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Virtual Journal for Biomedical Optics


  • Editor: Gregory W. Faris
  • Vol. 2, Iss. 9 — Sep. 26, 2007

Contrast polarity and edge integration in achromatic color perception

Michael E. Rudd and Iris K. Zemach  »View Author Affiliations

JOSA A, Vol. 24, Issue 8, pp. 2134-2156 (2007)

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Previous work has shown that the achromatic color of a target patch embedded in simple two-dimensional display depends not only on the luminance contrast between the target and its immediate surround but also on the contrasts of other nearby edges. Quantitative models have been proposed in which the target color is modeled as a spatially weighted sum of edge contrasts in which the target edge receives the largest weight. Rudd and Arrington [Vision Res. 41, 3649 (2001)] elaborated on this idea to include an additional mechanism whereby effects of individual color-inducing edges are “partially blocked” by edges lying along the path between the inducing edge and the target. We tested the blockage model in appearance matching experiments performed with disk-and-single-ring stimuli having all four possible combinations of inner and outer ring edge contrast polarities. Evidence was obtained for both “blockage” (attenuation) and “antiblockage” (amplification) of achromatic color induction signals, depending on the contrast polarities of the inner and outer ring edges. A neural model is proposed to account for our data on the basis of the contrast gain control occurring between cortical edge detector neurons.

© 2007 Optical Society of America

OCIS Codes
(330.1720) Vision, color, and visual optics : Color vision
(330.4060) Vision, color, and visual optics : Vision modeling

ToC Category:
Vision, Color, and Visual Optics

Original Manuscript: January 10, 2007
Manuscript Accepted: February 13, 2007
Published: July 11, 2007

Virtual Issues
Vol. 2, Iss. 9 Virtual Journal for Biomedical Optics

Michael E. Rudd and Iris K. Zemach, "Contrast polarity and edge integration in achromatic color perception," J. Opt. Soc. Am. A 24, 2134-2156 (2007)

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  1. M. E. Rudd and K. F. Arrington, "Darkness filling-in: a neural model of darkness induction," Vision Res. 41, 3649-3662 (2001). [CrossRef] [PubMed]
  2. M. E. Rudd and I. K. Zemach, "Quantitative studies of achromatic color induction: an edge integration analysis," Vision Res. 44, 971-981 (2004). [CrossRef] [PubMed]
  3. M. E. Rudd and I. K. Zemach, "The highest luminance anchoring rule in achromatic color perception: some counterexamples and an alternative theory," J. Vision 5, 983-1003 (2005). [CrossRef]
  4. M. E. Chevreul, The Principles of Harmony and Contrast of Colors and Their Applications to the Arts (Van Nostrand Reinhold, 1839/1967).
  5. J. W. von Goethe, Theory of Colors (Based on the 1840 English translation of Zur Farbenlehre by C. L. Eastlake) (MIT, 1810/1970).
  6. H. von Helmholtz, Helmholtz's Treatise on Physiological Optics (Dover, 1896/1962).
  7. E. Hering, Outlines of a Theory of the Light Sense, trans. L. M. Hurvich and D. Jameson (Harvard U. Press, 1874/1964).
  8. C. Hess and H. Pretori, "Quantitative investigation of the lawfulness of simultaneous brightness contrast," trans. H. Flock and J. H. Tenny, Percept. Mot. Skills 31, 947-969 (1884/1970). [CrossRef]
  9. A. Gelb, "Die "farbenkonstanz" der sehdinge," in Handbuch Normal und Pathologische Psychologie (Springer, 1929). [CrossRef]
  10. D. Katz, The World of Colour (Trench, Trubner & Co., 1935).
  11. H. Wallach, "Brightness constancy and the nature of achromatic colors," J. Exp. Psychol. 38, 310-324 (1948). [CrossRef]
  12. A. Diamond, "Foveal simultaneous brightness contrast as a function of inducing- and test-field luminances," J. Exp. Psychol. 45, 304-314 (1953). [CrossRef]
  13. H. Leibowitz, F. A. Mote, and W. R. Thurlow, "Simultaneous contrast as a function of separation between test and inducing fields," J. Exp. Psychol. 46, 453-456 (1953). [CrossRef] [PubMed]
  14. A. L. Diamond, "Foveal simultaneous brightness contrast as a function of inducing field area," J. Exp. Psychol. 50, 144-152 (1955). [CrossRef] [PubMed]
  15. E. G. Heinemann, "Simultaneous brightness induction as a function of inducing- and test-field luminances," J. Exp. Psychol. 50, 89-96 (1955). [CrossRef] [PubMed]
  16. V. O'Brien, "Contour perception, illusion, and reality," J. Opt. Soc. Am. 48, 112-119 (1958). [CrossRef]
  17. D. Jameson and L. M. Hurvich, "Opponent chromatic induction: experimental evaluation and theoretical account," J. Opt. Soc. Am. 51, 46-53 (1961). [CrossRef] [PubMed]
  18. H. Helson, "Studies of anomalous contrast and assimilation," J. Opt. Soc. Am. 53, 179-184 (1963). [CrossRef] [PubMed]
  19. A. Kozaki, "A further study in the relationship between brightness constancy and contrast," Jpn. Psychol. Res. 5, 129-136 (1963).
  20. J. Krauskopf, "Effect of retinal image stabilization on the appearance of heterochromatic targets," J. Opt. Soc. Am. 53, 741-744 (1963). [CrossRef] [PubMed]
  21. H. Wallach, "The perception of neutral colors," Sci. Am. 208, 107-116 (1963). [CrossRef] [PubMed]
  22. A. Kozaki, "The effect of co-existent stimuli other than test stimulus on brightness constancy," Jpn. Psychol. Res. 7, 138-147 (1965).
  23. F. Ratliff, Mach Bands: Quantitative Studies of Neural Networks in the Retina (Holden-Day, 1965), pp. 74-76.
  24. T. N. Cornsweet, "Stabilized image techniques," in Recent Developments in Vision Research, M.A.Whitcomb, ed. (National Research Council Publication No. 1272, 1966), pp. 171-179.
  25. K. J. W. Craik, The Nature of Psychology: A Selection of Papers, Essays, and Writings, S.L.Sherwood, ed. (Cambridge U. Press, 1966).
  26. H. J. M. Gerrits, B. De Haan, and A. J. H. Vendrik, "Experiments with retinal stabilized images. Relations between observations and neural data," Vision Res. 6, 427-440 (1966). [CrossRef] [PubMed]
  27. J. Krauskopf, "Heterochromatic stabilized images: a classroom demonstration," Am. J. Psychol. 80, 634-637 (1967). [CrossRef] [PubMed]
  28. H. J. M. Gerrits and G. J. M. E. N. Timmermann, "The filling-in process in patients with retinal scotoma," Vision Res. 9, 439-442 (1969). [CrossRef] [PubMed]
  29. P. Whittle and P. D. C. Challands, "The effect of background luminance on the brightness of flashes," Vision Res. 9, 1095-1110 (1969). [CrossRef] [PubMed]
  30. T. N. Cornsweet, Visual Perception (Academic, 1970).
  31. H. J. M. Gerrits and A. J. H. Vendrik, "Simultaneous contrast, filling-in process and information processing in man's visual system," Exp. Brain Res. 11, 411-430 (1970). [CrossRef] [PubMed]
  32. L. E. Arend, J. N. Buehler, and G. R. Lockhead, "Difference information in brightness perception," Percept. Psychophys. 9, 367-370 (1971). [CrossRef]
  33. E. G. Heinemann, "Simultaneous brightness induction," in Handbook of Sensory Physiology, D.Jameson and L.Hurvich, eds. (Springer, 1972), Vol. VII/4, pp. 146-1699.
  34. H. Wallach, On Perception (Quadrangle, 1976).
  35. A. L. Gilchrist, S. Delman, and A. Jacobsen, "The classification and integration of edges as critical to the perception of reflectance and illumination," Percept. Psychophys. 33, 425-436 (1983). [CrossRef] [PubMed]
  36. R. Shapley and R. C. Reid, "Contrast and assimilation in the perception of brightness," Proc. SPIE 82, 5983-5986 (1985).
  37. R. C. Reid and R. Shapley, "Brightness induction by local contrast and the spatial dependence of assimilation," Vision Res. 28, 115-132 (1988). [CrossRef] [PubMed]
  38. R. L. De Valois and K. K. De Valois, Spatial Vision (Oxford U. Press, 1988).
  39. A. Jacobsen and A. Gilchrist, "Hess and Pretori revisited: resolution of some old contradictions," Percept. Psychophys. 43, 7-14 (1988). [CrossRef] [PubMed]
  40. A. L. Gilchrist, "Lightness contrast and failures of contrast: a common explanation," Percept. Psychophys. 43, 415-424 (1988). [CrossRef] [PubMed]
  41. M. A. Paradiso and K. Nakayama, "Brightness perception and filling-in," Vision Res. 31, 1221-1236 (1991). [CrossRef] [PubMed]
  42. S. K. Shevell, I. Holliday, and P. Whittle, "Two separate neural mechanisms of brightness induction," Vision Res. 32, 2331-2340 (1992). [CrossRef] [PubMed]
  43. L. E. Arend and B. Spehar, "Lightness, brightness and brightness contrast: I. Illumination variation," Percept. Psychophys. 54, 446-456 (1993). [CrossRef] [PubMed]
  44. L. E. Arend and B. Spehar, "Lightness, brightness and brightness contrast: II. Reflectance variation," Percept. Psychophys. 54, 457-468 (1993). [CrossRef] [PubMed]
  45. N. Bruno, "Failures of lightness constancy, edge integration, and local edge enhancement," Vision Res. 34, 2205-2214 (1994). [CrossRef] [PubMed]
  46. P. Whittle, "Contrast brightness and ordinary seeing," in Lightness, Brightness, and Transparency, A.L.Gilchrist, ed. (Erlbaum, 1994), pp. 111-157.
  47. T. Agostini and N. Bruno, "Lightness contrast in CRT and paper-and-illuminant displays," Percept. Psychophys. 58, 250-258 (1996). [CrossRef] [PubMed]
  48. M. A. Paradiso and S. Hahn, "Filling-in percepts produced by luminance modulation," Vision Res. 36, 2657-2663 (1996). [CrossRef] [PubMed]
  49. A. F. Rossi and M. A. Paradiso, "Temporal limits of brightness induction and mechanisms of brightness perception," Vision Res. 36, 1391-1398 (1996). [CrossRef] [PubMed]
  50. M. P. Davey, T. Maddess, and M. V. Srinivasan, "The spatiotemporal properties of the Craik-O'Brien-Cornsweet effect are consistent with 'filling-in'," Vision Res. 22, 545-559. [CrossRef]
  51. J. Schirillo and S. Shevell, "Brightness contrast from inhomogeneous surrounds," Vision Res. 36, 1783-1796 (1996). [CrossRef] [PubMed]
  52. B. Blakeslee and M. E. McCourt, "Similar mechanisms underlie simultaneous brightness contrast and grating induction," Vision Res. 37, 2849-2869 (1997). [CrossRef]
  53. P. Bressan, E. Mingolla, L. Spillmann, and T. Watanabe, "Neon color spreading: a review," Prog. Aerosp. Sci. 26, 1353-1366 (1997).
  54. R. O. Brown and D. I. MacLeod, "Color appearance depends on the variance of surround colors," Curr. Biol. 7, 844-849 (1997). [CrossRef]
  55. N. Bruno, P. Bernardis, and J. Schirillo, "Lightness, equivalent backgrounds, and anchoring," Percept. Psychophys. 59, 643-654 (1997). [CrossRef] [PubMed]
  56. A. Gilchrist, C. Kossyfidis, F. Bonato, T. Agostini, J. Cataliotti, X. Li, B. Spehar, V. Annan, and E. Economou, "An anchoring theory of lightness perception," Psychol. Rev. 106, 795-834 (1999). [CrossRef] [PubMed]
  57. J. A. Schirillo, "Surround articulation. I. Brightness judgments," J. Opt. Soc. Am. 16, 793-803 (1999). [CrossRef]
  58. J. A. Schirillo, "Surround articulation. II. Lightness judgments," J. Opt. Soc. Am. 16, 804-811 (1999). [CrossRef]
  59. W. D. Ross and L. Pessoa, "Lightness from contrast: a selective integration model," Percept. Psychophys. 62, 1160-1181 (2000). [CrossRef] [PubMed]
  60. P. Bressan and R. Actis-Grosso, "Simultaneous lightness contrast with double-increments," Perception 30, 889-897 (2001). [CrossRef] [PubMed]
  61. M. E. Rudd, "Lightness computation by a neural filling-in mechanism," Proc. SPIE 4299, 400-413 (2001). [CrossRef]
  62. I. K. Zemach and M. E. Rudd, "Blocking of achromatic color induction signals by borders of different contrast polarities" [Abstract], J. Vision 2, 106a, (2002). [CrossRef]
  63. B. Pinna, "The watercolor effect: a new principle of grouping and figure-ground organization," Vision Res. 43, 43-52 (2003). [CrossRef]
  64. M. E. Rudd, "Progress on a computational model of human achromatic color processing," Proc. SPIE 5007, 170-181 (2003). [CrossRef]
  65. I. K. Zemach and M. E. Rudd, "Spatial decay of achromatic color induction differs for lightness and darkness induction processes" [Abstract], J. Vision 3, 421a, (2003). [CrossRef]
  66. D. Bindman and C. Chubb, "Brightness assimilation in bullseye displays," Vision Res. 44, 309-319 (2004). [CrossRef]
  67. D. Bindman and C. Chubb, "Mechanisms of contrast induction in heterogeneous displays," Vision Res. 44, 1601-1613 (2004). [CrossRef] [PubMed]
  68. S. W. Hong and S. K. Shevell, "Brightness induction: unequal spatial integration with increments and decrements," Visual Neurosci. 21, 353-357 (2004). [CrossRef]
  69. S. W. Hong and S. K. Shevell, "Brightness contrast and assimilation from patterned inducing backgrounds," Vision Res. 44, 35-43 (2004). [CrossRef]
  70. M. E. Rudd and D. Popa, "A theory of the neural processes underlying edge integration in human lightness perception" [Abstract], J. Vision 4, 345a, (2004). [CrossRef]
  71. M. E. Rudd and D. Popa, "Edge integration and edge interaction in achromatic color computation" [Abstract], J. Vision 4, 79a, (2004). [CrossRef]
  72. A. G. Shapiro, A. D. D'Antona, J. P. Charles, L. A. Belano, J. B. Smith, and M. Shear-Heyman, "Induced contrast asynchronies," J. Vision 4, 459-468, (2004). [CrossRef]
  73. F. Devinck, P. B. Delahunt, J. L. Hardy, L. Spillmann, and J. S. Werner, "The watercolor effect: quantitative evidence for luminance-dependent mechanisms of long-range color assimilation," Vision Res. 45, 1413-1424 (2005). [CrossRef] [PubMed]
  74. M. E. McCourt, B. Blakeslee, and W. Pasieka, "Temporal properties of brightness induction" [Abstract], J. Vision 5, 242a, (2005). [CrossRef]
  75. S. S. Shimozaki, M. P. Eckstein, and C. K. Abbey, "Spatial profiles of local and nonlocal effects upon contrast detection/discrimination from classification images," J. Vision 5, 45-57, (2005). [CrossRef]
  76. T. Vladusich, M. P. Lucassen, and F. W. Cornelissen, "Edge integration and the perception of brightness and darkness," J. Vision 6, (2006). [CrossRef]
  77. M. E. Rudd and D. Popa, "Steven's brightness law, contrast gain control, and edge integration in achromatic color perception: a unified model," J. Opt. Soc. Am. A (to be published).
  78. I. K. Zemach and M. E. Rudd, "Effects of surround articulation on lightness depend on the spatial arrangement of the articulated region,"J. Opt. Soc. Am. A 24, 1830-1841 (2007).
  79. M. E. Rudd is preparing a paper to be called "Edge integration and anchoring in the perception of lightness, brightness, and brightness contrast."
  80. G. Walls, "The filling-in process," Am. J. Optom. Arch. Am. Acad. Optom. 31, 329-340 (1954).
  81. E. H. Land and J. J. McCann, "Lightness and retinex theory," J. Opt. Soc. Am. 61, 1-11 (1971). [CrossRef]
  82. E. H. Land, "The retinex theory of color vision," Sci. Am. 237, 2-17 (1977). [CrossRef]
  83. E. H. Land, "Recent advances in retinex theory and some implications for cortical computations: color vision and the natural image," Proc. Natl. Acad. Sci. U.S.A. 80, 5163-5169 (1983). [CrossRef]
  84. M. A. Cohen and S. Grossberg, "Neural dynamics of brightness perception: features, boundaries, diffusion, and resonance," Percept. Psychophys. 36, 328-456 (1984). [CrossRef]
  85. S. Grossberg and E. Mingolla, "Neural dynamics of form perception: boundary completion, illusory figures, and neon color spreading," Psychol. Rev. 92, 173-211 (1985). [CrossRef] [PubMed]
  86. S. Grossberg and E. Mingolla, "Neural dynamics of surface perception: boundary webs, illuminants, and shape-from-shading," Comput. Vis. Graph. Image Process. 37, 116-165 (1987). [CrossRef]
  87. S. Grossberg and D. Todorovic, "A neural network architecture for preattentive vision," IEEE Trans. Biomed. Eng. 36, 65-84 (1988). [CrossRef]
  88. K. F. Arrington, "The temporal dynamics of brightness filling-in," Vision Res. 34, 3371-3387 (1994). [CrossRef] [PubMed]
  89. H. Neumann, L. Pessoa, and T. Hansen, "Visual filling-in for computing visual surface properties," Biol. Cybern. 85, 355-369 (2001). [CrossRef] [PubMed]
  90. A. F. Rossi, C. D. Rittenhouse, and M. A. Paradiso, "The representation of brightness in primary visual cortex," Science 273, 1104-1107 (1996). [CrossRef] [PubMed]
  91. S. P. MacEvoy, W. Kim, and M. A. Paradiso, "Integration of surface information in primary visual cortex," Nat. Neurosci. 1, 616-620 (1998). [CrossRef]
  92. A. F. Rossi and M. A. Paradiso, "Neural correlates of perceived brightness in the retina, lateral geniculate nucleus, and striate cortex," J. Neurosci. 19, 6145-6156 (1999). [PubMed]
  93. C. P. Hung, B. M. Ramsden, L. M. Chen, and A. W. Roe, "Building surfaces from borders in Areas 17 and 18 of the cat," Vision Res. 41, 1389-1407 (2001). [CrossRef] [PubMed]
  94. M. Kinoshita and H. Komatsu, "Neural representation of the luminance and brightness of a uniform surface in the macaque primary visual cortex," J. Neurophysiol. 86, 2559-2570 (2001). [PubMed]
  95. R. von der Heydt, H. S. Friedman, and H. Zhou, "Searching for the neural mechanisms of color filling-in," in Filling-In: From Perceptual Completion to Skill Learning, L.Pessoa and P.De Weerd, eds. (Oxford U. Press, 2003), pp. 106-127.
  96. J. D. Haynes, R. B. Lotto, and G. Rees, "Responses of human visual cortex to uniform surfaces," Proc. Natl. Acad. Sci. U.S.A. 101, 4286-4291 (2004). [CrossRef] [PubMed]
  97. Y. Sasaki and T. Watanabe, "The primary visual cortex fills in color," Proc. Natl. Acad. Sci. U.S.A. 101, 18251-18256 (2004). [CrossRef] [PubMed]
  98. F. W. Cornelissen, A. R. Wade, T. Vladusich, R. F. Dougherty, and B. A. Wandell, "No function magnetic resonance imaging evidence for brightness and color filling-in in early human visual cortex," J. Neurosci. 26, 3634-3641 (2006). [CrossRef] [PubMed]
  99. D. H. Brainard, "The psychophysics toolbox," Spatial Vis. 10, 433-436 (1997). [CrossRef]
  100. D. G. Pelli, "The VideoToolbox software for visual psychophysics: transforming numbers into movies," Spatial Vis. 10, 437-442 (1997). [CrossRef]
  101. J. Neter, M. H. Kutner, C. J. Nachtshein, and W. Wasserman, "One case per treatment designs," in Applied Linear Statistical Models (WCB/McGraw-Hill, Boston, 1996), Chap. 21.
  102. L. Arend, "Surface colors, illumination, and surface geometry: intrinsic-image models of human color perception," in Lightness, Brightness, and Transparency, A.L.Gilchrist, ed. (Erlbaum, 1994), pp. 111-157.
  103. R. L. De Valois, D. G. Albrecht, and L. G. Thorell, "Spatial frequency selectivity of cells in macaque visual cortex," Vision Res. 22, 545-559 (1982). [CrossRef] [PubMed]
  104. H. R. Wilson and D. J. Gelb, "Modified line-element theory for spatial-frequency and width discrimination," J. Opt. Soc. Am. A 1, 124-131 (1984). [CrossRef] [PubMed]
  105. H. R. Wilson and D. Regan, "Spatial frequency adaptation and grating discrimination: predictions of a line-element model," J. Opt. Soc. Am. A 1, 1091-1096 (1984). [CrossRef] [PubMed]
  106. J. G. Daugman, "Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters," J. Opt. Soc. Am. A 1, 1160-1169 (1985). [CrossRef]
  107. D. L. Ringach, "Spatial structure and symmetry of simple-cell receptive fields in macaque primary visual cortex," J. Neurophysiol. 88, 455-63 (2002). [PubMed]
  108. L. Maffei and A. Fiorentini, "The unresponsive regions of visual cortical receptive fields," Vision Res. 16, 1131-1139 (1976). [CrossRef] [PubMed]
  109. J. J. Knierim and D. D. Van Essen, "Neuronal responses to static texture patterns in area V1 of alert macaque monkey," J. Neurophysiol. 67, 961-970 (1992). [PubMed]
  110. G. C. De Angelis, R. D. Freeman, and I. Ohzawa, "Length and width tuning of neurons in the cat's primary visual cortex," J. Neurophysiol. 71, 347-374 (1994).
  111. C. Li and W. Li, "Extensive integration field beyond the classical receptive field of cat's striate cortical neurons--classification and tuning properties," Vision Res. 387, 73-86 (1994).
  112. A. M. Sillito, K. L. Grieve, H. E. Jones, J. Cudeiro, and J. Davis, "Visual cortical mechanisms detecting focal orientation discontinuities," Nature 378, 492-496 (1995). [CrossRef] [PubMed]
  113. J. B. Levitt and J. S. Lund, "Context dependence of contextual effects in visual cortex," Nature 387, 73-76 (1997). [CrossRef] [PubMed]
  114. F. Sengpiel, A. Sen, and C. Blakemore, "Characteristics of surround inhibition in cat area 17," Exp. Brain Res. 116, 216-238 (1997). [CrossRef] [PubMed]
  115. H. Nothdurft, J. L. Gallant, and D. Van Essen, "Response modulation by texture surround in primate area V1: correlates of "pop-out" under anesthesia," Visual Neurosci. 16, 15-34 (1999). [CrossRef]
  116. G. A. Walker, I. Ohzawa, and R. D. Freeman, "Asymmetric suppression outside the classical receptive field of the visual cortex," J. Neurosci. 19, 10536-10553 (1999). [PubMed]
  117. H. E. Jones, I. M. Andolina, N. M. Oakely, P. C. Murphy, and A. M. Sillito, "Spatial summation in lateral geniculate nucleus and visual cortex," Exp. Brain Res. 135, 279-284 (2000). [CrossRef] [PubMed]
  118. G. A. Walker, I. Ohzawa, and R. D. Freeman, "Suppression outside the classical receptive field," Visual Neurosci. 17, 369-379 (2000). [CrossRef]
  119. R. D. Freeman, I. Ohzawa, and G. Walker, "Beyond the classical receptive field in the visual cortex," Prog. Brain Res. 134, 157-170 (2001). [CrossRef] [PubMed]
  120. H. E. Jones, K. L. Grieve, W. Wang, and A. M. Sillito, "Surround suppression in primate V1," J. Neurophysiol. 86, 2011-2028 (2001). [PubMed]
  121. P. Series, J. Lorenceau, and Y. Fregnac, "The "silent" surround of V1 receptive fields: theory and experiment," J. Physiol. (Paris) 97, 453-474 (2003). [CrossRef]

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