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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 18, Iss. 9 — Sep. 1, 2001
  • pp: 2041–2053

Characterizing the spatial-frequency sensitivity of perceptual templates

Zhong-Lin Lu and Barbara Anne Dosher  »View Author Affiliations

JOSA A, Vol. 18, Issue 9, pp. 2041-2053 (2001)

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Filtered external noise has been an important tool in characterizing the spatial-frequency sensitivity of perceptual templates. Typically, low-pass- and/or high-pass-filtered external noise is added to the signal stimulus. Thresholds, the signal energy necessary to maintain given criterion performance levels, are measured as functions of the spatial-frequency passband of the external noise. An observer model is postulated to segregate the impact of the external noise and the internal noise. The spatial-frequency sensitivity of the perceptual template is determined by the relative impact exerted by external noise in each frequency band. The perceptual template model (PTM) is a general observer model that provides an excellent account of human performance in white external noise [Vision Res. 38, 1183 (1998); J. Opt. Soc. Am. A 16, 764 (1999)]. We further develop the PTM for filtered external noise and apply it to derive the spatial-frequency sensitivity of perceptual templates.

© 2001 Optical Society of America

OCIS Codes
(330.1880) Vision, color, and visual optics : Detection
(330.4060) Vision, color, and visual optics : Vision modeling
(330.5000) Vision, color, and visual optics : Vision - patterns and recognition
(330.5510) Vision, color, and visual optics : Psychophysics
(330.6100) Vision, color, and visual optics : Spatial discrimination
(330.6110) Vision, color, and visual optics : Spatial filtering

Original Manuscript: July 13, 2000
Revised Manuscript: February 13, 2001
Manuscript Accepted: February 13, 2001
Published: September 1, 2001

Zhong-Lin Lu and Barbara Anne Dosher, "Characterizing the spatial-frequency sensitivity of perceptual templates," J. Opt. Soc. Am. A 18, 2041-2053 (2001)

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  1. D. H. Hubel, T. N. Wiesel, “Receptive fields, binocular interaction and functional architecture in the cat’s striate cortex,” J. Physiol. 160, 106–154 (1962). [PubMed]
  2. H. R. Blackwell, “Neural theories of simple visual discriminations,” J. Opt. Soc. Am. 53, 129–160 (1963). [CrossRef] [PubMed]
  3. C. Enroth-Cugell, J. G. Robson, “The contrast sensitivity of retinal ganglion cells of the cat,” J. Physiol. 258, 517–552 (1966).
  4. F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. 197, 551–566 (1968). [PubMed]
  5. M. B. Sachs, J. Nachmias, J. G. Robson, “Spatial-frequency channels in human vision,” J. Opt. Soc. Am. 61, 1176–1186 (1971). [CrossRef] [PubMed]
  6. C. F. Stromeyer, B. Julesz, “Spatial-frequency masking in vision: critical bands and spread of masking,” J. Opt. Soc. Am. 64, 1221–1232 (1972). [CrossRef]
  7. P. H. Schiller, B. L. Finlay, S. F. Volman, “Quantitative studies of single cell properties in monkey striate cortex. III. Spatial-frequency,” J. Neurophysiol. 39, 1334–1351 (1976). [PubMed]
  8. A. B. Watson, J. G. Robson, “Discrimination at threshold: labelled detectors in human vision,” Vision Res. 21, 1115–1122 (1981). [CrossRef] [PubMed]
  9. R. L. DeValois, D. G. Albrecht, L. G. Thorell, “Spatial-frequency selectivity of cells in macaque visual cortex,” Vision Res. 22, 545–559 (1982). [CrossRef]
  10. N. V. S. Graham, Visual Pattern Analyzers (Oxford U. Press, New York, 1989).
  11. C. H. Graham, R. H. Brown, F. A. Mote, “The relation of size stimulus and intensity in the human eye. I. Intensity threshold for white light,” J. Exp. Psychol. 24, 554–573 (1939).
  12. J. P. Thomas, “Model of the function of receptive fields in human vision,” Psychol. Rev. 77, 121–134 (1977). [CrossRef]
  13. P. E. King-Smith, J. J. Kulikowski, “The detection of gratings by independent activation of line detectors,” J. Physiol. 247, 237–271 (1975). [PubMed]
  14. N. V. S. Graham, “Visual detection of aperiodic spatial stimuli by probability summation among narrowband channels,” Vision Res. 17, 637–652 (1977). [CrossRef] [PubMed]
  15. H. R. Wilson, J. R. Bergen, “A four mechanism model for threshold spatial vision,” Vision Res. 19, 19–32 (1979). [CrossRef] [PubMed]
  16. G. E. Legge, J. M. Foley, “Contrast masking in human vision,” J. Opt. Soc. Am. 70, 1458–1471 (1980). [CrossRef] [PubMed]
  17. G. B. Henning, B. G. Hertz, J. L. Hinton, “Effects of different hypothetical detection mechanisms on the shape of spatial-frequency filters inferred from masking experiments: I. Noise masks,” J. Opt. Soc. Am. 71, 574–581 (1981). [CrossRef] [PubMed]
  18. 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]
  19. A. Pantle, R. Sekuler, “Size detecting mechanisms in human vision,” Science 162, 1146–1148 (1969). [CrossRef]
  20. C. B. Blakemore, F. W. Campbell, “On the existence of neurons in the human visual system selectively sensitive to the orientation and size of retinal images,” J. Physiol. 203, 237–260 (1969). [PubMed]
  21. C. B. Blakemore, J. Nachmias, “The orientation specificity of two visual after-effects,” J. Physiol. 213, 157–174 (1971). [PubMed]
  22. A. S. Gilinsky, “Orientation-specific effects of patterns of adapting light on visual acuity,” J. Opt. Soc. Am. 58, 13–18 (1968). [CrossRef] [PubMed]
  23. L. Olzak, J. P. Thomas, “Gratings: why frequency discrimination is sometimes better than detection,” J. Opt. Soc. Am. 71, 64–70 (1981). [CrossRef] [PubMed]
  24. J. Nachmias, A. Weber, “Discrimination of simple and complex gratings,” Vision Res. 15, 217–223 (1975). [CrossRef] [PubMed]
  25. D. J. Tolhurst, R. S. Dealey, “The detection and identification of lines and edges,” Vision Res. 15, 1367–1372 (1975). [CrossRef] [PubMed]
  26. J. P. Thomas, J. Gille, “Bandwidths of orientation channels in human vision,” J. Opt. Soc. Am. 69, 652–660 (1979). [CrossRef] [PubMed]
  27. J. P. Thomas, J. Gille, R. Barker, “Simultaneous detection and identification: theory and data,” J. Opt. Soc. Am. 72, 1642–1651 (1982). [CrossRef] [PubMed]
  28. B. L. Beard, A. J. Ahumada, “Technique to extract relevant image features for visual tasks,” in Human Vision and Electronic Imaging III, B. E. Rogowitz, T. N. Pappas, eds., Proc. SPIE3299, 79–85 (1998). [CrossRef]
  29. B. L. Beard, A. J. Ahumada, “Detection in fixed and random noise in foveal and parafoveal vision explained by template learning,” J. Opt. Soc. Am. A 16, 755–763 (1999). [CrossRef]
  30. J. A. Solomon, M. J. Morgan, “Reverse correlation reveals psychophysical receptive fields,” Invest. Ophthalmol. Visual Sci. 40, S572 (1999).
  31. H. Fletcher, “Auditory patterns,” Rev. Mod. Phys. 12, 47–65 (1940). [CrossRef]
  32. H. B. Barlow, “Incremental thresholds at low intensities considered as signal/noise discrimination,” J. Physiol. 136, 469–488 (1957). [PubMed]
  33. J. A. Swets, D. M. Green, W. P. Tanner, “On the width of critical bands,” J. Acoust. Soc. Am. 34, 108–113 (1962). [CrossRef]
  34. U. Greis, R. Rohler, “Untersuchung der subjektiven Detailerkennbarkeit mit Hilfe der Ortsfrequenzfilterung,” Opt. Acta 17, 515–526 (1970). [CrossRef]
  35. H. Pollehn, H. Roehrig, “Effect of noise on the MTF of the visual channel,” J. Opt. Soc. Am. 60, 842–848 (1970). [CrossRef] [PubMed]
  36. B. E. Carter, G. B. Henning, “The detection of gratings in narrow-band visual noise,” J. Physiol. 219, 355–365 (1971). [PubMed]
  37. A. P. Ginsburg, “Psychological correlates of a model of the human visual system,” IEEE Trans. Aerosp. Electron. Syst. 71-C-AES, 283–290 (1971).
  38. L. D. Harmon, B. Julesz, “Masking in visual recognition: effects of two-dimensional filtered noise,” Science 180, 1194–1197 (1973). [CrossRef] [PubMed]
  39. A. P. Ginsburg, “Visual information processing based on spatial filters constrained by biological data,” Ph.D dissertation (University of Cambridge, Cambridge, UK, 1978), Library of Congress 79-600156.
  40. A. P. Ginsburg, D. W. Evans, “Predicting visual illusions from filtered images based on biological data,” J. Opt. Soc. Am. 69, 1443 (1979) (abstract).
  41. M. C. Morrone, D. C. Burr, J. Ross, “Added noise restores recognizability of coarse quantized images,” Nature 305, 226–228 (1983). [CrossRef] [PubMed]
  42. G. E. Legge, D. G. Pelli, G. S. Rubin, M. M. Schleske, “Psychophysics of reading: I. Normal vision,” Vision Res. 25, 239–252 (1985). [CrossRef]
  43. M. Pavel, G. Sperling, T. Riedl, A. Vanderbeek, “Limits of visual communication: the effect of signal-to-noise ratio on the intelligibility of American Sign Language,” J. Opt. Soc. Am. A 4, 2355–2365 (1987). [CrossRef] [PubMed]
  44. G. B. Henning, “Spatial-frequency tuning as a function of temporal frequency and stimulus motion,” J. Opt. Soc. Am. A 5, 1362–1373 (1988). [CrossRef] [PubMed]
  45. T. R. Riedl, G. Sperling, “Spatial-frequency bands in complex visual stimuli: American Sign Language,” J. Opt. Soc. Am. A 5, 606–616 (1988). [CrossRef] [PubMed]
  46. D. H. Parish, G. Sperling, “Object spatial frequencies, retinal spatial frequencies, noise, and the efficiency of letter discrimination,” Vision Res. 31, 1399–1415 (1991). [CrossRef] [PubMed]
  47. J. A. Solomon, D. G. Pelli, “The visual channel that mediates letter identification,” Nature 369, 395–397 (1994). [CrossRef] [PubMed]
  48. M. A. Losada, K. T. Muller, “Color and luminance spatial tuning estimated by noise masking in the absence of off-frequency looking,” J. Opt. Soc. Am. A 12, 250–260 (1995). [CrossRef]
  49. J. Nachmias, “Signal detection theory and its application to problems in vision,” in Handbook of Sensory Physiology, D. Jameson, L. M. Hurvich, eds. (Springer–Verlag, Berlin, 1972), Vol. 7/4, Chap. 8.
  50. N. S. Nagaraja, “Effect of luminance noise on contrast thresholds,” J. Opt. Soc. Am. 54, 950–955 (1964). [CrossRef]
  51. D. G. Pelli, “Effects of visual noise,” Ph.D. dissertation (University of Cambridge, Cambridge, UK, 1981).
  52. A. E. Burgess, R. F. Wagner, R. J. Jennings, H. B. Barlow, “Efficiency of human visual signal discrimination,” Science 214, 93–94 (1981). [CrossRef] [PubMed]
  53. A. J. Ahumada, A. B. Watson, “Equivalent-noise model for contrast detection and discrimination,” J. Opt. Soc. Am. A 2, 1133–1139 (1985). [CrossRef] [PubMed]
  54. D. G. Pelli, “Uncertainty explains many aspects of visual contrast detection and discrimination,” J. Opt. Soc. Am. A 2, 1508–1532 (1985). [CrossRef] [PubMed]
  55. A. E. Burgess, B. Colborne, “Visual signal detection: IV. Observer inconsistency,” J. Opt. Soc. Am. A 5, 617–627 (1988). [CrossRef] [PubMed]
  56. M. P. Eckstein, A. J. Ahumada, A. B. Watson, “Visual signal detection in structured backgrounds: II. Effects of contrast gain control, background variations, and white noise,” J. Opt. Soc. Am. A 14, 2406–2419 (1997). [CrossRef]
  57. Z.-L. Lu, B. A. Dosher, “External noise distinguishes mechanisms of attention,” Vision Res. 38, 1183–1198 (1998). [CrossRef] [PubMed]
  58. Z.-L. Lu, B. A. Dosher, “Characterizing human perceptual inefficiencies with equivalent internal noise,” J. Opt. Soc. Am. A 16, 764–778 (1999). [CrossRef]
  59. B. A. Dosher, Z.-L. Lu, “Mechanisms of perceptual learning,” Vision Res. 39, 3197–3221 (1999). [CrossRef]
  60. A. E. Burgess, “Visual signal detection: III. On Bayesian use of prior knowledge and cross correlation,” J. Opt. Soc. Am. A 2, 1498–1507 (1985). [CrossRef] [PubMed]
  61. J. Nachmias, R. V. Sansbury, “Grating contrast: Discrimination may be better than detection,” Vision Res. 14, 1039–1042 (1974). [CrossRef] [PubMed]
  62. J. M. Foley, G. E. Legge, “Contrast detection and near-threshold discrimination in human vision,” Vision Res. 21, 1041–1053 (1981). [CrossRef] [PubMed]
  63. D. J. Heeger, “Normalization of cell responses in cat striate cortex,” Visual Neurosci. 9, 181–197 (1992). [CrossRef]
  64. D. H. Hubel, T. N. Wiesel, “Uniformity of monkey striate cortex: a parallel relationship between field size, scatter, and magnification factor,” J. Comp. Neurol. 158, 295–306 (1974). [CrossRef] [PubMed]
  65. S. P. Mckee, G. Westheimer, “Improvement in vernier acuity with practice,” Percept. Psychophys. 24, 258–262 (1978). [CrossRef] [PubMed]
  66. N. Graham, “Spatial frequency channels in human vision: detecting edges without edge detectors,” in Visual Coding and Adaptability, C. S. Harris, ed. (Erlbaum, Hillsdale, N. J., 1980), pp. 215–262.
  67. 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]
  68. Alternatively, paradigms such as a partial report (Ref. 69) or a concurrent report (Refs. 70and 71) may be used to eliminate structural uncertainty.
  69. G. Sperling, “The information available in brief visual presentations,” Psychol. Monogr. 11, 1–74 (1960). [CrossRef]
  70. G. Sperling, B. Dosher, “Strategy and optimization in human information processing,” in Handbook of Perception and Performance, K. Boff, L. Kaufmon, J. Thomas, eds. (Wiley, New York, 1986), Vol. 1, Chap. 2, pp. 1–65.
  71. B. A. Dosher, Z.-L. Lu, “Noise exclusion in spatial attention,” Psychol. Sci. 11, 139–146 (2000). [CrossRef]
  72. B. A. Dosher, Z.-L. Lu, “Mechanisms of perceptual attention in precuing of location,” Vision Res. 40, 1269–1292 (2000). [CrossRef] [PubMed]
  73. N. A. MacMillan, C. D. Creelman, Detection Theory: A User’s Guide (Cambridge U. Press, New York, 1991).
  74. The assumption holds well for intermediate spatial and temporal frequencies. At low spatial frequencies, low temporal frequencies reduce contrast sensitivity; at high spatial frequencies, high temporal frequencies reduce contrast sensitivity [J. G. Robson, “Spatial and temporal contrast-sensitivity functions of the visual system,” J. Opt. Soc. Am. 56, 1141–1142 (1966);D. H. Kelly, “Flickering patterns and lateral inhibition,” J. Opt. Soc. Am. 59, 1361–1370 (1969).] Henning44 concluded that counterphase flicker at and below 10 Hz has no effect on the shape of spatial-frequency tuning below 4 c/deg, provided that both the masker and the signal have the same temporal characteristics. [CrossRef]
  75. This approximation becomes exact if (i) Ts(fx, fy)=Ts(f ) and Ss(fx, fy)=Ss(f ), that is, the template and the signal are radially symmetric in Fourier space; or (ii) Ts(fx, fy)= kSs(fx, fy),∀fx,fy; that is, the template is perfectly matched to the signal stimulus; or (iii) either the template or the signal stimulus (or both) are uniform for every radius where the template and the signal overlap in Fourier space. In the current application, condition (iii) holds because the stimulus is a pair of points in Fourier space, and condition (ii) is approximately true because humans tend to use nearly optimal templates in simple stimulus situations.60 If one or more of these conditions holds approximately, then the equations should provide reasonable approximations.
  76. This approximation becomes exact if (i) Ts(fx, fy)=Ts(f ) and F(fx, fy)=F(f ); that is, the template and the experimenter-applied filter are radially symmetric in Fourier space; or (ii) Ts(fx, fy)=kF(fx, fy),∀fx,fy; that is, the template is matched to the noise filter; or (iii) either the template or the noise filter (or both) are uniform for every radius where the template and the noise filter overlap in Fourier space. In the current application, F(fx, fy)= F(f )=constant, the expected spectrum of the Gaussian noise is uniform, and condition (iii) is met. In most applications it will be possible to construct filters such that condition (iii) holds.
  77. In the current development, cross products in the form (β2c2+Next2)γare eliminated in order to yield analytical solutions. The effects of the cross terms have been evaluated in two of our previous publications. In one study,59PTMs with full cross-product forms were fit to the data by methods of iterative solution. The results were equivalent in pattern to those from fits of PTMs without cross products, and the cross-product terms were small. In the other study,72the analytical PTMs without cross products were compared with full stochastic PTMs. The analytical form was found to be a good approximation of the stochastic model.
  78. W. L. Hays, Statistics, 3rd ed. (CBS College Publishing, New York, 1981).
  79. R. S. Woodworth, H. Schlosberg, Experimental Psychology, 2nd ed. (Holt, Rinehart & Winston, New York, 1954).
  80. D. G. Pelli, L. Zhang, “Accurate control of contrast on microcomputer displays,” Vision Res. 31, 1337–1350 (1991). [CrossRef] [PubMed]
  81. Z.-L. Lu, G. Sperling, “Second-order reversed phi,” Percept. Psychophys. 61, 1075–1088 (1999). [CrossRef] [PubMed]
  82. For an excellent discussion on fitting psychometric functions, see F. A. Wichmann, N. J. Hill, “The psychometric function I: fitting, sampling and goodness-of-fit,” Percept. Psychophys. accepted for publication.
  83. A resampling method (Refs. 84, 85) was used to compute the standard deviation of each threshold. We assumed that the number of correct responses at each signal contrast level on every psychometric function has a binomial distribution with a single-even probability p, which is the measured percent correct. We then generated a theoretically resampled psychometric function for a given condition by independently replacing the number of correct responses at each signal stimulus contrast on the psychometric function with a sample from the corresponding binomial distribution. Repeating this process 2000 times, we generated 2000 theoretically resampled psychometric functions in every external-noise condition. We estimated the standard deviation for each threshold by fitting Weibull to these theoretically resampled psychometric functions and computing the standard deviation of the 2000 resampled thresholds for each external-noise condition.
  84. L. T. Maloney, “Confidence intervals for the parameters of psychometric functions,” Percept. Psychophys. 47, 127–134 (1990). [CrossRef] [PubMed]
  85. F. A. Wichmann, N. J. Hill, “The psychometric function II: bootstrap based confidence intervals and sampling” Percept. Psychophys. (to be published).
  86. R. D. Patterson, “Auditory filter shapes derived with noise stimuli,” J. Acoust. Soc. Am. 59, 640–654 (1976). [CrossRef] [PubMed]
  87. D. G. Pelli, “Channel properties revealed by noise masking,” Invest. Ophthalmol. Visual Sci. 19, 44A (1980).
  88. M. E. Perkins, M. S. Landy, “Nonadditivity of masking by narrow-band noises,” Vision Res. 31, 1053–1065 (1991). [CrossRef] [PubMed]
  89. Implemented in Matlab 5.3, the procedure for a given model consisted of the following. (1) For a given set of the model parameters, using Eq. (21) to compute log(cτtheory)from the model for each external-noise condition at three different performance levels. (2) Computing the squared difference between the log threshold prediction from the model and the observed sqdiff=[log(cτ theory)-log(cτ)]2for each threshold. The log approximately equates the standard error over large ranges in contrast thresholds, corresponding to weighted least squares, an equivalent to the maximum likelihood solution for continuous data. In the current data set, this assumption is true. (3) Computing L: summation of sqdiff from all the thresholds across all the external-noise conditions. (4) Using a gradient-descent method to adjust the model parameters to find the minimum L. (5) After obtaining the minimum L, computing the r2statistic to evaluate the goodness of the model fit: (25)r2=1.0-∑[log(cτtheory)-log(cτ)]2∑{log(cτ)-mean[log(cτ)]}2,where Σ and mean( )run over all the thresholds for a particular observer. An Ftest for nested models was used to statistically compare the four models. An Fis defined: (26)F(df1, df2)=[(rfull2-rreduced2)/df1]/[(1-rfull2)/df2],where df1=kfull-kreduced,and df2=N-kfull.The kvariables are the number of parameters in each model, and Nis the number of predicted data points.
  90. B. A. Dosher, Z.-L. Lu, “Perceptual templates in spatial attention,” Invest. Ophthalmol. Visual Sci. 41, S750 (2000).
  91. Full sets of maximum-likelihood fits were performed on the psychometric functions for all four models: uPTM, cPTM, uLAM, and cLAM. For an observer who is correct in Kijtrials among a total of Nijtrials in the jthsignal contrast and ithfilter condition, the likelihood of a model that predicts a fraction of Pijcorrect in each condition is defined as (27)likelihood=∏i=1I∏j=1JNij!Kij!(Nij-Kij)! PijKij(1-Pij)Nij-Kij,where Pijis defined by Eq. (22). Asymptotically, χ2(df )statistics could be used to compare the proper set of models:(28)χ2(df )=2.0×loglikelihoodfulllikelihoodreduced,where dfis the difference of the number of parameters between the full and the reduced models.
  92. D. G. Pelli, “Close encounters—an artist shows that size affects shape,” Science 285, 844–846 (1999). [CrossRef] [PubMed]
  93. Z.-L. Lu, B. A. Dosher, “Spatial attention: different mechanisms for central and peripheral temporal precues?” J. Exp. Psychol. 26, 1534–1548 (2000).
  94. B. A. Dosher, Z.-L. Lu, “Perceptual learning reflects external noise filtering and internal noise reduction through channel reweighting,” in Proc. Natl. Acad. Sci. U.S.A. 95, 13 988–13 993.
  95. Y. Yeshurun, M. Carrasco, “Attention improves or impairs visual performance by enhancing spatial resolution,” Nature 396, 72–75 (1998). [CrossRef] [PubMed]
  96. Z.-L. Lu, B. A. Dosher, “Attention fine-tunes perceptual templates in spatial cuing,” Bull. Psychonom. Soc. 40, 52 (1999).

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