Psychophysical research on the Hermann grid illusion is reviewed and possible neurophysiological mechanisms are discussed. The illusion is most plausibly explained by lateral inhibition within the concentric receptive fields of retinal and/or geniculate ganglion cells, with contributions by the binocular orientation-specific cortical cells. Results may be summarized as follows: (a) For a strong Hermann grid illusion to be seen bar width must be matched to the mean size of receptive-field centers at any given retinal eccentricity. (b) With the use of this rationale, the diameter of foveal perceptive-field centers (the psychophysical correlate of receptive-field centers) has been found to be in the order of 4–5 min arc and that of total fields (centers plus surrounds) 18 min arc. These small diameters explain why the illusion tends to be absent in foveal vision. (c) With increasing distance from the fovea, perceptive-field centers increase to 1.7 deg at 15 deg eccentricity and then to 3.4 deg at 60 deg eccentricity. This doubling in diameter agrees with the change in size of retinal receptive-field centers in the monkey. (d) The Hermann grid illusion is diminished with dark adaptation. This finding is consistent with the reduction of the center—surround antagonism in retinal receptive fields. (e) The illusion is also weakened when the grid is presented diagonally, which suggests a contribution by the orientation-sensitive cells in the lateral geniculate nucleus and visual cortex. (f) Strong induction effects, similar to the bright and dark spots in the Hermann grid illusion, may be elicited by grids made of various shades of grey; and by grids varying only in chroma or hue.
Not accounted for are: the illusory spots occurring in an outline grid ie with hollow squares, and the absence of an illusion when extra bars are added to the grid. Alternative explanations are discussed for the spurious lines connecting the illusory spots along the diagonals and the fuzzy dark bands traversing the rhombi in modified Hermann grids.
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References
1.
AnstisS, 1993“Flickering test field enhances simultaneous brightness induction”Investigative Ophthalmology and Visual Science34706 (Abstract 17)
2.
AppelleS, 1972“Perception and discrimination as a function of stimulus orientation: The ‘oblique effect’ in man and animals”Psychological Bulletin18266–278
3.
BarlowH B, 1972“Single units and sensation: A neuron doctrine for perceptual psychology”Perception1371–394
4.
BarlowH B, 1985“The role of single neurons in the psychology of perception”Quarterly Journal of Experimental Psychology37121–146
5.
BarlowH BFitzhughRKufflerS W, 1957“Change of organization of the receptive fields of the cat's retina during dark adaptation”Journal of Physiology (London)137338–354
6.
BaumgartnerG, 1960“Indirekte Größenbestimmung der rezeptiven Felder der Retina beim Menschen mittels der Hermannschen Gittertäuschung”Pflügers Archiv für die gesamte Physiologic27221–22 (Abstract)
7.
BaumgartnerG, 1961“Die Reaktionen der Neurone des zentralen visuellen Systems der Katze im simultanen Helligkeitskontrast”, in Neurophysiologie und Psychophysik des visuellen Systems Eds JungRKornhuberH H (Berlin: Springer) pp 296–313
8.
BaumgartnerG, 1964“Neuronale Mechanismen des Kontrast- und Bewegungssehens”Berichte der Deutschen Ophthalmologischen Gesellschaft66111–125
9.
BaumgartnerG, 1988“Physiological constraints on the visual aesthetic response”, in Beauty and the Brain, Biological Aspects of Aesthetics Eds RentschlerIHerzbergerBEpsteinD (Basel: Birkhäuser) pp 165–180
10.
BaumgartnerG, 1990“Where do visual signals become a perception?”, in The Principles of Design and Operation of the Brain Eds EcclesJCreutzfeldtO (Pontificiae Academiae Scientiarum Scripta Varia, 78) pp 99–114
11.
BerbaumKChungC S, 1981“Perceptive field sizes and a new version of the Hermann grid”Perception1085–89
12.
BergenJ R, 1985“Hermann's grid: New and improved”Investigative Ophthalmology and Visual Science Supplement26280 (Abstract)
13.
BodeA, 1972“Gestaltung des Ausstellungsraumes (Fenster/Lichtquelle) zur Documenta 4”, in Documenta-Dokumente 1955–1968, Eds WesteckerWEberthCLengemannWMüllerE (Kassel: Wenderoth) p. 213
14.
BoulterJ F, 1977“Optical transforms and the ‘pincushion grid’ illusion?” (Reply to Schachar)”Science198960–961
15.
BrewsterDSir, 1844“A notice explaining the cause of an optical phenomenon observed by the Rev. W. Selwyn”Report of the Fourteenth Meeting of the British Association for the Advancement of Science (London: John Murray) p. 8
16.
BrookesAStevensK A, 1989“The analogy between stereo depth and brightness”Perception18601–614
17.
CampbellF WMaffeiL, 1970“Electrophysiological evidence for the existence of orientation and size detectors in the human visual system”Journal of Physiology (London)207635–652
18.
CorenSPoracCAksD JMorikawaK, 1988“A method to assess the relative contribution of lateral inhibition to the magnitude of visual-geometric illusions”Perception & Psychophysics43551–558
19.
DeMonasterioF MGourasP, 1975“Functional properties of ganglion cells of the rhesus monkey retina”Journal of Physiology (London)251167–195
20.
DombrowskyH, 1942Experimentelle Untersuchungen über das Hering—Ehrensteinsche Helligkeitsphänomen Philosophische Fakultät, Inaugural-Dissertation, Karls-Universität, Prague
21.
EhrensteinW, 1941“Über Abwandlungen der L. Hermannschen Helligkeitserscheinung”Zeitschrift für Psychologie15083–91 [“Modifications of the brightness phenomenon of L Hermann”; translation by HoggA, 1987, in The Perception of Illusory Contours Eds PetrySMeyerG E (1987, New York: Springer) pp 35–39]
22.
EhrensteinW, 1954Probleme der ganzheitspsychologischen Wahrnehmungslehrethird edition (Leipzig: Barth)
23.
EnochJ MBergerRBirnsR, 1970“A static perimetric technique believed to test receptive field properties. Extension and verification of the analysis”Documenta Ophthalmologica29154–167
24.
FoleyJ MMcCourtM E, 1985“Visual grating induction”Journal of the Optical Society of America A21220–1230
25.
FrisbyJ P, 1979Seeing: Illusion, Brain and Mind (London: Oxford University Press)
26.
GinsburgA P, 1984“Visual form perception based on biological filtering”, in Sensory Experience, Adaptation and Perception. Festschrift for Ivo Kohler Eds SpillmannLWootenR B (Hillsdale, NJ: Lawrence Erlbaum) pp 53–72
27.
GinsburgA PCampbellF W, 1977“Optical transforms and the ‘pincushion grid’ illusion? (Reply to Schachar)”Science198961–962
28.
GourasP, 1974“Opponent colour cells in different layers of foveal striate cortex”Journal of Physiology (London)238583–602
29.
GrossbergSMingollaE, 1985“Neural dynamics of form perception: Boundary completion, illusory figures, and neon color spreading”Psychological Review92173–211
30.
GrossbergSTodorovicD, 1988“Neural dynamics of 1-D and 2-D brightness perception: A unified model of classical and recent phenomena”Perception & Psychophysics43241–277
31.
HammondP, 1973“Contrast in spatial field organization of receptive fields at geniculate and retinal levels: Centre, surround and outer surround”Journal of Physiology (London)228115–137
32.
HeringE, 1878Zur Lehre vom Lichtsinne (Wien: Gerold)
33.
HeringE, 1907“Vom simultanen Grenzkontrast”, in Graefe-Saemisch Handbuch der gesamten Augenheilkundesecond edition, volume 3, Ed. SaemischT h (Leipzig: Engelmann) pp 135–139
34.
HeringE, 1920“Vom simultanen Grenzkontrast”, in Grundzüge der Lehre vom Lichtsinne chapter 32 (Berlin: Springer) [Outlines of the Theory of the Light Sense; translation by HurvichL MJamesonD (1964, Cambridge, MA: Harvard University Press)
35.
HermannL, 1870“Eine Erscheinung des simultanen Contrastes”Pflügers Archiv für die gesamte Physiologie313–15
36.
HoodDPetryS, “Is THE GRID really Hering's?”, unpublished manuscript (obtainable from first author)
37.
HoremisS, 1970Optical and Geometrical Patterns and Designs (New York: Dover)
38.
HubelD HWieselT N, 1960“Receptive fields of optic nerve fibres in the spider monkey”Journal of Physiology (London)154572–580
39.
HubelD HWieselT N, 1962“Receptive fields, binocular interaction and functional architecture in the cat's visual cortex”Journal of Physiology (London)160106–154
40.
HubelD HWieselT N, 1968“Receptive fields and functional architecture of monkey striate cortex”Journal of Physiology (London)195215–243
41.
JuleszB, 1965“Some neurophysiological problems of stereopsis”, in Proceedings of Symposium on Information Processing in Sight Sensory Systems Ed. NyeP W (Pasadena, CA: California Institute of Technology) pp 135–142
42.
JuleszB, 1971Foundations of Cyclopean Perception (Chicago, IL: University of Chicago Press)
43.
JungR, 1973“Visual perception and neurophysiology”, in Handbook of Sensory Physiology Volume VII/3 A Central Visual Information Ed. JungR (Berlin: Springer) pp 1–152
44.
JungRSpillmannL, 1970“Receptive-field estimation and perceptual integration in human vision”, in Early Experience and Visual Information Processing in Perceptual and Reading Disorders Eds YoungF ALindsleyD B (Washington, DC: National Academy of Sciences) pp 181–197
45.
KingdomF A AMcCourtM E, 1993“Do illusory gratings behave like real ones?”Perception22 (Supplement) 5 (Abstract) pp –
46.
KingdomFMouldenB, 1992“A multi-channel approach to brightness coding”Vision Research321565–1582
47.
KitterleF LCorwinT R, 1979“Enhancement of apparent contrast in flashed sinusoidal gratings”Vision Research1933–39
48.
KoenderinkJ, 1977“Current models of contrast processing”, in Spatial Contrast Eds SpekreijseHvan der TweelL H (Amsterdam: North-Holland) pp 116–119
49.
KornhuberH HSpillmannL, 1964“Zur visuellen Feldorganisation beim Menschen: Die receptiven Felder im peripheren und zentralen Gesichtsfeld bei Simultankontrast, Flimmerfusion, Scheinbewegung und Blickfolgebewegung”Pflügers Archiv für die gesamte Physiologie279R5–6 (Abstract)
50.
KufflerS W, 1953“Discharge patterns and functional organization of mammalian retina”Journal of Neurophysiology1637–68
51.
LamingD, 1992“Springer's lines and Hermann's grid”Ophthalmic and Physiological Optics12178–186
52.
LavinECostallA, 1978“Detection thresholds of the Hermann grid illusion”Vision Research181061–1062
53.
LevineJSpillmannLWolfE, 1980“Saturation enhancement in colored Hermann grids varying only in chroma”Vision Research20307–313
54.
LindsayP ANormanD A, 1977Human Information Processing (New York: Academic Press)
55.
LingelbachBBockBHatzkyBReisingerE, 1985“The Hermann grid illusion—retinal or cortical?”Perception14(1) A7 (Abstract)
56.
McCarterA, 1979“Chromatic induction effects in the Hermann grid illusion”Perception8105–114
57.
McCourtM E, 1982“A spatial frequency dependent grating induction effect”Vision Research22119–134
58.
McCourtM E, 1990“The disappearance of grating induction at scotopic illuminances”Vision Research30431–438
59.
McCourtM EBlakesleeB, 1994“Contrast matching analysis of grating induction and suprathreshold contrast perception”Journal of the Optical Society of America A1114–24
60.
MachE, 1865“Über die Wirkung der räumlichen Verteilung des Lichtreizes auf der Netzhaut”Sitzungsberichte der Wiener Akademie der Wissenschaften, Mathematisch-Naturwissenschaftliche Classe, Zweite Abteilung52303–322
61.
McLeodR D, 1978“Colored pin cushion grids, complements and color vision”Journal of the Optical Society of America681400 (Abstract WL8)
62.
MaffeiLFiorentiniA, 1972“Retinogeniculate convergence and analysis of contrast”Journal of Neurophysiology3565–72
63.
MarrD, 1982Vision: A Computational Investigation into the Human Representation and Processing of Visual Information (San Francisco, CA: W H Freeman)
64.
MassironiMSambinM, 1984“Ondulazione fenomenica: Un altro effetto del completamento amodale”, in Fenomenologia Sperimentale della Visione (Milano: F Angeli) pp 204–220
65.
MeurGPayanMVolaJ, 1968“Détermination indirecte de la dimension des champs réceptifs rétiniens de l'amblyope au moyen des grilles de Hermann (note préliminaire)”Bulletin de la Société Ophthalmologique Belge150615–622
66.
MonjéJ, 1955“Über die Lichtempfindlichkeit im Bereich des Rand- und Binnenkontrasts”Pflügers Archiv für die gesamte Physiologie26292–106
67.
MorganM JHotopfW H N, 1989“Perceived diagonals in grids and lattices”Vision Research291005–1015
68.
MotokawaK, 1950“Field of retinal induction and optical illusion”Journal of Neurophysiology18413–426
69.
MotokawaK, 1970Physiology of Color and Pattern Vision (Berlin: Springer)
70.
OchsA L, 1979“Is Fourier analysis performed by the visual system or by the visual investigator?”Journal of the Optical Society of America6995–98
71.
OehlerR, 1985“Spatial interactions in the rhesus monkey retina: A behavioural study using the Westheimer paradigm”Experimental Brain Research59217–225
72.
OehlerRSpillmannL, 1981“Illusory colour changes in Hermann grids varying only in hue”Vision Research21527–541
73.
PayneW HAndersonD E, 1969“Border-visibility investigation of the Hermann grid”Journal of the Optical Society of America59229–231
74.
PrandtlA, 1927“Über gleichsinnige Induktion und die Lichtverteilung in gitterartigen Mustern”Zeitschrift für Sinnesphysiologie58263–307
75.
PreyerW, 1897/98“On certain optical phenomena. Letter to Professor E C Sanford”American Journal of Psychology942–44
76.
PsotkaJ, 1977“A spatial frequency model of perceptual stick figures”, in Advances in the Psychophysical and Visual Aspects of Image Evaluation Ed DooleyR P (Washington, DC: Society of Photographic Scientists and Engineers) pp 30–33
77.
Ransom-HoggASpillmannL, 1980“Perceptive field size in fovea and periphery of the light- and dark-adapted retina”Vision Research20221–228
78.
RobsonJ G, 1966“Spatial and temporal contrast sensitivity functions of the visual system”Journal of the Optical Society of America561141–1142
79.
RonchiLBottaiG, 1964“Simultaneous contrast effects at the center of figures showing different degrees of symmetry”Atti della Fondazione Giorgio Ronchi1984–100
80.
RonchiLSalviG, 1965“The neural organization of the central retina as revealed by an experiment on simultaneous contrast”Atti della Fondazione Giorgio Ronchi20192–199
81.
RudeeM L, 1977“Optical transforms and the ‘pincushion grid’ illusion? (Reply to Schachar)”Science198960
82.
SambinM, 1979“Transphenomenal basis in the ‘Moire’ effect explanation”Italian Journal of Psychology6185–201
83.
SavardiUSavioloN, 1982“Effetto dell'adattamento a un campo bianco o nero sull'illusione della griglia di Hermann”Università di Padova, Istituto di Psicologia, Report 68
84.
SchacharR A, 1976“The ‘Pincushion grid’ illusion”Science192389–390
85.
SchacharR ABlackT DHartfieldK LGoldbergI S, 1977“Reply to Rudee, Boulter, Ginsburg and Campbell”Science198962
86.
SchepelmannFAschayeriHBaumgartnerG, 1967“Die Reaktionen der ‘simple field’-Neurone in Area 17 der Katze beim Hermann-Gitter-Kontrast”Pflügers Archiv für die gesamte Physiologie294R57 (Abstract)
87.
SchillerP H, 1992“The ON and OFF channels of the visual system”Trends in Neuroscience1586–92
88.
SegalJ, 1957Mechanismen des Farbensehens (Jena: VEB G Fischer)
89.
SindermannFDeeckeL, 1970“Subjektive Intensität des Hermann-Gitter-Phänomens in der Netzhautperipherie. Beziehungen zur rezeptiven Feldorganisation”Pflügers Archiv für die gesamte Physiologie316R95 (Abstract)
90.
SindermannFPieperE, 1965“Größenschätzung von fovealen Projektionen rezeptiver Kontrastfelder (Zentrum und Umfeld) beim Menschen im psychophysischen Versuch”Pflügers Archiv für die gesamte Physiologie283R47–48 (Abstract)
91.
SpillmannL, 1964Zur Feldorganisation der visuellen Wahrnehmung beim Menschen. Vergleichende psychophysische Untersuchung der Größe rezeptiver Felder im zentralen und peripheren Gesichtsfeld mit Simultankontrast, Flimmerfusion, Scheinbewegung und Blickfolgebewegung PhD Dissertation, Münster, Westfalen
92.
SpillmannL, 1971“Foveal perceptive fields in the human visual system measured with simultaneous contrast in grids and bars”Pflügers Archiv für die gesamte Physiologie326281–299
93.
SpillmannL, 1977“Contrast and brightness in illusions”, in Spatial Contrast Eds SpekreijseHvan der TweelL H (Amsterdam: North-Holland) pp 45–49
94.
SpillmannLFuldKNeumeyerC, 1984“Brightness matching, brightness cancellation, and increment threshold in the Ehrenstein illusion”Perception13513–520
95.
SpillmannLLevineJ, 1971“Contrast enhancement in a Hermann grid with variable figure—ground ratio”Experimental Brain Research13547–559
96.
SpillmannLRansom-HoggAOehlerR, 1987“A comparison of perceptive and receptive fields in man and monkey”Human Neurobiology651–62
97.
TellerD Y, 1980“Locus questions in visual science”, in Visual Coding and Adaptability Eds HarrisC S (Hillsdale, NJ: Lawrence Erlbaum) pp 151–176
98.
TrosciankoT, 1982a“A stereoscopic presentation of the Hermann grid”Vision Research22485–489
99.
TrosciankoT, 1982b“A given visual field location has a wide range of perceptive field sizes”Vision Research221363–1369
100.
TrosciankoT, 1983“Local and global processes in the Hermann grid illusion”Perception12(1) A23 (Abstract)
101.
TschermakA, 1929“Indirekte Reizwirkungen am Sehorgan”, in Handbuch der normalen und pathologischen Physiologievolume XII/2, Eds BetheAvon BergmannGEmbdenGEllingerA (Berlin: Springer) pp 478–500
102.
TyndallJ, 1867Sound. A Course of Eight Lectures Delivered at the Royal Institution of Great Britain (London: Longmans and Green) p. 143
103.
TyndallJ, 1869Der Schall. Acht Vorlesungen gehalten in der Royal Institution von Groß-Britannien (Braunschweig: Vieweg)
104.
UttalW R, 1973The Psychobiology of Sensory Coding (New York: Harper and Row) pp 452–453
105.
UttalW R, 1978The Psychobiology of Mind (Hillsdale, NJ: Lawrence Erlbaum) pp 225–229
106.
UttalW R, 1981A Taxonomy of Visual Processes (Hillsdale, NJ: Lawrence Erlbaum) pp 244–259
107.
UttalW RMathesonG, 1971“Some simple demonstrations of differences in the basic mechanisms of contour enhancement and simultaneous contrast”Bulletin of the Psychonomic Society (St Louis Meeting)
108.
VasarelyV, 1965Vasarely (Neuchâtel: Éditions du Griffon) volume 1 [German edition, translation by SchürmannH G (1969–1979, Ed. JorayM]
109.
VasarelyV, 1974a“Supernovae 1959–61”, in Op Art Ed. BarrettC (Köln: DuMont Schauberg) p. 25
110.
VasarelyV, 1974b“Eridan III”, in Op Art Ed. BarrettC (Köln: DuMont Schauberg) p. 31
111.
VerheyenF J, 1961“A simple after-image method demonstrating the involuntary multidirectional eye movements during fixation”Optical Acta8309–311
112.
VidyasagarT RUrbasG Z, 1982“Orientation sensitivity of cat LGN neurons with and without inputs from visual cortex areas 17 and 18”Experimental Brain Research46157–169
113.
von BékésyG, 1960“Neural inhibitory units of the eye and skin”Journal of the Optical Society of America501060–1070
114.
von HelversenO, 1965Back cover from B Hassenstein: Biologische Kybernetik (Heidelberg: Quelle und Meyer)
115.
WadeN J, 1978“Op art and visual perception”Perception721–46
116.
WadeN, 1982The Art and Science of Visual Illusions Note 47 (London: Routledge and Kegan Paul) p. 272
117.
WässleHPeichlLBoycottB B, 1983“A spatial analysis of on- and off-ganglion cells in the cat retina”Vision Research231151–1160
118.
WattR, 1988Visual Processing: Computational, Psychophysical and Cognitive Research (London: Lawrence Erlbaum Associates)
119.
WattR JMorganF, 1985“A theory of the primitive spatial code in human vision”Vision Research251661–1674
120.
WestheimerG, 1967“Spatial interaction in human cone vision”Journal of Physiology (London)190139–154
121.
WhiteM, 1979“The limits of lighting—a psychologist's view”IES Lighting Review4130–35
122.
WhiteM, 1981“The effect of the nature of the surround on the perceived lightness of grey bars within square-wave gratings”Perception10215–230
123.
WieselT NHubelD H, 1966“Spatial and chromatic interactions in the LGN of rhesus monkey”Journal of Neurophysiology291115–1156
124.
WilsonH RBergenJ R, 1979“A four mechanism model for threshold spatial vision”Vision Research1919–32
125.
WistE R, 1974“Mach bands and depth adjacency”Bulletin of the Psychonomic Society397–99
126.
WistE R, 1976“Dark adaptation in the Hermann grid illusion”Perception & Psychophysics2010–12
127.
WolfeJ, 1984“Global factors in the Hermann grid illusion”Perception1333–40
