli: psychophysical evaluation and analysis,” J. Opt. Soc. Am. A 18, 2385–2397 (2001).
    [CrossRef]
  49. R. M. Gray, D. L. Neuhoff, “Quantization,” IEEE Trans. Inf. Theory 44, 2325–2384 (1998).
    [CrossRef]
  50. D. M. Chandler, S. S. Hemami, “Additivity models for suprathreshold distortion in quantized wavelet-coded images,” in Human Vision and Electronic Imaging VII, B. Rogowitz, T. Pappas, eds., Proc. SPIE4662, 105–118 (2002).
    [CrossRef]
  51. A. B. Watson, D. G. Pelli, “QUEST: a Bayesian adaptive psychometric method,” Percept. Psychophys. 33, 113–120 (1983).
    [CrossRef] [PubMed]
  52. D. H. Brainard, “The Psychophysics Toolbox,” Spatial Vision 10, 433–436 (1997).
    [CrossRef] [PubMed]
  53. D. G. Pelli, “The VideoToolbox software for visual psychophysics: transforming numbers into movies,” Spatial Vision 10, 437–442 (1997).
    [CrossRef] [PubMed]
  54. R. A. Smith, D. J. Swift, “Spatial-frequency masking and Birdsall’s theorem,” J. Opt. Soc. Am. A 2, 1593–1599 (1985).
    [CrossRef] [PubMed]
  55. A. B. Watson, M. Taylor, R. Borthwick, “Image quality and entropy masking,” in Human Vision and Electronic Imaging II, B. Rogowitz, T. Pappas, eds., Proc. SPIE3016, 2–12 (1997).
    [CrossRef]
  56. Subject MM did not participate in the parts of experiments 2 and 4 that tested summation on the spatial-frequency dimension.
  57. K. Tiippana, R. Näsänen, J. Rovamo, “Contrast matching of two-dimensional compound gratings,” Vision Res. 34, 1157–1163 (1994).
    [CrossRef] [PubMed]
  58. B. Moulden, F. A. A. Kingdom, L. F. Gatley, “The standard deviation of luminance as a metric for contrast in random-dot images,” Perception 19, 79–101 (1990).
    [CrossRef] [PubMed]
  59. F. A. A. Kingdom, A. Hayes, D. J. Field, “Sensitivity to contrast histogram differences in synthetic wavelet-textures,” Vision Res. 41, 585–598 (2001).
    [CrossRef] [PubMed]
  60. E. Peli, L. E. Arend, G. M. Young, R. B. Goldstein, “Contrast sensitivity to patch stimuli: effects of spatial bandwidth and temporal presentation,” Spatial Vision 7, 1–14 (1993).
    [CrossRef] [PubMed]
  61. N. Graham, “Visual detection of aperiodic spatial stimuli by probability summation among narrowband channels,” Vision Res. 17, 637–652 (1977).
    [CrossRef] [PubMed]
  62. D. G. Pelli, “Effects of visual noise,” Ph.D. thesis (Cambridge University, Cambridge, UK, 1981).
  63. J. A. Solomon, “Channel selection with non-white-noise masks,” J. Opt. Soc. Am. A 17, 986–993 (2000).
    [CrossRef]
  64. R. J. Safranek, J. D. Johnston, “A perceptually tuned sub-band image coder with image dependent quantization and post-quantization data compression,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1989), Vol. 3, pp. 1945–1948.
  65. The data and the two images used in this study are available online at http://foulard.ece.cornell.edu/dmc27/ImageEffects.html .
  66. Only the LH and HL subbands have been quantized.
  67. M. Stokes, M. Anderson, S. Chandrasekar, R. Motta, “A standard default color space for the Internet–sRGB,” November1996, http://www.w3.org/Graphics/Color/sRGB.html .
  68. M. P. Eckert, A. P. Bradley, “Perceptual quality metrics applied to still image compression,” Signal Process. 70, 177–200 (1998).
    [CrossRef]

2002

P. O. Hoyer, A. Hyvärinen, “A multi-layer sparse coding network learns contour coding from natural images,” Vision Res. 42, 1593–1605 (2002).
[CrossRef] [PubMed]

T. S. Meese, D. J. Holmes, “Adaptation and gain pool summation: alternative models and masking data,” Vision Res. 42, 1113–1125 (2002).
[CrossRef] [PubMed]

W. Zeng, S. Daly, S. Lei, “An overview of the visual optimization tools in JPEG 2000,” Signal Process. Image Commun. 17, 85–104 (2002).
[CrossRef]

P. J. Bex, W. Makous, “Spatial frequency, phase, and the contrast of natural images,” J. Opt. Soc. Am. A 19, 1096–1106 (2002).
[CrossRef]

2001

M. G. Ramos, S. S. Hemami, “Suprathreshold wavelet coefficient quantization in complex stimuli: psychophysical evaluation and analysis,” J. Opt. Soc. Am. A 18, 2385–2397 (2001).
[CrossRef]

V. Manahilov, W. A. Simpson, “Energy model for contrast detection: spatial-frequency and orientation selectivity in grating summation,” Vision Res. 41, 1547–1560 (2001).
[CrossRef] [PubMed]

A. Hyvärinen, P. O. Hoyer, “A two-layer sparse coding model learns simple and complex cell receptive fields and topography from natural images,” Vision Res. 41, 2413–2423 (2001).
[CrossRef] [PubMed]

E. P. Simoncelli, B. A. Olshausen, “Natural image statistics and neural representation,” Annu. Rev. Neurosci. 24, 1193–1216 (2001).
[CrossRef] [PubMed]

W. S. Geisler, J. S. Perry, B. J. Super, D. P. Gallogly, “Edge co-occurrence in natural images predicts contour grouping performance,” Vision Res. 41, 711–724 (2001).
[CrossRef] [PubMed]

F. A. A. Kingdom, A. Hayes, D. J. Field, “Sensitivity to contrast histogram differences in synthetic wavelet-textures,” Vision Res. 41, 585–598 (2001).
[CrossRef] [PubMed]

2000

M. G. A. Thomson, D. H. Foster, R. J. Summers, “Human sensitivity to phase perturbations in natural images: a statistical framework,” Perception 29, 1057–1069 (2000).
[CrossRef]

C. A. Parraga, T. Troscianko, D. J. Tolhurst, “The human visual system is optimised for processing the spatial information in natural visual images,” Curr. Biol. 10, 35–38 (2000).
[CrossRef] [PubMed]

A. Hyvärinen, P. O. Hoyer, “Emergence of phase and shift invariant features by decomposition of natural images into independent feature subspaces,” Neural Comput. 12, 1705–1720 (2000).
[CrossRef]

J. A. Solomon, “Channel selection with non-white-noise masks,” J. Opt. Soc. Am. A 17, 986–993 (2000).
[CrossRef]

1999

J. M. Foley, C. C. Chen, “Pattern detection in the presence of maskers that differ in spatial phase and temporal offset: threshold measurements and a model,” Vision Res. 39, 3855–3872 (1999).
[CrossRef]

G. Meinhardt, “Evidence for different nonlinear summation schemes for lines and gratings at threshold,” Biol. Cybern. 81, 263–277 (1999).
[CrossRef] [PubMed]

1998

Y. Bonneh, D. Sagi, “Effects of spatial configuration on contrast detection,” Vision Res. 38, 3541–3553 (1998).
[CrossRef]

R. M. Gray, D. L. Neuhoff, “Quantization,” IEEE Trans. Inf. Theory 44, 2325–2384 (1998).
[CrossRef]

M. P. Eckert, A. P. Bradley, “Perceptual quality metrics applied to still image compression,” Signal Process. 70, 177–200 (1998).
[CrossRef]

1997

D. H. Brainard, “The Psychophysics Toolbox,” Spatial Vision 10, 433–436 (1997).
[CrossRef] [PubMed]

D. G. Pelli, “The VideoToolbox software for visual psychophysics: transforming numbers into movies,” Spatial Vision 10, 437–442 (1997).
[CrossRef] [PubMed]

A. B. Watson, G. Y. Yang, J. A. Solomon, J. Villasenor, “Visibility of wavelet quantization noise,” IEEE Trans. Image Process. 6, 1164–1175 (1997).
[CrossRef] [PubMed]

D. J. Jobson, Z. Rahman, G. A. Woodell, “A multi-scale Retinex for bridging the gap between color images and the human observation of scenes,” IEEE Trans. Image Process. 6, 965–976 (1997).
[CrossRef]

B. A. Olshausen, D. J. Field, “Sparse coding with an overcomplete basis set: a strategy employed by V1?” Vision Res. 37, 3311–3325 (1997).
[CrossRef]

M. A. Webster, E. Miyahara, “Contrast adaptation and the spatial structure of natural image,” J. Opt. Soc. Am. A 14, 2355–2366 (1997).
[CrossRef]

A. B. Watson, J. A. Solomon, “A model of visual contrast gain control and pattern masking,” J. Opt. Soc. Am. A 14, 2379–2390 (1997).
[CrossRef]

1995

J. Villasenor, B. Belzer, J. Liao, “Wavelet filter evaluation for image compression,” IEEE Trans. Image Process. 4, 1053–1060 (1995).
[CrossRef] [PubMed]

1994

K. Tiippana, R. Näsänen, J. Rovamo, “Contrast matching of two-dimensional compound gratings,” Vision Res. 34, 1157–1163 (1994).
[CrossRef] [PubMed]

J. M. Foley, “Human luminance pattern mechanisms: masking experiments require a new model,” J. Opt. Soc. Am. A 11, 1710–1719 (1994).
[CrossRef]

1993

E. Peli, L. E. Arend, G. M. Young, R. B. Goldstein, “Contrast sensitivity to patch stimuli: effects of spatial bandwidth and temporal presentation,” Spatial Vision 7, 1–14 (1993).
[CrossRef] [PubMed]

1992

D. J. Heeger, “Normalization of cell responses in cat striate cortex,” Visual Neurosci 9, 181–197 (1992).
[CrossRef]

J. J. Atick, “Could information theory provide an ecological theory of sensory processing?” Network 3, 213–251 (1992).
[CrossRef]

1991

D. G. Albrecht, W. S. Geisler, “Motion selectivity and the contrast-response function of simple cells in the visual cortex,” Visual Neurosci. 7, 531–546 (1991).
[CrossRef]

1990

1987

D. J. Field, “Relations between the statistics of natural images and the response properties of cortical cells,” J. Opt. Soc. Am. A 4, 2379–2394 (1987).
[CrossRef] [PubMed]

A. B. Watson, “The cortex transform: rapid computation of simulated neural images,” Comput. Vision Graph. Image Process. 39, 311–327 (1987).
[CrossRef]

1986

T. Caelli, G. Moraglia, “On the detection of signals embedded in natural scenes,” Percept. Psychophys. 39, 87–95 (1986).
[CrossRef] [PubMed]

1985

1983

A. B. Watson, D. G. Pelli, “QUEST: a Bayesian adaptive psychometric method,” Percept. Psychophys. 33, 113–120 (1983).
[CrossRef] [PubMed]

1982

A. B. Watson, “Summation of grating patches indicates many types of detector at one retinal location,” Vision Res. 22, 17–25 (1982).
[CrossRef] [PubMed]

1981

A. V. Oppenheim, J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529–541 (1981).
[CrossRef]

1980

1977

C. R. Carlson, R. W. Cohen, I. Gorog, “Visual processing of simple two-dimensional sine-wave luminance gratings,” Vision Res. 17, 351–358 (1977).
[CrossRef] [PubMed]

N. Graham, “Visual detection of aperiodic spatial stimuli by probability summation among narrowband channels,” Vision Res. 17, 637–652 (1977).
[CrossRef] [PubMed]

1974

R. F. Quick, “A vector magnitude model of contrast detection,” Kybernetik 16, 65–67 (1974).
[CrossRef]

1971

N. Graham, J. Nachmias, “Detection of grating patterns containing two spatial frequencies: a comparison of single-channel and multiple-channels models,” Vision Res. 11, 251–259 (1971).
[CrossRef] [PubMed]

M. B. Sachs, J. Nachmias, J. G. Robson, “Spatial-frequency channels in human vision,” J. Opt. Soc. Am. 61, 1176–1186 (1971).
[CrossRef] [PubMed]

1968

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

Albrecht, D. G.

D. G. Albrecht, W. S. Geisler, “Motion selectivity and the contrast-response function of simple cells in the visual cortex,” Visual Neurosci. 7, 531–546 (1991).
[CrossRef]

Arend, L. E.

E. Peli, L. E. Arend, G. M. Young, R. B. Goldstein, “Contrast sensitivity to patch stimuli: effects of spatial bandwidth and temporal presentation,” Spatial Vision 7, 1–14 (1993).
[CrossRef] [PubMed]

Atick, J. J.

J. J. Atick, “Could information theory provide an ecological theory of sensory processing?” Network 3, 213–251 (1992).
[CrossRef]

Belzer, B.

J. Villasenor, B. Belzer, J. Liao, “Wavelet filter evaluation for image compression,” IEEE Trans. Image Process. 4, 1053–1060 (1995).
[CrossRef] [PubMed]

Bergen, J. R.

D. J. Heeger, J. R. Bergen, “Pyramid-based texture analysis/synthesis,” in Proceedings of SIGGRAPH 95 (Association for Computing Machinery, Los Angeles, Calif., 1995), pp. 229–238.

Bex, P. J.

Bonneh, Y.

Y. Bonneh, D. Sagi, “Effects of spatial configuration on contrast detection,” Vision Res. 38, 3541–3553 (1998).
[CrossRef]

Borthwick, R.

A. B. Watson, M. Taylor, R. Borthwick, “Image quality and entropy masking,” in Human Vision and Electronic Imaging II, B. Rogowitz, T. Pappas, eds., Proc. SPIE3016, 2–12 (1997).
[CrossRef]

Bradley, A. P.

M. P. Eckert, A. P. Bradley, “Perceptual quality metrics applied to still image compression,” Signal Process. 70, 177–200 (1998).
[CrossRef]

Brainard, D. H.

D. H. Brainard, “The Psychophysics Toolbox,” Spatial Vision 10, 433–436 (1997).
[CrossRef] [PubMed]

Caelli, T.

T. Caelli, G. Moraglia, “On the detection of signals embedded in natural scenes,” Percept. Psychophys. 39, 87–95 (1986).
[CrossRef] [PubMed]

Campbell, F. W.

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

Carlson, C. R.

C. R. Carlson, R. W. Cohen, I. Gorog, “Visual processing of simple two-dimensional sine-wave luminance gratings,” Vision Res. 17, 351–358 (1977).
[CrossRef] [PubMed]

Chandler, D. M.

D. M. Chandler, S. S. Hemami, “Additivity models for suprathreshold distortion in quantized wavelet-coded images,” in Human Vision and Electronic Imaging VII, B. Rogowitz, T. Pappas, eds., Proc. SPIE4662, 105–118 (2002).
[CrossRef]

Chen, C. C.

J. M. Foley, C. C. Chen, “Pattern detection in the presence of maskers that differ in spatial phase and temporal offset: threshold measurements and a model,” Vision Res. 39, 3855–3872 (1999).
[CrossRef]

Cohen, R. W.

C. R. Carlson, R. W. Cohen, I. Gorog, “Visual processing of simple two-dimensional sine-wave luminance gratings,” Vision Res. 17, 351–358 (1977).
[CrossRef] [PubMed]

Cox, I. J.

I. J. Cox, M. L. Miller, “A review of watermarking and the importance of perceptual modeling,” in Human Vision and Electronic Imaging II, B. Rogowitz, T. Pappas, eds., Proc. SPIE3016, 92–99 (1997).
[CrossRef]

Daly, S.

W. Zeng, S. Daly, S. Lei, “An overview of the visual optimization tools in JPEG 2000,” Signal Process. Image Commun. 17, 85–104 (2002).
[CrossRef]

S. Daly, “Visible differences predictor: an algorithm for the assessment of image fidelity,” in Digital Images and Human Vision, A. B. Watson, ed. (MIT Press, Cambridge, Mass., 1993), pp. 179–206.

P. W. Jones, S. Daly, R. S. Gaborsky, M. Rabbani, “Comparative study of wavelet and DCT decompositions with equivalent quantization and encoding strategies for medical images,” in Medical Imaging, Y. Kim, ed., Proc. SPIE2431, 571–582 (1995).
[CrossRef]

W. Zeng, S. Daly, S. Lei, “Point-wise extended visual masking for JPEG-2000 image compression,” in Proceedings of the IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 2000), pp. 657–660.

Devalois, K. K.

R. L. DeValois, K. K. Devalois, Spatial Vision (Oxford U. Press, New York, 1990).

DeValois, R. L.

R. L. DeValois, K. K. Devalois, Spatial Vision (Oxford U. Press, New York, 1990).

Eckert, M. P.

M. P. Eckert, A. P. Bradley, “Perceptual quality metrics applied to still image compression,” Signal Process. 70, 177–200 (1998).
[CrossRef]

Field, D. J.

F. A. A. Kingdom, A. Hayes, D. J. Field, “Sensitivity to contrast histogram differences in synthetic wavelet-textures,” Vision Res. 41, 585–598 (2001).
[CrossRef] [PubMed]

B. A. Olshausen, D. J. Field, “Sparse coding with an overcomplete basis set: a strategy employed by V1?” Vision Res. 37, 3311–3325 (1997).
[CrossRef]

D. C. Knill, D. J. Field, D. Kersten, “Human discrimination of fractal images,” J. Opt. Soc. Am. A 7, 1113–1123 (1990).
[CrossRef] [PubMed]

D. J. Field, “Relations between the statistics of natural images and the response properties of cortical cells,” J. Opt. Soc. Am. A 4, 2379–2394 (1987).
[CrossRef] [PubMed]

Foley, J. M.

J. M. Foley, C. C. Chen, “Pattern detection in the presence of maskers that differ in spatial phase and temporal offset: threshold measurements and a model,” Vision Res. 39, 3855–3872 (1999).
[CrossRef]

J. M. Foley, “Human luminance pattern mechanisms: masking experiments require a new model,” J. Opt. Soc. Am. A 11, 1710–1719 (1994).
[CrossRef]

G. E. Legge, J. M. Foley, “Contrast masking in human vision,” J. Opt. Soc. Am. 70, 1458–1470 (1980).
[CrossRef] [PubMed]

Foster, D. H.

M. G. A. Thomson, D. H. Foster, R. J. Summers, “Human sensitivity to phase perturbations in natural images: a statistical framework,” Perception 29, 1057–1069 (2000).
[CrossRef]

Gaborsky, R. S.

P. W. Jones, S. Daly, R. S. Gaborsky, M. Rabbani, “Comparative study of wavelet and DCT decompositions with equivalent quantization and encoding strategies for medical images,” in Medical Imaging, Y. Kim, ed., Proc. SPIE2431, 571–582 (1995).
[CrossRef]

Gallogly, D. P.

W. S. Geisler, J. S. Perry, B. J. Super, D. P. Gallogly, “Edge co-occurrence in natural images predicts contour grouping performance,” Vision Res. 41, 711–724 (2001).
[CrossRef] [PubMed]

Gatley, L. F.

B. Moulden, F. A. A. Kingdom, L. F. Gatley, “The standard deviation of luminance as a metric for contrast in random-dot images,” Perception 19, 79–101 (1990).
[CrossRef] [PubMed]

Geisler, W. S.

W. S. Geisler, J. S. Perry, B. J. Super, D. P. Gallogly, “Edge co-occurrence in natural images predicts contour grouping performance,” Vision Res. 41, 711–724 (2001).
[CrossRef] [PubMed]

D. G. Albrecht, W. S. Geisler, “Motion selectivity and the contrast-response function of simple cells in the visual cortex,” Visual Neurosci. 7, 531–546 (1991).
[CrossRef]

Goldstein, R. B.

E. Peli, L. E. Arend, G. M. Young, R. B. Goldstein, “Contrast sensitivity to patch stimuli: effects of spatial bandwidth and temporal presentation,” Spatial Vision 7, 1–14 (1993).
[CrossRef] [PubMed]

Gorog, I.

C. R. Carlson, R. W. Cohen, I. Gorog, “Visual processing of simple two-dimensional sine-wave luminance gratings,” Vision Res. 17, 351–358 (1977).
[CrossRef] [PubMed]

Graham, N.

N. Graham, “Visual detection of aperiodic spatial stimuli by probability summation among narrowband channels,” Vision Res. 17, 637–652 (1977).
[CrossRef] [PubMed]

N. Graham, J. Nachmias, “Detection of grating patterns containing two spatial frequencies: a comparison of single-channel and multiple-channels models,” Vision Res. 11, 251–259 (1971).
[CrossRef] [PubMed]

N. Graham, Visual Pattern Analyzers (Oxford U. Press, New York, 1989).

Gray, R. M.

R. M. Gray, D. L. Neuhoff, “Quantization,” IEEE Trans. Inf. Theory 44, 2325–2384 (1998).
[CrossRef]

Hayes, A.

F. A. A. Kingdom, A. Hayes, D. J. Field, “Sensitivity to contrast histogram differences in synthetic wavelet-textures,” Vision Res. 41, 585–598 (2001).
[CrossRef] [PubMed]

Heeger, D. J.

D. J. Heeger, “Normalization of cell responses in cat striate cortex,” Visual Neurosci 9, 181–197 (1992).
[CrossRef]

D. J. Heeger, J. R. Bergen, “Pyramid-based texture analysis/synthesis,” in Proceedings of SIGGRAPH 95 (Association for Computing Machinery, Los Angeles, Calif., 1995), pp. 229–238.

P. C. Teo, D. J. Heeger, “Perceptual image distortion,” in Human Vision, Visual Processing, and Digital Display V, B. Rogowitz, J. Allebach, eds., Proc. SPIE2179, 127–141 (1994).
[CrossRef]

Hemami, S. S.

M. G. Ramos, S. S. Hemami, “Suprathreshold wavelet coefficient quantization in complex stimuli: psychophysical evaluation and analysis,” J. Opt. Soc. Am. A 18, 2385–2397 (2001).
[CrossRef]

D. M. Chandler, S. S. Hemami, “Additivity models for suprathreshold distortion in quantized wavelet-coded images,” in Human Vision and Electronic Imaging VII, B. Rogowitz, T. Pappas, eds., Proc. SPIE4662, 105–118 (2002).
[CrossRef]

Holmes, D. J.

T. S. Meese, D. J. Holmes, “Adaptation and gain pool summation: alternative models and masking data,” Vision Res. 42, 1113–1125 (2002).
[CrossRef] [PubMed]

Hoyer, P. O.

P. O. Hoyer, A. Hyvärinen, “A multi-layer sparse coding network learns contour coding from natural images,” Vision Res. 42, 1593–1605 (2002).
[CrossRef] [PubMed]

A. Hyvärinen, P. O. Hoyer, “A two-layer sparse coding model learns simple and complex cell receptive fields and topography from natural images,” Vision Res. 41, 2413–2423 (2001).
[CrossRef] [PubMed]

A. Hyvärinen, P. O. Hoyer, “Emergence of phase and shift invariant features by decomposition of natural images into independent feature subspaces,” Neural Comput. 12, 1705–1720 (2000).
[CrossRef]

Hyvärinen, A.

P. O. Hoyer, A. Hyvärinen, “A multi-layer sparse coding network learns contour coding from natural images,” Vision Res. 42, 1593–1605 (2002).
[CrossRef] [PubMed]

A. Hyvärinen, P. O. Hoyer, “A two-layer sparse coding model learns simple and complex cell receptive fields and topography from natural images,” Vision Res. 41, 2413–2423 (2001).
[CrossRef] [PubMed]

A. Hyvärinen, P. O. Hoyer, “Emergence of phase and shift invariant features by decomposition of natural images into independent feature subspaces,” Neural Comput. 12, 1705–1720 (2000).
[CrossRef]

Jobson, D. J.

D. J. Jobson, Z. Rahman, G. A. Woodell, “A multi-scale Retinex for bridging the gap between color images and the human observation of scenes,” IEEE Trans. Image Process. 6, 965–976 (1997).
[CrossRef]

Johnston, J. D.

R. J. Safranek, J. D. Johnston, “A perceptually tuned sub-band image coder with image dependent quantization and post-quantization data compression,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1989), Vol. 3, pp. 1945–1948.

Jones, P. W.

P. W. Jones, S. Daly, R. S. Gaborsky, M. Rabbani, “Comparative study of wavelet and DCT decompositions with equivalent quantization and encoding strategies for medical images,” in Medical Imaging, Y. Kim, ed., Proc. SPIE2431, 571–582 (1995).
[CrossRef]

Kersten, D.

Kingdom, F. A. A.

F. A. A. Kingdom, A. Hayes, D. J. Field, “Sensitivity to contrast histogram differences in synthetic wavelet-textures,” Vision Res. 41, 585–598 (2001).
[CrossRef] [PubMed]

B. Moulden, F. A. A. Kingdom, L. F. Gatley, “The standard deviation of luminance as a metric for contrast in random-dot images,” Perception 19, 79–101 (1990).
[CrossRef] [PubMed]

Knill, D. C.

Legge, G. E.

Lei, S.

W. Zeng, S. Daly, S. Lei, “An overview of the visual optimization tools in JPEG 2000,” Signal Process. Image Commun. 17, 85–104 (2002).
[CrossRef]

W. Zeng, S. Daly, S. Lei, “Point-wise extended visual masking for JPEG-2000 image compression,” in Proceedings of the IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 2000), pp. 657–660.

Liao, J.

J. Villasenor, B. Belzer, J. Liao, “Wavelet filter evaluation for image compression,” IEEE Trans. Image Process. 4, 1053–1060 (1995).
[CrossRef] [PubMed]

Lim, J. S.

A. V. Oppenheim, J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529–541 (1981).
[CrossRef]

Makous, W.

Manahilov, V.

V. Manahilov, W. A. Simpson, “Energy model for contrast detection: spatial-frequency and orientation selectivity in grating summation,” Vision Res. 41, 1547–1560 (2001).
[CrossRef] [PubMed]

Meese, T. S.

T. S. Meese, D. J. Holmes, “Adaptation and gain pool summation: alternative models and masking data,” Vision Res. 42, 1113–1125 (2002).
[CrossRef] [PubMed]

Meinhardt, G.

G. Meinhardt, “Evidence for different nonlinear summation schemes for lines and gratings at threshold,” Biol. Cybern. 81, 263–277 (1999).
[CrossRef] [PubMed]

Miller, M. L.

I. J. Cox, M. L. Miller, “A review of watermarking and the importance of perceptual modeling,” in Human Vision and Electronic Imaging II, B. Rogowitz, T. Pappas, eds., Proc. SPIE3016, 92–99 (1997).
[CrossRef]

Miyahara, E.

Moraglia, G.

T. Caelli, G. Moraglia, “On the detection of signals embedded in natural scenes,” Percept. Psychophys. 39, 87–95 (1986).
[CrossRef] [PubMed]

Moulden, B.

B. Moulden, F. A. A. Kingdom, L. F. Gatley, “The standard deviation of luminance as a metric for contrast in random-dot images,” Perception 19, 79–101 (1990).
[CrossRef] [PubMed]

Nachmias, J.

M. B. Sachs, J. Nachmias, J. G. Robson, “Spatial-frequency channels in human vision,” J. Opt. Soc. Am. 61, 1176–1186 (1971).
[CrossRef] [PubMed]

N. Graham, J. Nachmias, “Detection of grating patterns containing two spatial frequencies: a comparison of single-channel and multiple-channels models,” Vision Res. 11, 251–259 (1971).
[CrossRef] [PubMed]

Näsänen, R.

K. Tiippana, R. Näsänen, J. Rovamo, “Contrast matching of two-dimensional compound gratings,” Vision Res. 34, 1157–1163 (1994).
[CrossRef] [PubMed]

Neuhoff, D. L.

R. M. Gray, D. L. Neuhoff, “Quantization,” IEEE Trans. Inf. Theory 44, 2325–2384 (1998).
[CrossRef]

Olshausen, B. A.

E. P. Simoncelli, B. A. Olshausen, “Natural image statistics and neural representation,” Annu. Rev. Neurosci. 24, 1193–1216 (2001).
[CrossRef] [PubMed]

B. A. Olshausen, D. J. Field, “Sparse coding with an overcomplete basis set: a strategy employed by V1?” Vision Res. 37, 3311–3325 (1997).
[CrossRef]

Oppenheim, A. V.

A. V. Oppenheim, J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529–541 (1981).
[CrossRef]

Parraga, C. A.

C. A. Parraga, T. Troscianko, D. J. Tolhurst, “The human visual system is optimised for processing the spatial information in natural visual images,” Curr. Biol. 10, 35–38 (2000).
[CrossRef] [PubMed]

Peli, E.

E. Peli, L. E. Arend, G. M. Young, R. B. Goldstein, “Contrast sensitivity to patch stimuli: effects of spatial bandwidth and temporal presentation,” Spatial Vision 7, 1–14 (1993).
[CrossRef] [PubMed]

E. Peli, “Contrast in complex images,” J. Opt. Soc. Am. A 7, 2032–2040 (1990).
[CrossRef] [PubMed]

Pelli, D. G.

D. G. Pelli, “The VideoToolbox software for visual psychophysics: transforming numbers into movies,” Spatial Vision 10, 437–442 (1997).
[CrossRef] [PubMed]

A. B. Watson, D. G. Pelli, “QUEST: a Bayesian adaptive psychometric method,” Percept. Psychophys. 33, 113–120 (1983).
[CrossRef] [PubMed]

D. G. Pelli, “Effects of visual noise,” Ph.D. thesis (Cambridge University, Cambridge, UK, 1981).

Perry, J. S.

W. S. Geisler, J. S. Perry, B. J. Super, D. P. Gallogly, “Edge co-occurrence in natural images predicts contour grouping performance,” Vision Res. 41, 711–724 (2001).
[CrossRef] [PubMed]

Quick, R. F.

R. F. Quick, “A vector magnitude model of contrast detection,” Kybernetik 16, 65–67 (1974).
[CrossRef]

Rabbani, M.

P. W. Jones, S. Daly, R. S. Gaborsky, M. Rabbani, “Comparative study of wavelet and DCT decompositions with equivalent quantization and encoding strategies for medical images,” in Medical Imaging, Y. Kim, ed., Proc. SPIE2431, 571–582 (1995).
[CrossRef]

Rahman, Z.

D. J. Jobson, Z. Rahman, G. A. Woodell, “A multi-scale Retinex for bridging the gap between color images and the human observation of scenes,” IEEE Trans. Image Process. 6, 965–976 (1997).
[CrossRef]

Ramos, M. G.

Regan, D.

D. Regan, Human Perception of Objects: Early Visual Processing of Spatial Form Defined by Luminance, Color, Texture, Motion, and Binocular Disparity (Sinauer, Sunderland, Mass., 2000).

Robson, J. G.

M. B. Sachs, J. Nachmias, J. G. Robson, “Spatial-frequency channels in human vision,” J. Opt. Soc. Am. 61, 1176–1186 (1971).
[CrossRef] [PubMed]

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

Rovamo, J.

K. Tiippana, R. Näsänen, J. Rovamo, “Contrast matching of two-dimensional compound gratings,” Vision Res. 34, 1157–1163 (1994).
[CrossRef] [PubMed]

Sachs, M. B.

Safranek, R. J.

R. J. Safranek, J. D. Johnston, “A perceptually tuned sub-band image coder with image dependent quantization and post-quantization data compression,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1989), Vol. 3, pp. 1945–1948.

Sagi, D.

Y. Bonneh, D. Sagi, “Effects of spatial configuration on contrast detection,” Vision Res. 38, 3541–3553 (1998).
[CrossRef]

Simoncelli, E. P.

E. P. Simoncelli, B. A. Olshausen, “Natural image statistics and neural representation,” Annu. Rev. Neurosci. 24, 1193–1216 (2001).
[CrossRef] [PubMed]

Simpson, W. A.

V. Manahilov, W. A. Simpson, “Energy model for contrast detection: spatial-frequency and orientation selectivity in grating summation,” Vision Res. 41, 1547–1560 (2001).
[CrossRef] [PubMed]

Smith, R. A.

Solomon, J. A.

Summers, R. J.

M. G. A. Thomson, D. H. Foster, R. J. Summers, “Human sensitivity to phase perturbations in natural images: a statistical framework,” Perception 29, 1057–1069 (2000).
[CrossRef]

Super, B. J.

W. S. Geisler, J. S. Perry, B. J. Super, D. P. Gallogly, “Edge co-occurrence in natural images predicts contour grouping performance,” Vision Res. 41, 711–724 (2001).
[CrossRef] [PubMed]

Swift, D. J.

Taylor, M.

A. B. Watson, M. Taylor, R. Borthwick, “Image quality and entropy masking,” in Human Vision and Electronic Imaging II, B. Rogowitz, T. Pappas, eds., Proc. SPIE3016, 2–12 (1997).
[CrossRef]

Teo, P. C.

P. C. Teo, D. J. Heeger, “Perceptual image distortion,” in Human Vision, Visual Processing, and Digital Display V, B. Rogowitz, J. Allebach, eds., Proc. SPIE2179, 127–141 (1994).
[CrossRef]

Thomson, M. G. A.

M. G. A. Thomson, D. H. Foster, R. J. Summers, “Human sensitivity to phase perturbations in natural images: a statistical framework,” Perception 29, 1057–1069 (2000).
[CrossRef]

Tiippana, K.

K. Tiippana, R. Näsänen, J. Rovamo, “Contrast matching of two-dimensional compound gratings,” Vision Res. 34, 1157–1163 (1994).
[CrossRef] [PubMed]

Tolhurst, D. J.

C. A. Parraga, T. Troscianko, D. J. Tolhurst, “The human visual system is optimised for processing the spatial information in natural visual images,” Curr. Biol. 10, 35–38 (2000).
[CrossRef] [PubMed]

Troscianko, T.

C. A. Parraga, T. Troscianko, D. J. Tolhurst, “The human visual system is optimised for processing the spatial information in natural visual images,” Curr. Biol. 10, 35–38 (2000).
[CrossRef] [PubMed]

Villasenor, J.

A. B. Watson, G. Y. Yang, J. A. Solomon, J. Villasenor, “Visibility of wavelet quantization noise,” IEEE Trans. Image Process. 6, 1164–1175 (1997).
[CrossRef] [PubMed]

J. Villasenor, B. Belzer, J. Liao, “Wavelet filter evaluation for image compression,” IEEE Trans. Image Process. 4, 1053–1060 (1995).
[CrossRef] [PubMed]

Watson, A. B.

A. B. Watson, G. Y. Yang, J. A. Solomon, J. Villasenor, “Visibility of wavelet quantization noise,” IEEE Trans. Image Process. 6, 1164–1175 (1997).
[CrossRef] [PubMed]

A. B. Watson, J. A. Solomon, “A model of visual contrast gain control and pattern masking,” J. Opt. Soc. Am. A 14, 2379–2390 (1997).
[CrossRef]

A. B. Watson, “The cortex transform: rapid computation of simulated neural images,” Comput. Vision Graph. Image Process. 39, 311–327 (1987).
[CrossRef]

A. B. Watson, D. G. Pelli, “QUEST: a Bayesian adaptive psychometric method,” Percept. Psychophys. 33, 113–120 (1983).
[CrossRef] [PubMed]

A. B. Watson, “Summation of grating patches indicates many types of detector at one retinal location,” Vision Res. 22, 17–25 (1982).
[CrossRef] [PubMed]

A. B. Watson, M. Taylor, R. Borthwick, “Image quality and entropy masking,” in Human Vision and Electronic Imaging II, B. Rogowitz, T. Pappas, eds., Proc. SPIE3016, 2–12 (1997).
[CrossRef]

Webster, M. A.

Woodell, G. A.

D. J. Jobson, Z. Rahman, G. A. Woodell, “A multi-scale Retinex for bridging the gap between color images and the human observation of scenes,” IEEE Trans. Image Process. 6, 965–976 (1997).
[CrossRef]

Yang, G. Y.

A. B. Watson, G. Y. Yang, J. A. Solomon, J. Villasenor, “Visibility of wavelet quantization noise,” IEEE Trans. Image Process. 6, 1164–1175 (1997).
[CrossRef] [PubMed]

Young, G. M.

E. Peli, L. E. Arend, G. M. Young, R. B. Goldstein, “Contrast sensitivity to patch stimuli: effects of spatial bandwidth and temporal presentation,” Spatial Vision 7, 1–14 (1993).
[CrossRef] [PubMed]

Zeng, W.

W. Zeng, S. Daly, S. Lei, “An overview of the visual optimization tools in JPEG 2000,” Signal Process. Image Commun. 17, 85–104 (2002).
[CrossRef]

W. Zeng, S. Daly, S. Lei, “Point-wise extended visual masking for JPEG-2000 image compression,” in Proceedings of the IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 2000), pp. 657–660.

Annu. Rev. Neurosci.

E. P. Simoncelli, B. A. Olshausen, “Natural image statistics and neural representation,” Annu. Rev. Neurosci. 24, 1193–1216 (2001).
[CrossRef] [PubMed]

Biol. Cybern.

G. Meinhardt, “Evidence for different nonlinear summation schemes for lines and gratings at threshold,” Biol. Cybern. 81, 263–277 (1999).
[CrossRef] [PubMed]

Comput. Vision Graph. Image Process.

A. B. Watson, “The cortex transform: rapid computation of simulated neural images,” Comput. Vision Graph. Image Process. 39, 311–327 (1987).
[CrossRef]

Curr. Biol.

C. A. Parraga, T. Troscianko, D. J. Tolhurst, “The human visual system is optimised for processing the spatial information in natural visual images,” Curr. Biol. 10, 35–38 (2000).
[CrossRef] [PubMed]

IEEE Trans. Image Process.

D. J. Jobson, Z. Rahman, G. A. Woodell, “A multi-scale Retinex for bridging the gap between color images and the human observation of scenes,” IEEE Trans. Image Process. 6, 965–976 (1997).
[CrossRef]

A. B. Watson, G. Y. Yang, J. A. Solomon, J. Villasenor, “Visibility of wavelet quantization noise,” IEEE Trans. Image Process. 6, 1164–1175 (1997).
[CrossRef] [PubMed]

J. Villasenor, B. Belzer, J. Liao, “Wavelet filter evaluation for image compression,” IEEE Trans. Image Process. 4, 1053–1060 (1995).
[CrossRef] [PubMed]

IEEE Trans. Inf. Theory

R. M. Gray, D. L. Neuhoff, “Quantization,” IEEE Trans. Inf. Theory 44, 2325–2384 (1998).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Physiol. (London)

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

Kybernetik

R. F. Quick, “A vector magnitude model of contrast detection,” Kybernetik 16, 65–67 (1974).
[CrossRef]

Network

J. J. Atick, “Could information theory provide an ecological theory of sensory processing?” Network 3, 213–251 (1992).
[CrossRef]

Neural Comput.

A. Hyvärinen, P. O. Hoyer, “Emergence of phase and shift invariant features by decomposition of natural images into independent feature subspaces,” Neural Comput. 12, 1705–1720 (2000).
[CrossRef]

Percept. Psychophys.

T. Caelli, G. Moraglia, “On the detection of signals embedded in natural scenes,” Percept. Psychophys. 39, 87–95 (1986).
[CrossRef] [PubMed]

A. B. Watson, D. G. Pelli, “QUEST: a Bayesian adaptive psychometric method,” Percept. Psychophys. 33, 113–120 (1983).
[CrossRef] [PubMed]

Perception

B. Moulden, F. A. A. Kingdom, L. F. Gatley, “The standard deviation of luminance as a metric for contrast in random-dot images,” Perception 19, 79–101 (1990).
[CrossRef] [PubMed]

M. G. A. Thomson, D. H. Foster, R. J. Summers, “Human sensitivity to phase perturbations in natural images: a statistical framework,” Perception 29, 1057–1069 (2000).
[CrossRef]

Proc. IEEE

A. V. Oppenheim, J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529–541 (1981).
[CrossRef]

Signal Process.

M. P. Eckert, A. P. Bradley, “Perceptual quality metrics applied to still image compression,” Signal Process. 70, 177–200 (1998).
[CrossRef]

Signal Process. Image Commun.

W. Zeng, S. Daly, S. Lei, “An overview of the visual optimization tools in JPEG 2000,” Signal Process. Image Commun. 17, 85–104 (2002).
[CrossRef]

Spatial Vision

D. H. Brainard, “The Psychophysics Toolbox,” Spatial Vision 10, 433–436 (1997).
[CrossRef] [PubMed]

D. G. Pelli, “The VideoToolbox software for visual psychophysics: transforming numbers into movies,” Spatial Vision 10, 437–442 (1997).
[CrossRef] [PubMed]

E. Peli, L. E. Arend, G. M. Young, R. B. Goldstein, “Contrast sensitivity to patch stimuli: effects of spatial bandwidth and temporal presentation,” Spatial Vision 7, 1–14 (1993).
[CrossRef] [PubMed]

Vision Res.

N. Graham, “Visual detection of aperiodic spatial stimuli by probability summation among narrowband channels,” Vision Res. 17, 637–652 (1977).
[CrossRef] [PubMed]

F. A. A. Kingdom, A. Hayes, D. J. Field, “Sensitivity to contrast histogram differences in synthetic wavelet-textures,” Vision Res. 41, 585–598 (2001).
[CrossRef] [PubMed]

K. Tiippana, R. Näsänen, J. Rovamo, “Contrast matching of two-dimensional compound gratings,” Vision Res. 34, 1157–1163 (1994).
[CrossRef] [PubMed]

V. Manahilov, W. A. Simpson, “Energy model for contrast detection: spatial-frequency and orientation selectivity in grating summation,” Vision Res. 41, 1547–1560 (2001).
[CrossRef] [PubMed]

A. B. Watson, “Summation of grating patches indicates many types of detector at one retinal location,” Vision Res. 22, 17–25 (1982).
[CrossRef] [PubMed]

J. M. Foley, C. C. Chen, “Pattern detection in the presence of maskers that differ in spatial phase and temporal offset: threshold measurements and a model,” Vision Res. 39, 3855–3872 (1999).
[CrossRef]

Y. Bonneh, D. Sagi, “Effects of spatial configuration on contrast detection,” Vision Res. 38, 3541–3553 (1998).
[CrossRef]

C. R. Carlson, R. W. Cohen, I. Gorog, “Visual processing of simple two-dimensional sine-wave luminance gratings,” Vision Res. 17, 351–358 (1977).
[CrossRef] [PubMed]

N. Graham, J. Nachmias, “Detection of grating patterns containing two spatial frequencies: a comparison of single-channel and multiple-channels models,” Vision Res. 11, 251–259 (1971).
[CrossRef] [PubMed]

W. S. Geisler, J. S. Perry, B. J. Super, D. P. Gallogly, “Edge co-occurrence in natural images predicts contour grouping performance,” Vision Res. 41, 711–724 (2001).
[CrossRef] [PubMed]

B. A. Olshausen, D. J. Field, “Sparse coding with an overcomplete basis set: a strategy employed by V1?” Vision Res. 37, 3311–3325 (1997).
[CrossRef]

A. Hyvärinen, P. O. Hoyer, “A two-layer sparse coding model learns simple and complex cell receptive fields and topography from natural images,” Vision Res. 41, 2413–2423 (2001).
[CrossRef] [PubMed]

P. O. Hoyer, A. Hyvärinen, “A multi-layer sparse coding network learns contour coding from natural images,” Vision Res. 42, 1593–1605 (2002).
[CrossRef] [PubMed]

T. S. Meese, D. J. Holmes, “Adaptation and gain pool summation: alternative models and masking data,” Vision Res. 42, 1113–1125 (2002).
[CrossRef] [PubMed]

Visual Neurosci

D. J. Heeger, “Normalization of cell responses in cat striate cortex,” Visual Neurosci 9, 181–197 (1992).
[CrossRef]

Visual Neurosci.

D. G. Albrecht, W. S. Geisler, “Motion selectivity and the contrast-response function of simple cells in the visual cortex,” Visual Neurosci. 7, 531–546 (1991).
[CrossRef]

Other

“Information technology–JPEG 2000 image coding system: core coding system,” (International Organization for Standardization, Geneva, Switzerland, 2000).

R. L. DeValois, K. K. Devalois, Spatial Vision (Oxford U. Press, New York, 1990).

D. Regan, Human Perception of Objects: Early Visual Processing of Spatial Form Defined by Luminance, Color, Texture, Motion, and Binocular Disparity (Sinauer, Sunderland, Mass., 2000).

I. J. Cox, M. L. Miller, “A review of watermarking and the importance of perceptual modeling,” in Human Vision and Electronic Imaging II, B. Rogowitz, T. Pappas, eds., Proc. SPIE3016, 92–99 (1997).
[CrossRef]

D. J. Heeger, J. R. Bergen, “Pyramid-based texture analysis/synthesis,” in Proceedings of SIGGRAPH 95 (Association for Computing Machinery, Los Angeles, Calif., 1995), pp. 229–238.

S. Daly, “Visible differences predictor: an algorithm for the assessment of image fidelity,” in Digital Images and Human Vision, A. B. Watson, ed. (MIT Press, Cambridge, Mass., 1993), pp. 179–206.

P. W. Jones, S. Daly, R. S. Gaborsky, M. Rabbani, “Comparative study of wavelet and DCT decompositions with equivalent quantization and encoding strategies for medical images,” in Medical Imaging, Y. Kim, ed., Proc. SPIE2431, 571–582 (1995).
[CrossRef]

W. Zeng, S. Daly, S. Lei, “Point-wise extended visual masking for JPEG-2000 image compression,” in Proceedings of the IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 2000), pp. 657–660.

N. Graham, Visual Pattern Analyzers (Oxford U. Press, New York, 1989).

P. C. Teo, D. J. Heeger, “Perceptual image distortion,” in Human Vision, Visual Processing, and Digital Display V, B. Rogowitz, J. Allebach, eds., Proc. SPIE2179, 127–141 (1994).
[CrossRef]

D. M. Chandler, S. S. Hemami, “Additivity models for suprathreshold distortion in quantized wavelet-coded images,” in Human Vision and Electronic Imaging VII, B. Rogowitz, T. Pappas, eds., Proc. SPIE4662, 105–118 (2002).
[CrossRef]

R. J. Safranek, J. D. Johnston, “A perceptually tuned sub-band image coder with image dependent quantization and post-quantization data compression,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1989), Vol. 3, pp. 1945–1948.

The data and the two images used in this study are available online at http://foulard.ece.cornell.edu/dmc27/ImageEffects.html .

Only the LH and HL subbands have been quantized.

M. Stokes, M. Anderson, S. Chandrasekar, R. Motta, “A standard default color space for the Internet–sRGB,” November1996, http://www.w3.org/Graphics/Color/sRGB.html .

D. G. Pelli, “Effects of visual noise,” Ph.D. thesis (Cambridge University, Cambridge, UK, 1981).

A. B. Watson, M. Taylor, R. Borthwick, “Image quality and entropy masking,” in Human Vision and Electronic Imaging II, B. Rogowitz, T. Pappas, eds., Proc. SPIE3016, 2–12 (1997).
[CrossRef]

Subject MM did not participate in the parts of experiments 2 and 4 that tested summation on the spatial-frequency dimension.

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Figures (19)

Fig. 1
Fig. 1

One-dimensional frequency response of a five-level hierarchical 9/7 biorthogonal synthesis filter bank.

Fig. 2
Fig. 2

Tiling of the two-dimensional frequency plane by a five-level hierarchical wavelet decomposition. Only the upper right quadrant is shown, and the fifth-level bands are not labeled. The labels refer to the subbands described in Subsection 2.C.

Fig. 3
Fig. 3

Quantization of a DWT subband induces artifacts in the reconstructed image; this process is modeled as the addition of distortions to the original image. The distortions depicted in this figure were generated by quantizing the LH4 subband (obtained by using the 9/7 biorthogonal filters) with a step size Δ=600.

Fig. 4
Fig. 4

Two 512×512 natural images (balloon and horse) used as masks in this study.

Fig. 5
Fig. 5

Representative stimuli used in experiment 1: horizontal wavelet subband quantization distortions at center frequencies (a) 4.6 c/deg, (b) 2.3 c/deg, and (c) 1.15 c/deg; vertical wavelet subband quantization distortions at center frequencies (d) 4.6 c/deg, (e) 2.3 c/deg, and (f) 1.15 c/deg. Distortions were generated by quantizing subbands from the balloon image. Stimuli containing quantization distortions at center frequencies 9.2 and 18.4 c/deg, and distortions generated from the horse image, are not depicted.

Fig. 6
Fig. 6

Contrast detection thresholds for simple wavelet subband quantization distortions generated through quantization of the balloon and horse images measured in the unmasked paradigm (experiment 1). Black circles, data for horizontal targets; gray circles, data for vertical targets. Error bars indicate ±1 SE. Note that the vertical axis represents increasing contrast in the downward direction.

Fig. 7
Fig. 7

Representative stimuli used in experiment 2: balloon image containing simple wavelet subband quantization distortions at center frequency 2.3 c/deg oriented (a) horizontally and (b) vertically and at center frequency 1.15 c/deg oriented (c) horizontally and (d) vertically. Stimuli containing quantization distortions at center frequencies 4.6, 9.2, and 18.4 c/deg, and stimuli containing the horse image, are not depicted.

Fig. 8
Fig. 8

Contrast detection thresholds for simple wavelet subband quantization distortions measured in the masked paradigm (experiment 2). Black circles, data for horizontal targets; gray circles, data for vertical targets. Error bars indicate ±1 SE. Light-gray data correspond to unmasked thresholds, which are replotted from Fig. 6. Note that the vertical axis represents increasing contrast in the downward direction.  

Fig. 9
Fig. 9

Contrast threshold elevations (masked/unmasked) imposed by each natural image on the detectability of wavelet distortions. Black circles, data for horizontal targets; gray circles, data for vertical targets.

Fig. 10
Fig. 10

Representative stimuli used in experiment 3: compound wavelet subband quantization distortions composed of horizontal+vertical components at center frequencies (a) 2.3 c/deg and (b) 1.15 c/deg and compound wavelet subband quantization distortions composed of 2 octaves of frequencies centered at 1.15+2.3 c/deg oriented (c) horizontally and (d) vertically. Distortions were generated by quantizing subbands from the horse image. Stimuli containing quantization distortions at center frequencies 4.6, 9.2, and 18.4 c/deg, and distortions generated from the balloon image, are not depicted.

Fig. 11
Fig. 11

Relative contrast thresholds measured in the unmasked paradigm (experiment 3) for compound wavelet subband quantization distortions containing orthogonal components of equal spatial frequencies. Distortions were generated by quantizing the LH and HL subbands of the balloon and horse images. The horizontal and vertical axes of each plot represent the relative rms contrasts of the horizontal and vertical components, respectively. Open circles, 4.6-c/deg components; gray circles, 2.3-c/deg components; black circles, 1.15-c/deg components. Solid curves indicate fits of Eq. (3) to the data (one curve for each data point); each curve is color coded and corresponds to the data point through which it runs.

Fig. 12
Fig. 12

Relative contrast thresholds measured in the unmasked paradigm (experiment 3) for compound wavelet subband quantization distortions containing equally oriented components of different center spatial frequencies. Distortions were generated by quantizing the LHn (HLn) and LHn+1 (HLn+1) subbands (n=3, 4) of the balloon and horse images. The horizontal and vertical axes represent the relative rms contrasts of the higher-frequency and lower-frequency components, respectively. Black circles, horizontal 2.3+4.6 c/deg; gray circles, vertical 2.3+4.6 c/deg; black squares, horizontal 1.15+2.3 c/deg; gray squares, vertical 1.15+2.3 c/deg. Solid curves indicate fits of Eq. (3) to the data (one curve for each data point); each curve is color coded and corresponds to the data point through which it runs.

Fig. 13
Fig. 13

Example of a summation-square plot denoting regions of linear summation, probability summation, and no summation. The horizontal axis corresponds to the relative contrast of one of the compound target’s components; the vertical axis corresponds to the relative contrast of the other component. For linear (complete) summation (RS=2, β=1), relative contrast thresholds would fall on the diagonal line connecting coordinates (0,1) to (1,0). For no summation (RS=1, β=), relative contrast thresholds would fall on the lines formed by connecting (0,1) to (1,1) and (1,1) to (1,0). The majority of summation-at-threshold experiments have found relative contrast thresholds to lie between these two extremes, typically with RS1.2 (probability summation, see Ref. 36).

Fig. 14
Fig. 14

Representative stimuli used in experiment 4: horse image containing compound wavelet subband quantization distortions composed of horizontal+vertical components at center frequencies (a) 2.3 c/deg and (b) 1.15 c/deg; horse image containing compound wavelet subband quantization distortions composed of 2 octaves of frequencies centered at 1.15+2.3 c/deg oriented (c) horizontally and (d) vertically. Stimuli containing quantization distortions at center frequencies 4.6, 9.2, and 18.4 c/deg, and stimuli containing the balloon image, are not depicted.

Fig. 15
Fig. 15

Relative contrast thresholds measured in the masked paradigm (experiment 4) for compound wavelet subband quantization distortions containing orthogonal components of equal spatial frequencies. Distortions were generated by quantizing the LH and HL subbands of the natural images described in Subsection 3.B. The horizontal and vertical axes of each plot represent the relative rms contrasts of the horizontal and vertical components, respectively. Open circles, 4.6-c/deg components; gray circles, 2.3-c/deg components; black circles, 1.15-c/deg components. Solid curves indicate fits of Eq. (3) to the data (one curve for each data point); each curve is color coded and corresponds to the data point through which it runs.

Fig. 16
Fig. 16

Relative contrast thresholds measured in the masked paradigm (experiment 4) for compound wavelet subband quantization distortions containing equally oriented components of different center spatial frequencies. Distortions were generated by quantizing the LHn (HLn) and LHn+1 (HLn+1) subbands (n=3, 4) of the natural images described in Subsection 3.B. The horizontal and vertical axes represent the relative rms contrasts of the higher-frequency and lower-frequency components, respectively. Black circles, horizontal 2.3+4.6 c/deg; gray circles, vertical 2.3+4.6 c/deg; black squares, horizontal 1.15+2.3 c/deg; gray squares, vertical 1.15+2.3 c/deg. Solid curves indicate fits of Eq. (3) to the data (one curve for each data point); each curve is color coded and corresponds to the data point through which it runs.

Fig. 17
Fig. 17

Threshold elevation data of Subsection 4.B replotted with the contrast energy (averaged over both orientations) of each natural image at the spatial scale centered at the frequency indicated by the horizontal axis. Circles, threshold elevations; squares, masker contrast energy at each spatial scale.

Fig. 18
Fig. 18

Two regions of the wall image used in a previous masked-summation study50 yielding nearly linear summation. The top region, “antenna,” contains horizontal and vertical components that are spatially separated, whereas the bottom region, “people,” contains overlapped edges of multiple orientations.

Fig. 19
Fig. 19

Balloon image reconstructed from quantized LH and HL subbands; the LL and HH subbands were not modified. In (a) the subbands were quantized such that the rms contrasts of the distortions are as specified by the thresholds of Fig. 8 for the balloon image and subject DC (i.e., β=). In (b) the subbands were quantized such that the rms contrast of the distortions are approximately 22% of the thresholds specified in Fig. 8 (β=1.5). The distortions in (a) should be suprathreshold. These images were designed to be viewed from a distance of approximately three picture heights. Compare these images with the original balloon image depicted in Fig. 4. Pay particular attention to the sky region near the top of the balloon and to the interior of the symbol “11” located in the center of the balloon’s envelope. These images can also be viewed online.65

Tables (5)

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Table 1 Summary of Results from Previous Summation Studies Using Far-Apart Targets

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Table 2 Relative Sensitivities for Unmasked Wavelet Targets of the Balloon Image

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Table 3 Relative Sensitivities for Unmasked Wavelet Targets of the Horse Image

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Table 4 Relative Sensitivities for Masked Wavelet Targets of the Balloon Image

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Table 5 Relative Sensitivities for Masked Wavelet Targets of the Horse Image

Equations (5)

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

RC(t)=C(t)CT(t),
RCT(ti; t¯)=CT(ti|t¯)CT(ti),
[RCT(t1; t¯)]β+[RCT(t2; t¯)]β=1.
Crms=1Lmask1Ni=0N(Li-Lmask)21/2,
C(ti)=10-1/β×CT(ti),

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