Abstract

Hypothetical schemes for neural representation of visual information can be expressed as explicit image codes. We may test whether a given code is sufficient, in the sense of retaining all the information that the human perceives, and necessary, in the sense of retaining only that information. The latter is a test of efficiency. Here, we explore a code modeled on the simple cells of the primate striate cortex. The Cortex transform maps a digital image into a set of subimages (layers) that are bandpass in spatial frequency and orientation. The layers are sampled so as to minimize the number of samples and still avoid aliasing. Samples are quantized in a manner that exploits the bandpass contrast-masking properties of human vision. The entropy of the samples is computed to provide a lower bound on the code size. Finally, the image is reconstructed from the code. We devise psychophysical methods for comparing the original and reconstructed images to evaluate the sufficiency of the code. When each resolution is coded at the threshold for detection artifacts, the image-codesize is about 1 bit/pixel.

© 1987 Optical Society of America

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  1. A. B. Watson, “The Cortex transform: rapid computation of simulated neural images,” Comput. Vision Graph. Image Process. 39, 311–327 (1987).
    [CrossRef]
  2. P. Lennie, “Parallel visual pathways: a review,” Vision Res. 20, 561–594 (1980).
    [CrossRef] [PubMed]
  3. R. M. Shapley, P. Lennie, “Spatial frequency analysis in the visual system,” Annu. Rev. Neurosci. 8, 547–583 (1985).
    [CrossRef] [PubMed]
  4. R. L. De Valois, D. G. Albrecht, L. G. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vision Res. 22, 545–559 (1982).
    [CrossRef] [PubMed]
  5. M. A. Webster, R. L. De Valois, “Relationship between spatial frequency and orientation tuning of striate-cortex cells,” J. Opt. Soc. Am. A 2, 1124–1132 (1985).
    [CrossRef] [PubMed]
  6. R. L. De Valois, E. W. Yund, H. Hepler, “The orientation and direction selectivity of cells in macaque visual cortex,” Vision Res. 22, 531–544 (1982).
    [CrossRef] [PubMed]
  7. B. Sakitt, H. B. Barlow, “A model for the economical encoding of the visual image in cerebral cortex,” Biol. Cybern. 43, 97–108 (1982).
    [CrossRef] [PubMed]
  8. A. B. Watson, “Detection and recognition of simple spatial forms,” in Physical and Biological Processing of Images, O. J. Braddick, A. C. Sleigh, eds. (Springer-Verlag, New York, 1983), pp. 100–114.
    [CrossRef]
  9. S. A. Klein, D. M. Levi, “Hyperacuity thresholds of 1 sec: theoretical predictions and empirical validation,” J. Opt. Soc. Am. A 2, 1170–1190 (1985).
    [CrossRef] [PubMed]
  10. The parameters of the filters used here, in the terms defined in Ref. 1, are β= 0.9, γ= 8, s= 2. The filters have center orientations of 22.5, 67.5, 112 .5 , and 157 .5 .
  11. A. Weber, “Image base base,” (Image Processing Institute, University of Southern California, Los Angeles, Calif., 1983).
  12. A. B. Watson, “Ideal shrinking and expansion of discrete sequences,” NASA Technical Memorandum 88202 (National Aeronautics and Space Adminstration, Moffett Field, Calif., 1986).
  13. S. Tanimoto, T. Pavlidis, “A hierarchical data structure for picture processing,” Comput. Graph. Image Process. 4, 104–119 (1975).
    [CrossRef]
  14. P. J. Burt, E. H. Adelson, “The Laplacian pyramid as a compact image code,”IEEE Trans. Commun. COM-31, 532–540 (1983).
    [CrossRef]
  15. J. L. Crowley, R. M. Stern, “Fast computation of the difference of low-pass transform,”IEEE Trans. Pattern Anal. Mach. Intell. PAMI-6, 212–222 (1984).
    [CrossRef]
  16. Consider a filter f(x) at orientation θ. By analogy to analytic signals in one dimension [R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1978), p. 267], we define the analytic filterfa(x)=½[f(x)-ifh(x)],where fh(x) is the Hilbert transform of f(x) taken along the direction vector d= [cos θ, sin θ],fh(x)=f(x)*-1πx·d.The Fourier transform of fa(x) isFa(u)=12[F(u)+sign(u·d)F(u)]={F(u),u·d>00,u·d<0.Since the filter transform consists of two identical lobes symmetrically placed on either side of the line u· d= 0, the analytic filter discards one of these lobes. Since f(x) is even along d, fh(x) will be odd along d. Thus the analytic filter consists of the original real even filter plus the corresponding complex odd filter, all divided by 2. These two components of the analytic filter correspond to odd and even receptive fields.
  17. D. A. Pollen, S. F. Ronner, “Phase relationship between adjacent simple cells in the visual cortex,” Science 212, 1409–1411 (1981).
    [CrossRef] [PubMed]
  18. A. B. Watson, A. J. Ahumada, “A look at motion in the frequency domain,” in Motion: Perception and Representation, J. K. Tsotsos, ed. (Association for Computing Machinery, New York, 1983), pp. 1–10.
  19. A. B. Watson, A. J. Ahumada, “Model of human visual-motion sensing,” J. Opt. Soc. Am. A 2, 322–342 (1985).
    [CrossRef] [PubMed]
  20. J. P. H. van Santen, G. Sperling, “Elaborated Reichardt detectors,” J. Opt. Soc. Am. A 2, 300–321 (1985).
    [CrossRef] [PubMed]
  21. E. H. Adelson, J. R. Bergen, “Spatiotemporal energy models for the perception of motion,” J. Opt. Soc. Am. A 2, 284–299 (1985).
    [CrossRef] [PubMed]
  22. D. A. Dudgeon, R. M. Mersereau, Multidimensional Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1984).
  23. R. E. Williamson, H. F. Trotter, Multivariate Mathematics (Prentice-Hall, Englewood Cliffs, N.J., 1974).
  24. P. J. Burt, “Fast filter transforms for image processing,” Comput. Graph. Image Process. 16, 20–51 (1981).
    [CrossRef]
  25. A. Rosenfeld, A. C. Kak, Digital Picture Processing (Academic, New York, 1982), p. 191.
  26. J. Max, “Quantizing for minimum distortion,”IRE Trans. Inf. Theory IT-6, 7–12 (1960).
    [CrossRef]
  27. F. W. Campbell, J. J. Kulikowski, “Orientation selectivity of the human visual system,”J. Physiol. 187, 437–445 (1966).
    [PubMed]
  28. J. Nachmias, R. Sansbury, “Grating contrast: discrimination may be better than detection,” Vision Res. 14, 1039–1042 (1974).
    [CrossRef] [PubMed]
  29. G. E. Legge, J. M. Foley, “Contrast making in human vision,”J. Opt. Soc. Am. 70, 1458–1471 (1980).
    [CrossRef] [PubMed]
  30. J. M. Foley, G. E. Legge, “Contrast detection and near-threshold discrimination in human vision,” Vision Res. 21, 1041–1053 (1981).
    [CrossRef] [PubMed]
  31. G. E. Legge, “A power law for contrast discrimination,” Vision Res. 21, 457–467 (1981).
    [CrossRef] [PubMed]
  32. H. R. Wilson, D. K. McFarlane, G. C. Phillips, “Spatial frequency tuning of orientation selective units estimated by oblique masking,” Vision Res. 23, 873–882 (1983).
    [CrossRef] [PubMed]
  33. A. Bradley, I. Ohzawa, “A comparison of contrast detection and discrimination,” Vision Res. 26, 991–997 (1986).
    [CrossRef] [PubMed]
  34. D. J. Sharma, A. N. Netravali, “Design of quantizers for dpcm coding of picture signals,”IEEE Trans. Commun. COM-25, 1267–1274 (1977).
    [CrossRef]
  35. G. C. Phillips, H. R. Wilson, “Orientation bandwidths of spatial mechanisms measured by masking,” J. Opt. Soc. Am. A 1, 226–232 (1984).
    [CrossRef] [PubMed]
  36. W. K. Pratt, Digital Image Processing (Wiley, New York, 1978).
  37. G. Sperling, M. Landy, Y. Cohen, M. Pavel, “Intelligible coding of ASL image sequences at extremely low information rates,” Comput. Vision Graph. Image Process. 31, 335–391 (1985).
    [CrossRef]
  38. D. E. Pearson, J. A. Robinson, “Visual communication at very low data rates,” Proc. IEEE 73, 795–812 (1985).
    [CrossRef]
  39. The 82% value is chosen for mathematical convenience (it is the probability reached when the Weibull exponent is 1). Any percentage point that can be accurately estimated would do as well.
  40. A. B. Watson, K. R. K. Nielsen, A. Poirson, A. Fitzhugh, A. Bilson, K. Nguyen, A. J. Ahumada, “Use of a raster framebuffer in vision research,” Behav. Res. Methods Instrum. 18, 587–594 (1986).
    [CrossRef]
  41. A. B. Watson, D. G. Pelli, “QUEST: a Bayesian adaptive psychometric method,” Percept. Psychophys. 33, 113–120 (1983).
    [CrossRef] [PubMed]
  42. A. B. Watson, “Probability summation over time,” Vision Res. 19, 515–522 (1979).
    [CrossRef] [PubMed]
  43. J. G. Robson, N. G. Graham, “Probability summation and regional variation in contrast sensitivity across the visual field,” Vision Res. 21, 409–418 (1981).
    [CrossRef] [PubMed]
  44. N. Ahmed, T. Nataragan, K. R. Rao, “Discrete cosine transform,”IEEE Trans. Comput. C-23, 90–93 (1974).
    [CrossRef]
  45. J. W. Modestino, N. Farvardin, M. A. Ogrinc, “Performance of block cosine image coding with adaptive quantization,”IEEE Trans. Commun. COM-33, 210–217 (1985).
    [CrossRef]
  46. E. J. Delp, O. R. Mitchell, “Image compression using block truncation coding,”IEEE Trans. Commun. COM-27, 1335–1342 (1979).
    [CrossRef]
  47. J. W. Woods, S. D. O’Neil, “Subband coding of images,”IEEE Trans. Acoust. Speech Signal Process. ASSP-43, 1278–1288 (1986).
    [CrossRef]
  48. D. J. Sakrison, “Image coding applications of vision models,” in Image Transmission Techniques, W. K. Pratt, ed. (Academic, New York, 1979).
  49. J. O. Limb, C. B. Rubinstein, “On the design of quantizers for dpcm coders: a functional relationship between visibility, probability, and masking,”IEEE Trans. Commun. COM-26, 573–578 (1978).
    [CrossRef]
  50. J. C. Candy, R. H. Bosworth, “Methods of designing differential quantizers based on subjective evaluations of edge busyness,” Bell Sys. Tech. J. 51, 1495–1516 (1972).
  51. A. N. Netravali, B. Prasada, “Adaptive quantization of picture signals using spatial masking,” Proc. IEEE 65, 536–548 (1977).
    [CrossRef]
  52. W. F. Schreiber, C. F. Knapp, N. D. Kay, “Synthetic highs—an experimental TV bandwidth reduction system,”J. Soc. Motion Pict. Eng. 68, 525–537 (1959).
  53. M. Kunt, A. Ikonomopoulos, M. Kocher, “Second-generation image-coding techniques,” Proc. IEEE 73, 549–574 (1985).
    [CrossRef]
  54. M. S. Livingstone, D. H. Hubel, “Anatomy and physiology of a color system in the primate visual cortex,”J. Neurosci. 4, 309–356 (1984).
    [PubMed]
  55. D. H. Hubel, T. N. Wiesel, “Receptive fields and functional architecture of monkey striate cortex,”J. Physiol. 195, 215–243 (1968).
    [PubMed]
  56. D. H. Hubel, T. N. Wiesel, “Functional architecture of the macaque monkey visual cortex. Ferrier lecture,” Proc. R. Soc. London Ser. B 198, 1–59 (1977).
    [CrossRef]
  57. D. H. Hubel, T. N. Wiesel, “Sequence regularity and geometry of orientation columns in the monkey striate cortex,”J. Comp. Neurol. 158, 267–294 (1974).
    [CrossRef] [PubMed]

1987 (1)

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

1986 (3)

A. Bradley, I. Ohzawa, “A comparison of contrast detection and discrimination,” Vision Res. 26, 991–997 (1986).
[CrossRef] [PubMed]

A. B. Watson, K. R. K. Nielsen, A. Poirson, A. Fitzhugh, A. Bilson, K. Nguyen, A. J. Ahumada, “Use of a raster framebuffer in vision research,” Behav. Res. Methods Instrum. 18, 587–594 (1986).
[CrossRef]

J. W. Woods, S. D. O’Neil, “Subband coding of images,”IEEE Trans. Acoust. Speech Signal Process. ASSP-43, 1278–1288 (1986).
[CrossRef]

1985 (10)

M. Kunt, A. Ikonomopoulos, M. Kocher, “Second-generation image-coding techniques,” Proc. IEEE 73, 549–574 (1985).
[CrossRef]

G. Sperling, M. Landy, Y. Cohen, M. Pavel, “Intelligible coding of ASL image sequences at extremely low information rates,” Comput. Vision Graph. Image Process. 31, 335–391 (1985).
[CrossRef]

D. E. Pearson, J. A. Robinson, “Visual communication at very low data rates,” Proc. IEEE 73, 795–812 (1985).
[CrossRef]

J. W. Modestino, N. Farvardin, M. A. Ogrinc, “Performance of block cosine image coding with adaptive quantization,”IEEE Trans. Commun. COM-33, 210–217 (1985).
[CrossRef]

R. M. Shapley, P. Lennie, “Spatial frequency analysis in the visual system,” Annu. Rev. Neurosci. 8, 547–583 (1985).
[CrossRef] [PubMed]

M. A. Webster, R. L. De Valois, “Relationship between spatial frequency and orientation tuning of striate-cortex cells,” J. Opt. Soc. Am. A 2, 1124–1132 (1985).
[CrossRef] [PubMed]

S. A. Klein, D. M. Levi, “Hyperacuity thresholds of 1 sec: theoretical predictions and empirical validation,” J. Opt. Soc. Am. A 2, 1170–1190 (1985).
[CrossRef] [PubMed]

A. B. Watson, A. J. Ahumada, “Model of human visual-motion sensing,” J. Opt. Soc. Am. A 2, 322–342 (1985).
[CrossRef] [PubMed]

J. P. H. van Santen, G. Sperling, “Elaborated Reichardt detectors,” J. Opt. Soc. Am. A 2, 300–321 (1985).
[CrossRef] [PubMed]

E. H. Adelson, J. R. Bergen, “Spatiotemporal energy models for the perception of motion,” J. Opt. Soc. Am. A 2, 284–299 (1985).
[CrossRef] [PubMed]

1984 (3)

J. L. Crowley, R. M. Stern, “Fast computation of the difference of low-pass transform,”IEEE Trans. Pattern Anal. Mach. Intell. PAMI-6, 212–222 (1984).
[CrossRef]

G. C. Phillips, H. R. Wilson, “Orientation bandwidths of spatial mechanisms measured by masking,” J. Opt. Soc. Am. A 1, 226–232 (1984).
[CrossRef] [PubMed]

M. S. Livingstone, D. H. Hubel, “Anatomy and physiology of a color system in the primate visual cortex,”J. Neurosci. 4, 309–356 (1984).
[PubMed]

1983 (3)

H. R. Wilson, D. K. McFarlane, G. C. Phillips, “Spatial frequency tuning of orientation selective units estimated by oblique masking,” Vision Res. 23, 873–882 (1983).
[CrossRef] [PubMed]

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

P. J. Burt, E. H. Adelson, “The Laplacian pyramid as a compact image code,”IEEE Trans. Commun. COM-31, 532–540 (1983).
[CrossRef]

1982 (3)

R. L. De Valois, E. W. Yund, H. Hepler, “The orientation and direction selectivity of cells in macaque visual cortex,” Vision Res. 22, 531–544 (1982).
[CrossRef] [PubMed]

B. Sakitt, H. B. Barlow, “A model for the economical encoding of the visual image in cerebral cortex,” Biol. Cybern. 43, 97–108 (1982).
[CrossRef] [PubMed]

R. L. De Valois, D. G. Albrecht, L. G. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vision Res. 22, 545–559 (1982).
[CrossRef] [PubMed]

1981 (5)

D. A. Pollen, S. F. Ronner, “Phase relationship between adjacent simple cells in the visual cortex,” Science 212, 1409–1411 (1981).
[CrossRef] [PubMed]

P. J. Burt, “Fast filter transforms for image processing,” Comput. Graph. Image Process. 16, 20–51 (1981).
[CrossRef]

J. G. Robson, N. G. Graham, “Probability summation and regional variation in contrast sensitivity across the visual field,” Vision Res. 21, 409–418 (1981).
[CrossRef] [PubMed]

J. M. Foley, G. E. Legge, “Contrast detection and near-threshold discrimination in human vision,” Vision Res. 21, 1041–1053 (1981).
[CrossRef] [PubMed]

G. E. Legge, “A power law for contrast discrimination,” Vision Res. 21, 457–467 (1981).
[CrossRef] [PubMed]

1980 (2)

1979 (2)

E. J. Delp, O. R. Mitchell, “Image compression using block truncation coding,”IEEE Trans. Commun. COM-27, 1335–1342 (1979).
[CrossRef]

A. B. Watson, “Probability summation over time,” Vision Res. 19, 515–522 (1979).
[CrossRef] [PubMed]

1978 (1)

J. O. Limb, C. B. Rubinstein, “On the design of quantizers for dpcm coders: a functional relationship between visibility, probability, and masking,”IEEE Trans. Commun. COM-26, 573–578 (1978).
[CrossRef]

1977 (3)

A. N. Netravali, B. Prasada, “Adaptive quantization of picture signals using spatial masking,” Proc. IEEE 65, 536–548 (1977).
[CrossRef]

D. H. Hubel, T. N. Wiesel, “Functional architecture of the macaque monkey visual cortex. Ferrier lecture,” Proc. R. Soc. London Ser. B 198, 1–59 (1977).
[CrossRef]

D. J. Sharma, A. N. Netravali, “Design of quantizers for dpcm coding of picture signals,”IEEE Trans. Commun. COM-25, 1267–1274 (1977).
[CrossRef]

1975 (1)

S. Tanimoto, T. Pavlidis, “A hierarchical data structure for picture processing,” Comput. Graph. Image Process. 4, 104–119 (1975).
[CrossRef]

1974 (3)

J. Nachmias, R. Sansbury, “Grating contrast: discrimination may be better than detection,” Vision Res. 14, 1039–1042 (1974).
[CrossRef] [PubMed]

N. Ahmed, T. Nataragan, K. R. Rao, “Discrete cosine transform,”IEEE Trans. Comput. C-23, 90–93 (1974).
[CrossRef]

D. H. Hubel, T. N. Wiesel, “Sequence regularity and geometry of orientation columns in the monkey striate cortex,”J. Comp. Neurol. 158, 267–294 (1974).
[CrossRef] [PubMed]

1972 (1)

J. C. Candy, R. H. Bosworth, “Methods of designing differential quantizers based on subjective evaluations of edge busyness,” Bell Sys. Tech. J. 51, 1495–1516 (1972).

1968 (1)

D. H. Hubel, T. N. Wiesel, “Receptive fields and functional architecture of monkey striate cortex,”J. Physiol. 195, 215–243 (1968).
[PubMed]

1966 (1)

F. W. Campbell, J. J. Kulikowski, “Orientation selectivity of the human visual system,”J. Physiol. 187, 437–445 (1966).
[PubMed]

1960 (1)

J. Max, “Quantizing for minimum distortion,”IRE Trans. Inf. Theory IT-6, 7–12 (1960).
[CrossRef]

1959 (1)

W. F. Schreiber, C. F. Knapp, N. D. Kay, “Synthetic highs—an experimental TV bandwidth reduction system,”J. Soc. Motion Pict. Eng. 68, 525–537 (1959).

Adelson, E. H.

E. H. Adelson, J. R. Bergen, “Spatiotemporal energy models for the perception of motion,” J. Opt. Soc. Am. A 2, 284–299 (1985).
[CrossRef] [PubMed]

P. J. Burt, E. H. Adelson, “The Laplacian pyramid as a compact image code,”IEEE Trans. Commun. COM-31, 532–540 (1983).
[CrossRef]

Ahmed, N.

N. Ahmed, T. Nataragan, K. R. Rao, “Discrete cosine transform,”IEEE Trans. Comput. C-23, 90–93 (1974).
[CrossRef]

Ahumada, A. J.

A. B. Watson, K. R. K. Nielsen, A. Poirson, A. Fitzhugh, A. Bilson, K. Nguyen, A. J. Ahumada, “Use of a raster framebuffer in vision research,” Behav. Res. Methods Instrum. 18, 587–594 (1986).
[CrossRef]

A. B. Watson, A. J. Ahumada, “Model of human visual-motion sensing,” J. Opt. Soc. Am. A 2, 322–342 (1985).
[CrossRef] [PubMed]

A. B. Watson, A. J. Ahumada, “A look at motion in the frequency domain,” in Motion: Perception and Representation, J. K. Tsotsos, ed. (Association for Computing Machinery, New York, 1983), pp. 1–10.

Albrecht, D. G.

R. L. De Valois, D. G. Albrecht, L. G. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vision Res. 22, 545–559 (1982).
[CrossRef] [PubMed]

Barlow, H. B.

B. Sakitt, H. B. Barlow, “A model for the economical encoding of the visual image in cerebral cortex,” Biol. Cybern. 43, 97–108 (1982).
[CrossRef] [PubMed]

Bergen, J. R.

Bilson, A.

A. B. Watson, K. R. K. Nielsen, A. Poirson, A. Fitzhugh, A. Bilson, K. Nguyen, A. J. Ahumada, “Use of a raster framebuffer in vision research,” Behav. Res. Methods Instrum. 18, 587–594 (1986).
[CrossRef]

Bosworth, R. H.

J. C. Candy, R. H. Bosworth, “Methods of designing differential quantizers based on subjective evaluations of edge busyness,” Bell Sys. Tech. J. 51, 1495–1516 (1972).

Bracewell, R. N.

Consider a filter f(x) at orientation θ. By analogy to analytic signals in one dimension [R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1978), p. 267], we define the analytic filterfa(x)=½[f(x)-ifh(x)],where fh(x) is the Hilbert transform of f(x) taken along the direction vector d= [cos θ, sin θ],fh(x)=f(x)*-1πx·d.The Fourier transform of fa(x) isFa(u)=12[F(u)+sign(u·d)F(u)]={F(u),u·d>00,u·d<0.Since the filter transform consists of two identical lobes symmetrically placed on either side of the line u· d= 0, the analytic filter discards one of these lobes. Since f(x) is even along d, fh(x) will be odd along d. Thus the analytic filter consists of the original real even filter plus the corresponding complex odd filter, all divided by 2. These two components of the analytic filter correspond to odd and even receptive fields.

Bradley, A.

A. Bradley, I. Ohzawa, “A comparison of contrast detection and discrimination,” Vision Res. 26, 991–997 (1986).
[CrossRef] [PubMed]

Burt, P. J.

P. J. Burt, E. H. Adelson, “The Laplacian pyramid as a compact image code,”IEEE Trans. Commun. COM-31, 532–540 (1983).
[CrossRef]

P. J. Burt, “Fast filter transforms for image processing,” Comput. Graph. Image Process. 16, 20–51 (1981).
[CrossRef]

Campbell, F. W.

F. W. Campbell, J. J. Kulikowski, “Orientation selectivity of the human visual system,”J. Physiol. 187, 437–445 (1966).
[PubMed]

Candy, J. C.

J. C. Candy, R. H. Bosworth, “Methods of designing differential quantizers based on subjective evaluations of edge busyness,” Bell Sys. Tech. J. 51, 1495–1516 (1972).

Cohen, Y.

G. Sperling, M. Landy, Y. Cohen, M. Pavel, “Intelligible coding of ASL image sequences at extremely low information rates,” Comput. Vision Graph. Image Process. 31, 335–391 (1985).
[CrossRef]

Crowley, J. L.

J. L. Crowley, R. M. Stern, “Fast computation of the difference of low-pass transform,”IEEE Trans. Pattern Anal. Mach. Intell. PAMI-6, 212–222 (1984).
[CrossRef]

De Valois, R. L.

M. A. Webster, R. L. De Valois, “Relationship between spatial frequency and orientation tuning of striate-cortex cells,” J. Opt. Soc. Am. A 2, 1124–1132 (1985).
[CrossRef] [PubMed]

R. L. De Valois, D. G. Albrecht, L. G. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vision Res. 22, 545–559 (1982).
[CrossRef] [PubMed]

R. L. De Valois, E. W. Yund, H. Hepler, “The orientation and direction selectivity of cells in macaque visual cortex,” Vision Res. 22, 531–544 (1982).
[CrossRef] [PubMed]

Delp, E. J.

E. J. Delp, O. R. Mitchell, “Image compression using block truncation coding,”IEEE Trans. Commun. COM-27, 1335–1342 (1979).
[CrossRef]

Dudgeon, D. A.

D. A. Dudgeon, R. M. Mersereau, Multidimensional Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1984).

Farvardin, N.

J. W. Modestino, N. Farvardin, M. A. Ogrinc, “Performance of block cosine image coding with adaptive quantization,”IEEE Trans. Commun. COM-33, 210–217 (1985).
[CrossRef]

Fitzhugh, A.

A. B. Watson, K. R. K. Nielsen, A. Poirson, A. Fitzhugh, A. Bilson, K. Nguyen, A. J. Ahumada, “Use of a raster framebuffer in vision research,” Behav. Res. Methods Instrum. 18, 587–594 (1986).
[CrossRef]

Foley, J. M.

J. M. Foley, G. E. Legge, “Contrast detection and near-threshold discrimination in human vision,” Vision Res. 21, 1041–1053 (1981).
[CrossRef] [PubMed]

G. E. Legge, J. M. Foley, “Contrast making in human vision,”J. Opt. Soc. Am. 70, 1458–1471 (1980).
[CrossRef] [PubMed]

Graham, N. G.

J. G. Robson, N. G. Graham, “Probability summation and regional variation in contrast sensitivity across the visual field,” Vision Res. 21, 409–418 (1981).
[CrossRef] [PubMed]

Hepler, H.

R. L. De Valois, E. W. Yund, H. Hepler, “The orientation and direction selectivity of cells in macaque visual cortex,” Vision Res. 22, 531–544 (1982).
[CrossRef] [PubMed]

Hubel, D. H.

M. S. Livingstone, D. H. Hubel, “Anatomy and physiology of a color system in the primate visual cortex,”J. Neurosci. 4, 309–356 (1984).
[PubMed]

D. H. Hubel, T. N. Wiesel, “Functional architecture of the macaque monkey visual cortex. Ferrier lecture,” Proc. R. Soc. London Ser. B 198, 1–59 (1977).
[CrossRef]

D. H. Hubel, T. N. Wiesel, “Sequence regularity and geometry of orientation columns in the monkey striate cortex,”J. Comp. Neurol. 158, 267–294 (1974).
[CrossRef] [PubMed]

D. H. Hubel, T. N. Wiesel, “Receptive fields and functional architecture of monkey striate cortex,”J. Physiol. 195, 215–243 (1968).
[PubMed]

Ikonomopoulos, A.

M. Kunt, A. Ikonomopoulos, M. Kocher, “Second-generation image-coding techniques,” Proc. IEEE 73, 549–574 (1985).
[CrossRef]

Kak, A. C.

A. Rosenfeld, A. C. Kak, Digital Picture Processing (Academic, New York, 1982), p. 191.

Kay, N. D.

W. F. Schreiber, C. F. Knapp, N. D. Kay, “Synthetic highs—an experimental TV bandwidth reduction system,”J. Soc. Motion Pict. Eng. 68, 525–537 (1959).

Klein, S. A.

Knapp, C. F.

W. F. Schreiber, C. F. Knapp, N. D. Kay, “Synthetic highs—an experimental TV bandwidth reduction system,”J. Soc. Motion Pict. Eng. 68, 525–537 (1959).

Kocher, M.

M. Kunt, A. Ikonomopoulos, M. Kocher, “Second-generation image-coding techniques,” Proc. IEEE 73, 549–574 (1985).
[CrossRef]

Kulikowski, J. J.

F. W. Campbell, J. J. Kulikowski, “Orientation selectivity of the human visual system,”J. Physiol. 187, 437–445 (1966).
[PubMed]

Kunt, M.

M. Kunt, A. Ikonomopoulos, M. Kocher, “Second-generation image-coding techniques,” Proc. IEEE 73, 549–574 (1985).
[CrossRef]

Landy, M.

G. Sperling, M. Landy, Y. Cohen, M. Pavel, “Intelligible coding of ASL image sequences at extremely low information rates,” Comput. Vision Graph. Image Process. 31, 335–391 (1985).
[CrossRef]

Legge, G. E.

J. M. Foley, G. E. Legge, “Contrast detection and near-threshold discrimination in human vision,” Vision Res. 21, 1041–1053 (1981).
[CrossRef] [PubMed]

G. E. Legge, “A power law for contrast discrimination,” Vision Res. 21, 457–467 (1981).
[CrossRef] [PubMed]

G. E. Legge, J. M. Foley, “Contrast making in human vision,”J. Opt. Soc. Am. 70, 1458–1471 (1980).
[CrossRef] [PubMed]

Lennie, P.

R. M. Shapley, P. Lennie, “Spatial frequency analysis in the visual system,” Annu. Rev. Neurosci. 8, 547–583 (1985).
[CrossRef] [PubMed]

P. Lennie, “Parallel visual pathways: a review,” Vision Res. 20, 561–594 (1980).
[CrossRef] [PubMed]

Levi, D. M.

Limb, J. O.

J. O. Limb, C. B. Rubinstein, “On the design of quantizers for dpcm coders: a functional relationship between visibility, probability, and masking,”IEEE Trans. Commun. COM-26, 573–578 (1978).
[CrossRef]

Livingstone, M. S.

M. S. Livingstone, D. H. Hubel, “Anatomy and physiology of a color system in the primate visual cortex,”J. Neurosci. 4, 309–356 (1984).
[PubMed]

Max, J.

J. Max, “Quantizing for minimum distortion,”IRE Trans. Inf. Theory IT-6, 7–12 (1960).
[CrossRef]

McFarlane, D. K.

H. R. Wilson, D. K. McFarlane, G. C. Phillips, “Spatial frequency tuning of orientation selective units estimated by oblique masking,” Vision Res. 23, 873–882 (1983).
[CrossRef] [PubMed]

Mersereau, R. M.

D. A. Dudgeon, R. M. Mersereau, Multidimensional Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1984).

Mitchell, O. R.

E. J. Delp, O. R. Mitchell, “Image compression using block truncation coding,”IEEE Trans. Commun. COM-27, 1335–1342 (1979).
[CrossRef]

Modestino, J. W.

J. W. Modestino, N. Farvardin, M. A. Ogrinc, “Performance of block cosine image coding with adaptive quantization,”IEEE Trans. Commun. COM-33, 210–217 (1985).
[CrossRef]

Nachmias, J.

J. Nachmias, R. Sansbury, “Grating contrast: discrimination may be better than detection,” Vision Res. 14, 1039–1042 (1974).
[CrossRef] [PubMed]

Nataragan, T.

N. Ahmed, T. Nataragan, K. R. Rao, “Discrete cosine transform,”IEEE Trans. Comput. C-23, 90–93 (1974).
[CrossRef]

Netravali, A. N.

A. N. Netravali, B. Prasada, “Adaptive quantization of picture signals using spatial masking,” Proc. IEEE 65, 536–548 (1977).
[CrossRef]

D. J. Sharma, A. N. Netravali, “Design of quantizers for dpcm coding of picture signals,”IEEE Trans. Commun. COM-25, 1267–1274 (1977).
[CrossRef]

Nguyen, K.

A. B. Watson, K. R. K. Nielsen, A. Poirson, A. Fitzhugh, A. Bilson, K. Nguyen, A. J. Ahumada, “Use of a raster framebuffer in vision research,” Behav. Res. Methods Instrum. 18, 587–594 (1986).
[CrossRef]

Nielsen, K. R. K.

A. B. Watson, K. R. K. Nielsen, A. Poirson, A. Fitzhugh, A. Bilson, K. Nguyen, A. J. Ahumada, “Use of a raster framebuffer in vision research,” Behav. Res. Methods Instrum. 18, 587–594 (1986).
[CrossRef]

O’Neil, S. D.

J. W. Woods, S. D. O’Neil, “Subband coding of images,”IEEE Trans. Acoust. Speech Signal Process. ASSP-43, 1278–1288 (1986).
[CrossRef]

Ogrinc, M. A.

J. W. Modestino, N. Farvardin, M. A. Ogrinc, “Performance of block cosine image coding with adaptive quantization,”IEEE Trans. Commun. COM-33, 210–217 (1985).
[CrossRef]

Ohzawa, I.

A. Bradley, I. Ohzawa, “A comparison of contrast detection and discrimination,” Vision Res. 26, 991–997 (1986).
[CrossRef] [PubMed]

Pavel, M.

G. Sperling, M. Landy, Y. Cohen, M. Pavel, “Intelligible coding of ASL image sequences at extremely low information rates,” Comput. Vision Graph. Image Process. 31, 335–391 (1985).
[CrossRef]

Pavlidis, T.

S. Tanimoto, T. Pavlidis, “A hierarchical data structure for picture processing,” Comput. Graph. Image Process. 4, 104–119 (1975).
[CrossRef]

Pearson, D. E.

D. E. Pearson, J. A. Robinson, “Visual communication at very low data rates,” Proc. IEEE 73, 795–812 (1985).
[CrossRef]

Pelli, D. G.

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

Phillips, G. C.

G. C. Phillips, H. R. Wilson, “Orientation bandwidths of spatial mechanisms measured by masking,” J. Opt. Soc. Am. A 1, 226–232 (1984).
[CrossRef] [PubMed]

H. R. Wilson, D. K. McFarlane, G. C. Phillips, “Spatial frequency tuning of orientation selective units estimated by oblique masking,” Vision Res. 23, 873–882 (1983).
[CrossRef] [PubMed]

Poirson, A.

A. B. Watson, K. R. K. Nielsen, A. Poirson, A. Fitzhugh, A. Bilson, K. Nguyen, A. J. Ahumada, “Use of a raster framebuffer in vision research,” Behav. Res. Methods Instrum. 18, 587–594 (1986).
[CrossRef]

Pollen, D. A.

D. A. Pollen, S. F. Ronner, “Phase relationship between adjacent simple cells in the visual cortex,” Science 212, 1409–1411 (1981).
[CrossRef] [PubMed]

Prasada, B.

A. N. Netravali, B. Prasada, “Adaptive quantization of picture signals using spatial masking,” Proc. IEEE 65, 536–548 (1977).
[CrossRef]

Pratt, W. K.

W. K. Pratt, Digital Image Processing (Wiley, New York, 1978).

Rao, K. R.

N. Ahmed, T. Nataragan, K. R. Rao, “Discrete cosine transform,”IEEE Trans. Comput. C-23, 90–93 (1974).
[CrossRef]

Robinson, J. A.

D. E. Pearson, J. A. Robinson, “Visual communication at very low data rates,” Proc. IEEE 73, 795–812 (1985).
[CrossRef]

Robson, J. G.

J. G. Robson, N. G. Graham, “Probability summation and regional variation in contrast sensitivity across the visual field,” Vision Res. 21, 409–418 (1981).
[CrossRef] [PubMed]

Ronner, S. F.

D. A. Pollen, S. F. Ronner, “Phase relationship between adjacent simple cells in the visual cortex,” Science 212, 1409–1411 (1981).
[CrossRef] [PubMed]

Rosenfeld, A.

A. Rosenfeld, A. C. Kak, Digital Picture Processing (Academic, New York, 1982), p. 191.

Rubinstein, C. B.

J. O. Limb, C. B. Rubinstein, “On the design of quantizers for dpcm coders: a functional relationship between visibility, probability, and masking,”IEEE Trans. Commun. COM-26, 573–578 (1978).
[CrossRef]

Sakitt, B.

B. Sakitt, H. B. Barlow, “A model for the economical encoding of the visual image in cerebral cortex,” Biol. Cybern. 43, 97–108 (1982).
[CrossRef] [PubMed]

Sakrison, D. J.

D. J. Sakrison, “Image coding applications of vision models,” in Image Transmission Techniques, W. K. Pratt, ed. (Academic, New York, 1979).

Sansbury, R.

J. Nachmias, R. Sansbury, “Grating contrast: discrimination may be better than detection,” Vision Res. 14, 1039–1042 (1974).
[CrossRef] [PubMed]

Schreiber, W. F.

W. F. Schreiber, C. F. Knapp, N. D. Kay, “Synthetic highs—an experimental TV bandwidth reduction system,”J. Soc. Motion Pict. Eng. 68, 525–537 (1959).

Shapley, R. M.

R. M. Shapley, P. Lennie, “Spatial frequency analysis in the visual system,” Annu. Rev. Neurosci. 8, 547–583 (1985).
[CrossRef] [PubMed]

Sharma, D. J.

D. J. Sharma, A. N. Netravali, “Design of quantizers for dpcm coding of picture signals,”IEEE Trans. Commun. COM-25, 1267–1274 (1977).
[CrossRef]

Sperling, G.

J. P. H. van Santen, G. Sperling, “Elaborated Reichardt detectors,” J. Opt. Soc. Am. A 2, 300–321 (1985).
[CrossRef] [PubMed]

G. Sperling, M. Landy, Y. Cohen, M. Pavel, “Intelligible coding of ASL image sequences at extremely low information rates,” Comput. Vision Graph. Image Process. 31, 335–391 (1985).
[CrossRef]

Stern, R. M.

J. L. Crowley, R. M. Stern, “Fast computation of the difference of low-pass transform,”IEEE Trans. Pattern Anal. Mach. Intell. PAMI-6, 212–222 (1984).
[CrossRef]

Tanimoto, S.

S. Tanimoto, T. Pavlidis, “A hierarchical data structure for picture processing,” Comput. Graph. Image Process. 4, 104–119 (1975).
[CrossRef]

Thorell, L. G.

R. L. De Valois, D. G. Albrecht, L. G. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vision Res. 22, 545–559 (1982).
[CrossRef] [PubMed]

Trotter, H. F.

R. E. Williamson, H. F. Trotter, Multivariate Mathematics (Prentice-Hall, Englewood Cliffs, N.J., 1974).

van Santen, J. P. H.

Watson, A. B.

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, K. R. K. Nielsen, A. Poirson, A. Fitzhugh, A. Bilson, K. Nguyen, A. J. Ahumada, “Use of a raster framebuffer in vision research,” Behav. Res. Methods Instrum. 18, 587–594 (1986).
[CrossRef]

A. B. Watson, A. J. Ahumada, “Model of human visual-motion sensing,” J. Opt. Soc. Am. A 2, 322–342 (1985).
[CrossRef] [PubMed]

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

A. B. Watson, “Probability summation over time,” Vision Res. 19, 515–522 (1979).
[CrossRef] [PubMed]

A. B. Watson, “Ideal shrinking and expansion of discrete sequences,” NASA Technical Memorandum 88202 (National Aeronautics and Space Adminstration, Moffett Field, Calif., 1986).

A. B. Watson, “Detection and recognition of simple spatial forms,” in Physical and Biological Processing of Images, O. J. Braddick, A. C. Sleigh, eds. (Springer-Verlag, New York, 1983), pp. 100–114.
[CrossRef]

A. B. Watson, A. J. Ahumada, “A look at motion in the frequency domain,” in Motion: Perception and Representation, J. K. Tsotsos, ed. (Association for Computing Machinery, New York, 1983), pp. 1–10.

Weber, A.

A. Weber, “Image base base,” (Image Processing Institute, University of Southern California, Los Angeles, Calif., 1983).

Webster, M. A.

Wiesel, T. N.

D. H. Hubel, T. N. Wiesel, “Functional architecture of the macaque monkey visual cortex. Ferrier lecture,” Proc. R. Soc. London Ser. B 198, 1–59 (1977).
[CrossRef]

D. H. Hubel, T. N. Wiesel, “Sequence regularity and geometry of orientation columns in the monkey striate cortex,”J. Comp. Neurol. 158, 267–294 (1974).
[CrossRef] [PubMed]

D. H. Hubel, T. N. Wiesel, “Receptive fields and functional architecture of monkey striate cortex,”J. Physiol. 195, 215–243 (1968).
[PubMed]

Williamson, R. E.

R. E. Williamson, H. F. Trotter, Multivariate Mathematics (Prentice-Hall, Englewood Cliffs, N.J., 1974).

Wilson, H. R.

G. C. Phillips, H. R. Wilson, “Orientation bandwidths of spatial mechanisms measured by masking,” J. Opt. Soc. Am. A 1, 226–232 (1984).
[CrossRef] [PubMed]

H. R. Wilson, D. K. McFarlane, G. C. Phillips, “Spatial frequency tuning of orientation selective units estimated by oblique masking,” Vision Res. 23, 873–882 (1983).
[CrossRef] [PubMed]

Woods, J. W.

J. W. Woods, S. D. O’Neil, “Subband coding of images,”IEEE Trans. Acoust. Speech Signal Process. ASSP-43, 1278–1288 (1986).
[CrossRef]

Yund, E. W.

R. L. De Valois, E. W. Yund, H. Hepler, “The orientation and direction selectivity of cells in macaque visual cortex,” Vision Res. 22, 531–544 (1982).
[CrossRef] [PubMed]

Annu. Rev. Neurosci. (1)

R. M. Shapley, P. Lennie, “Spatial frequency analysis in the visual system,” Annu. Rev. Neurosci. 8, 547–583 (1985).
[CrossRef] [PubMed]

Behav. Res. Methods Instrum. (1)

A. B. Watson, K. R. K. Nielsen, A. Poirson, A. Fitzhugh, A. Bilson, K. Nguyen, A. J. Ahumada, “Use of a raster framebuffer in vision research,” Behav. Res. Methods Instrum. 18, 587–594 (1986).
[CrossRef]

Bell Sys. Tech. J. (1)

J. C. Candy, R. H. Bosworth, “Methods of designing differential quantizers based on subjective evaluations of edge busyness,” Bell Sys. Tech. J. 51, 1495–1516 (1972).

Biol. Cybern. (1)

B. Sakitt, H. B. Barlow, “A model for the economical encoding of the visual image in cerebral cortex,” Biol. Cybern. 43, 97–108 (1982).
[CrossRef] [PubMed]

Comput. Graph. Image Process. (2)

S. Tanimoto, T. Pavlidis, “A hierarchical data structure for picture processing,” Comput. Graph. Image Process. 4, 104–119 (1975).
[CrossRef]

P. J. Burt, “Fast filter transforms for image processing,” Comput. Graph. Image Process. 16, 20–51 (1981).
[CrossRef]

Comput. Vision Graph. Image Process. (2)

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

G. Sperling, M. Landy, Y. Cohen, M. Pavel, “Intelligible coding of ASL image sequences at extremely low information rates,” Comput. Vision Graph. Image Process. 31, 335–391 (1985).
[CrossRef]

IEEE Trans. Acoust. Speech Signal Process. (1)

J. W. Woods, S. D. O’Neil, “Subband coding of images,”IEEE Trans. Acoust. Speech Signal Process. ASSP-43, 1278–1288 (1986).
[CrossRef]

IEEE Trans. Commun. (5)

J. O. Limb, C. B. Rubinstein, “On the design of quantizers for dpcm coders: a functional relationship between visibility, probability, and masking,”IEEE Trans. Commun. COM-26, 573–578 (1978).
[CrossRef]

J. W. Modestino, N. Farvardin, M. A. Ogrinc, “Performance of block cosine image coding with adaptive quantization,”IEEE Trans. Commun. COM-33, 210–217 (1985).
[CrossRef]

E. J. Delp, O. R. Mitchell, “Image compression using block truncation coding,”IEEE Trans. Commun. COM-27, 1335–1342 (1979).
[CrossRef]

P. J. Burt, E. H. Adelson, “The Laplacian pyramid as a compact image code,”IEEE Trans. Commun. COM-31, 532–540 (1983).
[CrossRef]

D. J. Sharma, A. N. Netravali, “Design of quantizers for dpcm coding of picture signals,”IEEE Trans. Commun. COM-25, 1267–1274 (1977).
[CrossRef]

IEEE Trans. Comput. (1)

N. Ahmed, T. Nataragan, K. R. Rao, “Discrete cosine transform,”IEEE Trans. Comput. C-23, 90–93 (1974).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

J. L. Crowley, R. M. Stern, “Fast computation of the difference of low-pass transform,”IEEE Trans. Pattern Anal. Mach. Intell. PAMI-6, 212–222 (1984).
[CrossRef]

IRE Trans. Inf. Theory (1)

J. Max, “Quantizing for minimum distortion,”IRE Trans. Inf. Theory IT-6, 7–12 (1960).
[CrossRef]

J. Comp. Neurol. (1)

D. H. Hubel, T. N. Wiesel, “Sequence regularity and geometry of orientation columns in the monkey striate cortex,”J. Comp. Neurol. 158, 267–294 (1974).
[CrossRef] [PubMed]

J. Neurosci. (1)

M. S. Livingstone, D. H. Hubel, “Anatomy and physiology of a color system in the primate visual cortex,”J. Neurosci. 4, 309–356 (1984).
[PubMed]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (6)

J. Physiol. (2)

F. W. Campbell, J. J. Kulikowski, “Orientation selectivity of the human visual system,”J. Physiol. 187, 437–445 (1966).
[PubMed]

D. H. Hubel, T. N. Wiesel, “Receptive fields and functional architecture of monkey striate cortex,”J. Physiol. 195, 215–243 (1968).
[PubMed]

J. Soc. Motion Pict. Eng. (1)

W. F. Schreiber, C. F. Knapp, N. D. Kay, “Synthetic highs—an experimental TV bandwidth reduction system,”J. Soc. Motion Pict. Eng. 68, 525–537 (1959).

Percept. Psychophys. (1)

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

Proc. IEEE (3)

D. E. Pearson, J. A. Robinson, “Visual communication at very low data rates,” Proc. IEEE 73, 795–812 (1985).
[CrossRef]

M. Kunt, A. Ikonomopoulos, M. Kocher, “Second-generation image-coding techniques,” Proc. IEEE 73, 549–574 (1985).
[CrossRef]

A. N. Netravali, B. Prasada, “Adaptive quantization of picture signals using spatial masking,” Proc. IEEE 65, 536–548 (1977).
[CrossRef]

Proc. R. Soc. London Ser. B (1)

D. H. Hubel, T. N. Wiesel, “Functional architecture of the macaque monkey visual cortex. Ferrier lecture,” Proc. R. Soc. London Ser. B 198, 1–59 (1977).
[CrossRef]

Science (1)

D. A. Pollen, S. F. Ronner, “Phase relationship between adjacent simple cells in the visual cortex,” Science 212, 1409–1411 (1981).
[CrossRef] [PubMed]

Vision Res. (10)

J. Nachmias, R. Sansbury, “Grating contrast: discrimination may be better than detection,” Vision Res. 14, 1039–1042 (1974).
[CrossRef] [PubMed]

J. M. Foley, G. E. Legge, “Contrast detection and near-threshold discrimination in human vision,” Vision Res. 21, 1041–1053 (1981).
[CrossRef] [PubMed]

G. E. Legge, “A power law for contrast discrimination,” Vision Res. 21, 457–467 (1981).
[CrossRef] [PubMed]

H. R. Wilson, D. K. McFarlane, G. C. Phillips, “Spatial frequency tuning of orientation selective units estimated by oblique masking,” Vision Res. 23, 873–882 (1983).
[CrossRef] [PubMed]

A. Bradley, I. Ohzawa, “A comparison of contrast detection and discrimination,” Vision Res. 26, 991–997 (1986).
[CrossRef] [PubMed]

R. L. De Valois, E. W. Yund, H. Hepler, “The orientation and direction selectivity of cells in macaque visual cortex,” Vision Res. 22, 531–544 (1982).
[CrossRef] [PubMed]

P. Lennie, “Parallel visual pathways: a review,” Vision Res. 20, 561–594 (1980).
[CrossRef] [PubMed]

R. L. De Valois, D. G. Albrecht, L. G. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vision Res. 22, 545–559 (1982).
[CrossRef] [PubMed]

A. B. Watson, “Probability summation over time,” Vision Res. 19, 515–522 (1979).
[CrossRef] [PubMed]

J. G. Robson, N. G. Graham, “Probability summation and regional variation in contrast sensitivity across the visual field,” Vision Res. 21, 409–418 (1981).
[CrossRef] [PubMed]

Other (12)

The 82% value is chosen for mathematical convenience (it is the probability reached when the Weibull exponent is 1). Any percentage point that can be accurately estimated would do as well.

D. J. Sakrison, “Image coding applications of vision models,” in Image Transmission Techniques, W. K. Pratt, ed. (Academic, New York, 1979).

A. B. Watson, “Detection and recognition of simple spatial forms,” in Physical and Biological Processing of Images, O. J. Braddick, A. C. Sleigh, eds. (Springer-Verlag, New York, 1983), pp. 100–114.
[CrossRef]

The parameters of the filters used here, in the terms defined in Ref. 1, are β= 0.9, γ= 8, s= 2. The filters have center orientations of 22.5, 67.5, 112 .5 , and 157 .5 .

A. Weber, “Image base base,” (Image Processing Institute, University of Southern California, Los Angeles, Calif., 1983).

A. B. Watson, “Ideal shrinking and expansion of discrete sequences,” NASA Technical Memorandum 88202 (National Aeronautics and Space Adminstration, Moffett Field, Calif., 1986).

Consider a filter f(x) at orientation θ. By analogy to analytic signals in one dimension [R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1978), p. 267], we define the analytic filterfa(x)=½[f(x)-ifh(x)],where fh(x) is the Hilbert transform of f(x) taken along the direction vector d= [cos θ, sin θ],fh(x)=f(x)*-1πx·d.The Fourier transform of fa(x) isFa(u)=12[F(u)+sign(u·d)F(u)]={F(u),u·d>00,u·d<0.Since the filter transform consists of two identical lobes symmetrically placed on either side of the line u· d= 0, the analytic filter discards one of these lobes. Since f(x) is even along d, fh(x) will be odd along d. Thus the analytic filter consists of the original real even filter plus the corresponding complex odd filter, all divided by 2. These two components of the analytic filter correspond to odd and even receptive fields.

W. K. Pratt, Digital Image Processing (Wiley, New York, 1978).

A. B. Watson, A. J. Ahumada, “A look at motion in the frequency domain,” in Motion: Perception and Representation, J. K. Tsotsos, ed. (Association for Computing Machinery, New York, 1983), pp. 1–10.

A. Rosenfeld, A. C. Kak, Digital Picture Processing (Academic, New York, 1982), p. 191.

D. A. Dudgeon, R. M. Mersereau, Multidimensional Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1984).

R. E. Williamson, H. F. Trotter, Multivariate Mathematics (Prentice-Hall, Englewood Cliffs, N.J., 1974).

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Figures (20)

Fig. 1
Fig. 1

Stages in the compression and reconstruction of an image.

Fig. 2
Fig. 2

Frequency spectra of the cortex filters. Filters differ in resolution down each column and in orientation across each row. The high-residue filter is shown in the upper left, and the low-residue filter is in the lower left. For each filter, the frequency origin is at the center. All filters are purely real.

Fig. 3
Fig. 3

Impulse response of the cortex filter at one frequency and orientation.

Fig. 4
Fig. 4

Cortex transform layers for the image of the woman. The original is at the upper right. The high and low residues are at the upper left and lower left, respectively. The layers vary in orientation across a row and in resolution down a column. All layers are shown at maximum contrast.

Fig. 5
Fig. 5

Creation of an analytic cortex filter by removal of one lobe of a cortex filter.

Fig. 6
Fig. 6

Periodic extension of a rectangular finite-extent discrete sequence of size N1 by N2. The periodicity vectors are n1 = [N1,0] and n2 = [0, N2].

Fig. 7
Fig. 7

A sampling matrix S and its corresponding replication matrix F. The two sampling vectors (the column vectors of the matrix) are shown. In the picture, sampling is applied to an 8 × 8 discrete sequence, reducing the number of samples from 64 to 8 and producing 8 spectrum replicas in the Fourier domain at the locations specified by the replication matrix F. Samples are numbered from 0 from the lower left.

Fig. 8
Fig. 8

Periodic sampling of a cortex layer. The real component of a cortex layer is shown A, before and B, after subsampling by means of the matrix S = [1 3 3 1]. The amplitude spectrum of the layer is shown in C, and that of the sampled layer is in D. The replicas in D are placed according to the replicating matrix F = [−1 3 3 −1].

Fig. 9
Fig. 9

Replications of cortex filter spectrum obtained by sampling with various matrices with determinant 8. The sampling matrix is shown above each spectrum. Note that matrix [1 3 2 −2] is functionally equivalent to the matrix [1 3 3 1] used in Fig. 8.

Fig. 10
Fig. 10

Quantization terminology. Max and mm are the largest and smallest input values. T’s and L’s are thresholds and levels. All input values between Ti and Ti+1 are replaced by Li.

Fig. 11
Fig. 11

Contrast-masking function and quantizer design. The heavy line represents the hypothetical contrast increment threshold function. The abscissa is the contrast of a signal relative to the threshold; the ordinate is the increment threshold, relative to the threshold. The dashed line illustrates the construction of quantizer levels and thresholds (see the text).

Fig. 12
Fig. 12

Entropy versus quantization strength Q. Separate curves are shown for the four resolutions and the total.

Fig. 13
Fig. 13

The sequence of operations used to code and reconstruct an image, shown for one layer only. The triangle representing the result of subsampling indicates that the image is no longer represented in a square sample lattice. The circles indicate operations: D, DFT; M, complex multiplication; S, subsampling; Q, quantization; U, upsampling; I, inverse DFT; E, entropy computation. Sections enclosed in dashed lines are discussed in Subsection 12.A.4.

Fig. 14
Fig. 14

Process of coding and reconstruction for one layer. From left to right, top to bottom, the images are the original, the analytic cortex filter, the spectrum of the layer response, the real layer, the imaginary layer, the real layer after sampling by the matrix [1 3 3 1] and quantization at Q = 4, the sampled and quantized imaginary layer, the spectrum of the sampled and quantized layers, the spectrum after application of the reconstruction filter, the reconstructed layer, the error owing to sampling and quantization (shown at full contrast), and the sum of the original and the error.

Fig. 15
Fig. 15

Images in which one resolution band (6) has been quantized by varying amounts, as indicated by the quantization strength Q.

Fig. 16
Fig. 16

Quantization detection as a function of quantization strength Q for one observer at one resolution. The square symbols represent percent correct, the number of trials at each strength is indicated by the histogram, and the heavy line is the best-fitting Weibull function used to estimate a value of quantization threshold. The upper and lower thin lines are binomial confidence limits about the data.

Fig. 17
Fig. 17

Quantization sensitivity (1/threshold) at each resolution for eight observers for the image of the woman (two replications for subject WCP). The upper line shows the mean. The lower line shows contrast-detection sensitivities for single reconstruction signals for observer WCP.

Fig. 18
Fig. 18

Original image of the woman and reconstruction at 1.11 bits/pixel. Quantization strengths of 3, 2,4, and 6 were used at resolutions of 5, 6, 7, and 8.

Fig. 19
Fig. 19

Image of woman reconstructed from codes of various sizes. Entropies and Q at resolutions 5, 6, 7, and 8, respectively: 0.66 bit/pixel, 4, 3, 5, 7; 0.45 bit/pixel, 4, 5, 6, 7; 0.36 bit/pixel, 5, 4, 6, 8; 0.23 bit/pixel, 5, 5, 7, 8.

Fig. 20
Fig. 20

Mandrill image reconstructed from codes of various sizes. Entropies and Q at resolutions 5, 6, 7, and 8, respectively: 0.75 bit/pixel, 4, 5, 6, 7; 0.45 bit/pixel, 5, 4, 6, 8; 0.26 bit/pixel, 5, 5, 7, 8.

Equations (9)

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x ˜ ( n + Nr ) = x ˜ ( n ) ,
n = Sr ,
F = ( S T ) - 1 N .
H = - v = min max p ( v ) log 2 p ( v ) ,
det S - i 2 2 ( R max - R ) - 1 ,
Δ c ( c ) = C max [ 1 , ( c / C ) W ] ,
L 0 = 0 , T i = L i - 1 + Δ c ( L i - 1 ) , L i = T i + Δ c ( T i ) .
Q = log 2 C + 10.9.
i q i / Δ c ( c i ) β .

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