A stereoscopic presentation of the hermann grid

Vision Rm. Vol. 22. pp. 485 to 489. Prinled in Great Britain

0042.6989/82/~5-05~3.00/0 Pergamon Press Ltd

1982

RESEARCH

NOTE

A STEREOSCOPIC PRESENTATION OF THE ~ER~A~~ GRID TOM TROSCIANKO Brain and Perception Laboratory, Department of Anatomy, University of Bristol, University Walk, Bristol BS8 lTD, England (Received 12 August 1981)

In a separate paper, Troscianko will describe his findings on the amount of light which has to be added to an intersection of the “streets” of a variant of the Hermann Grid illusion in order to cancel the illusion This version of the grid is shown in Fig. 1. It is distinguished from the traditional Hermann Grid by the fact that the squares are only drawn in black outline. These still give an illusion, as reported by Spillmann (1977) and Berbaum and Chan Sup Chung (1981). In the work by Troscianko, one intersection of this hollow grid was presented, and the illusory grey spot nulled with a test spot equal in diameter to the inner separation of the black lines. The Hermann Grid illusion is commonly explained in terms of concentric excitato~/inhibitory perceptive fields, this explanation being due to Baumgartner (1960). Perceptive fields are psychophysical correlates of the electrophysiologically-determined receptive fields. Such configurations are known to exist in the retina; hence, this kind of explanation must, in part at least, ascribe the illusion to peripheral (i.e. retinal) mechanisms. Lavin and Costa11 (1978) performed an experiment designed to test whether the illusion was retinal in origin, or whether central (e.g. cortical) factors played a major role in producing the illusory grey spots. They presented a traditional grid to their subjects, who then moved away from the display until the grey spots were no longer visible. Subjects then moved towards the display again, and the point (i.e. angular subtense of the streets) at which they reported seeing the illusion again, was noted. Various square/ street contrast levels were used. No independent estimate of the strength of illusion was made. Lavin and Costa11 then repeated the experiment with a dichoptic presentation of the display. Their display suffered from severe binocular rivalry, estimates being made in the short period during which both rivalrous percepts could be seen. Their data point to a dichoptic illusion being observed, but with observers closer to the display in the diehoptic case, by a factor of about six. Under normal conditions (monocular or binocular viewing), such large stimulus 485

sizes give a considerably weaker illusion than is observed at the optimum grid subtense: see Spillmann’s (1971) data on spot appearance and disappearance thresholds, and Troscianko’s cancellation data. In view of this, the present author disagrees with Lavin and Costall’s conclusion that “the central site is a major, if not the major site, for its (the illusion’s) generation.” (L & C’s italics). When stimulus subtense is kept constant, a dichoptic presentation of the grid results in an abolition of the illusion, Uttal (1973) pp. 451-454. Again, rivalry presents a problem. The presence of a dichoptic illusion, however weak, does suggest that there is a central site. Schepelmann et al. (1967) have argued that the laterai inhibition explanation of the illusion can equally well be in terms of cortical edge detecting units, provided that these have inhibitory flanks. Data from Troscianko’s experiments suggest that when retinal lateral inhibition is abolished, e.g. in scotopic viewing, an illusion is seen only when the spot subtense is much larger than normal (by about a factor of 5 at a 3 degree eccentricity). Presumably, the site of such an illusion generator could well be central. Some evidence from Lennie and MacLeod (1973) and Ransom-Hogg and Spillmann (1980) suggests similar conclusions for scotopic viewing. However, the strength of this possibly central mechanism is weaker than that of retinal receptive field interaction: hence, even if Lavin and Costa11 have found such a mechanism in their dichoptic case, it leads to a weak illusion which is not normally observed under normal binocular viewing. In view of the difficulty of interpreting data from an experiment in which decisions about a weak illusion have to be made during the .short time in which both rivalrous percepts could be seen, it is desirable to devise a different, stable method of performing the binocular/dichoptic experiment. A stereoscopic presentation could give the required stability. The present method suggested itself since we already possessed an apparatus which could project images of stereo pairs with varying disparity as described by Gregory (1970). The apparatus is shown in Fig. 2. Two point sources (equated for luminous flux), separated by about 1

486

Research Note

cl cl q cl cl cl cl cl

cl cl cl cl cl cl cl cl

Fig. I. A “hollow” Hermann Grid. Most subjects can see illusory dark spots at the intersections.

inter-ocular distance, project a beam of light onto a parabolic mirror. The two beams are cross-polarised.

The beam reflected from the parabolic mirror is parallel, since the point sources are located at the mirror’s focal length. Any opaque outline on a clear perspex disc placed in the parallel beam will cast two shadows onto the translucent perspex viewing screen. When a subject views the screen through cross-polarised filters, he sees a different image for each eye. If two sets of shadows are produced by two shadow-

spot

projector 45’

Neutral wrdge

-

casting discs located at different distances from the translucent screen, they form a stereo pair which is seen in depth. The image on the rear disc appears behind the image on the front disc, provided that the binocular disparity is not too large to prevent fusion. In the present experiment, each disc contained two diagonally opposed pairs of the black cross forming one intersection of the hollow Hermann Grid illusion. These are represented in Fig. 2. The subject sat with his head on a chin-rest and wore cross-polarising

port - solvered Perapex half of

mirror

discs. each arid pattern

containmg

Polaro$d

filters

Parabl olic mirror

Fig. 2. Diagram of stereo off-axis collimator used to present two halves of a “hollow” Hermann Grid intersection at different depths.

Research Note spectacles. The viewing distance was 0.75 m. The inner separation of the black lines forming the cross (i.e. the width of the “street” in the Hermann Grid) was 0.46 deg. The cross subtended 5 deg. and was seen at the centre of a circular illuminated area which subtended 9.2 deg, and gave a luminance in each eye of 4.2 cd/me2 (allowing for the polarising spectacles). A small fixation light was provided 5.2 deg above the centre of the cross. The rest of the surround appeared black. A projector, at the rear as seen in Fig. 2, projected a spot whose subtense was also 0.46 deg, and which was slightly out of focus, onto the centre of the cross. It did so by being reflected off the large 45 deg partsilvered mirror. The spot beam passed through a neutral density wedge driven by a motor under the subject’s control. A Wratten 78A filter was inserted into the spot beam to bring its colour temperature to a visual match to the temperature of the quartz-halogen “point source” bulbs. As in Troscianko’s cancellation experiments, continuous exposure was used, with adaptation being in a steady state. Four subjects were used. Of these, one (C.S.) had never taken part in a psychophysical experiment. Two others (S.B. and J.H.) had served as subjects in the author’s previous Hermann Grid cancellation experiments. The fourth subject was the author. The rationale of the experiment is shown in Fig. 3. There were six conditions: 1. No disparity eye 2. No disparity eye 3. No disparity eyes 4. 18’ disparity eye 5. 18’ disparity 6. 18’ disparity eyes

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fixation light, and reduce the intensity of a suprathreshold test spot until it could no longer be seen. The spot was at the centre of the display; its position is shown in Fig. 3. It is assumed that the stronger the illusion, the higher the luminance of the test spot could be without the latter being visible. Six determinations of the wedge setting were made in each of the six conditions. In Troscianko’s other cancellation experiments, the increment threshold with the grid present was compared to the increment threshold on a blank field. This was necessary because different spot sizes were used, which may have led to different blank-field increment thresholds. In the present experiment, spot size was kept constant, so the reference baseline was also constant. Hence, the cancellation strength of the illusion is solely dependent on the increment threshold with the grid in place. With a separation between the two discs, the cross (if viewed interocularly) was seen in depth, i.e. the top right and bottom left portions were seen behind the other two. This is represented at the centre of the bottom row of Fig. 3. Each subject confirmed that he could see the stimulus in depth (i.e. was able to say what was in front and what behind). Each monocular image, however, appeared as shown on the left and right of the bottom row of Fig. 3. These images no longer correspond to the “classical” Hermann Grid.

between two stimulus halves, right between two stimulus halves, left between two stimulus halves, both between two stimulus halves, right between two stimulus halves, left eye between two stimulus halves, both

With no disparity (discs touching), the stimulus cross appeared flat. The subject was instructed to fixate the

___JL -f?-

no disbhrity

0

RE 18

,, '0

binocular 18’ disparity Fig. 3. Subjects’ views of stimuli. Circles denote position of test spot. Top: both half-images at same depth-no disparity. Bottom row: 18’ disparity between the two half images. Left to right: left eye’s view. both eyes’ fused view (f = forward. b = back). and right eye’s view. V.R.22 4 I

LE , 18"'

R+LE' 0 18

disparity

Fig. 4. Results for all subjects. Ordinate: log luminance of

test spot at threshold (arbitrary units). Abscissa: the six experimental conditions. From left to right, these are: (a) Right eye, no disparity between the half-images; (b) Right eye, 18’ disparity; (c) Left eye. no disparity; (d) Left eye, 18’ disparity; (e) Both eyes. no disparity; (I) Both eyes, 18’ disparity (with stereo fusion: cross appears in depth).

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Research Note

On a concentric perceptive-field explanation, Baumgartner (1960), such stimuli are expected to produce a weaker illusion than the traditional intersection at the top of Fig. 3. The two disparities (0 and 18’) were presented in random order, and the three determinations in each disparity condition were also randomised. The logic of the experiment was as follows: if the illusion is primarily due to peripheral mechanisms, then degrading the stimulus for the illusion in each eye should also reduce the illusion when the scene is viewed with both eyes, and binocular fusion occurs. In other words, conditions 1 to 6 above should give illusions which are: 1. strong 2. strong 3. strong 4. weak 5. weak 6. weak However, if the illusion is caused by a central mechanism which is optimally activated by a cross intersection. the fused disparate percept should also give a strong illusion. since the cross is seen “correctly” by a post-fusion mechanism. The predictions for the strength of the illusion here would be:

1. strong 2. strong 3. strong 4. weak 5. weak 6. strong For this experiment, it is not necessary to postulate concentric excitatory/inhibitory mechanisms. Any others would do, provided that conditions 4 and 5 give weaker illusions than 1 and 2. This question is easily settled empirically. Figure 4 shows the results obtained. The ordinate is the log. luminance of the test spot at which the latter just disappeared. Error bars show + or - one standard error on the mean setting. The six conditions are shown on the abscissa. From left to right, they are 1,4; 2,5; 3,6 in the notation given earlier. It is clear that conditions 4 and 5 do degrade the illusion compared to 1 and 2: so the experiment is valid. The disparate binocular case (6) gives an illusion which is just as weak as the disparate monocular cases. This is distinctly in keeping with the first set of predictions. i.e. with a peripheral explanation. An objection might be made by saying that the perception of depth reduces the efficiency of any central mechanism responsible for the illusion; however. evidence against this objection can be found in Wist (1974). who found that introducing depth into the Hermann Grid display has no effect on the strength of the illusion. Additional evidence that the Hermann

Grid illusion persists when different parts of the display are seen at different depths can be observed directly in Julesz (1971), p. 322. The “inverse cyclopean Hermann-Hering grid” in Julesz’s Fig. 2.7-3 gives a strong illusion even though rows and columns of the random-dot stereogram are seen at different depths. As a side issue, the results also show that the illusion as determined by an increment threshold--cancellation technique is no different when measured monocularly than it is when measured binocularly. It may be of interest to note the subjective appearance of the stimuli. In the no-disparity case, a dark spot could clearly be seen at the crossroads. Introduction of a small disparity (about 8 min) did not markedly reduce the illusion (nor were the shapes of the monocular stimuli significantly degraded). Depth could clearly be seen, but the apparent depth of the illusory spot was difficult to ascertain. Increasing the disparity to 18 min (the value used in this paper) did reduce the apparent strength of the illusion, though some was still seen (and its depth became even more difficult to judge). In conclusion, the present results argue in favour of a peripheral mechanism being largely responsible for the Hermann Grid illusion under these experimental conditions (most importantly, a crossroad subtense of well under 1 degree). Data from other experiments show that a centrally-generated illusion is different from (and weaker than) the peripheral illusion: the central mechanism only provides an illusion for much larger stimulus sizes. The present results are strongly indicative of a concentric peripheral perceptive field mechanism being responsible for the large part of the illusion as normally observed.

would like to thank Mr Cohn Shipton for helping with apparatus construction. and Mr A. Osman of the Glass Workshop, Department of Physics, University of Bristol for kindly making the large partsilvered mirror. Thanks are due to all the subjects, and to Lothar Spillmann for his comments on an earlier version of the manuscript. Acknowkdgrmmts-I

REFERENCES Baumgartner G. (1960) Indirekte GrBssenbestimmung der rezepiven Felder der Retina beim Menschen mittels der Hermannschen Gittertauschung (abstract). Pjtigers. Arch. ges. Physiol. 272, 21-22. Berbaum K. and Chan Sup Chung (1981) Perceptive field sizes and a new version of the Hermann Grid. Perception 10, 85-89. Gregory R. L. (1970) Techniques and apparatus for the study of visual perception. Sci. frog.. Oxford 58, 359-378. Julesz B. (1971) Foundations qf C~clopea~~ Pwcrprion. University of Chicago Press. Chicago. Lavin E. and Costa11 A. (1978) Detection thresholds of the Hermann Grid illusion. Vision Res. 18, 1061-1062. Lennie P. and MacLeod D. I. A. (1973) Background configuration and rod threshold. J. Physio/. 233, 143-156.

Research Note Ransom-Hogg A. and Spillmann L. (1980) Perceptive field size in fovea and periphery of the light- and darkadapted retina. Vision Res. 20, 221-228. Schepelman F. v., Aschayeri H. and Baumgartner G. (1967) Die Reaktionen der “simple field”-Neurone in Area I7 der Katze beim Hermann-Gitter-Kontrast (abstract). Pjfiigrrs. Arch. Grs. Physiol. 294, R57. Spillmann L. (1971) Fovea1 perceptive fields in the human visual system measured by simultaneous contrast in

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grids and bars. Pjiiiyers. Arch. Grs. Physiol. 326, 28 l-299. Spillmann L. (1977) Contrast and brightness in illusions. In Spatial Contrast (Edited by Spekreijse H. and Tweel L. H. v.d.), pp. 45-49. North-Holland, Amsterdam. Uttal W. R. (1973) The Psychobiology of Sensory Coding. Harper & Row, New York. Wist E. R. (1974) Mach bands and depth adjacency. Bull. Psychon. Sot. 3,97-99.