- Email: [email protected]
The abutting grating illusion
Vision Res. Vol. 36, No. I, pp. 109-116, 1996
Pergamon
0042-6989(95)00107-7
Copyright (c) 1995 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0042-6989/96 $9.50 + 0.00
The Abutting Grating Illusion* M A N U E L SORIANO,t L O T H A R SPILLMANN,$§ M I C H A E L BACH? Received 22 November 1993; in revised form 20 March 1995
Two line gratings abutting each other with a phase shift of half a cycle elicit the perception of an illusory line running orthogonany between the two sets of grating lines. We found that rating strength increases with increasing number of lines, line length, and phase angle. In contrast, rating strength decreases with increasing spacing of lines, lateral misalignment, rotation of one grating relative to the other, and line width. There is a pronounced oblique effect at 45 deg when the orientation of the abutting gratings is changed from horizontal through diagonal to vertical. Findings are interpreted in terms of a neurophysiological model. We conclude that the end-stopped receptive fields activated by the grating lines are about 6 deg long and 2 deg wide. On the other hand, the "response fields" of the cells, integrating orthogonally across line ends, are assumed to be 5 deg long and less than 1 deg wide. The psyehophysical data compare favorably with available neurophysiological data in Area V2 of the macaque suggesting that the perception of illusory contours in human observers may be based on cortical cell properties similar to those found in the monkey.
Abutting grating illusion
Illusory contour End-stopped cells
INTRODUCTION We have studied an illusion first described by Kanizsa (1974). Figure 1 shows the stimulus pattern used. It consists of two horizontal line gratings shifted in phase and juxtaposed at the vertical. When this pattern is freely viewed, one perceives a straight illusory line where the two gratings meet. Alternatively, one may also perceive an apparent edge between two texture planes located at different depths (Coren, 1972; Kennedy, 1975). Free viewing is recommended. If one fixates at the region of the illusory line, the illusion becomes weak or disappears. (For further studies of this illusion see Appendix.) Neurophysiological experiments have shown that illusory contours arising from stimuli such as used here may be represented at relatively early stages in the visual system. Baumgartner and collaborators (Peterhans & yon der Heydt, 1982; Baumgartner, von der Heydt & Peterhans, 1984; v o n d e r Heydt, Peterhans & Baumgartner, 1984), recording from Area V2 of the awake rhesus monkey, found that over 30% of the cells responding to a real bar, or edge, also responded to a partially occluded bar, or a pair of abutting gratings eliciting perception of an illusory contour. Occasionally, the response to an illusory contour stimulus was even *Dedicated to the memory of Professor Gaetano Kanizsa, deceased 14 March, 1993. tUniversit/its-Augenklinik, Freiburg im Breisgau, Germany. ++Neurologische Klinik, Freiburg im Breisgau, Germany. §To whom reprint requests should be addressed at: lnstitut ffir Biophysik und Strahlenbiologie, Hansastrasse 9, D-79104 Freiburg, Germany. 109
stronger than to a real contour of the same orientation (Baumgartner et al., 1984). Similar results were obtained by Redies, Crook and Creutzfeldt (1986) and Redies (1989) who found responses in Areas 17 and 18 of the anesthetized cat. More recently, Grosof, Shapley and Hawken (1993) have reported neuronal responses to abutting gratings also in Area VI of the macaque monkey. From these findings it appears that bottom-up processing is sufficient to explain the occurrence of subjective contours and that a higher cognitive function (i.e. top-down processing) is not warranted. Several observations support this conclusion: (i) subjective contours may arise pre-attentively (Gurnsey, Humphrey & Kapitan, 1992). (ii) In a preferential looking test, young infants look at an abutting grating edge longer and more often than at continuous gratings (Rieth & Sireteanu, 1993; see also Bertenthal, Campos & Haith, 1980; Ghim, 1990). (iii) Cats likewise appear to respond to illusory contours in abutting grating patterns (Bravo, Blake & Morrison, 1988; DeWeerd, Vandenbussche, DeBruyn & Orban, 1990). (iv) Even insects behave as though they react to such stimuli (Hateren, Srinivasan & Wait, 1990; Horridge, Zhang & O'Carroll, 1992). A hypothesis which plausibly accounts for the emergence of the illusory line between abutting gratings has been advanced by Peterhans, von der Heydt and Baumgartner (1986) (see also Peterhans & von der Heydt, 1987, 1989a, 1991a; v o n d e r Heydt & Peterhans, 1989b, c). Figure 2 shows schematically the hypothetical contour mechanism proposed. The authors assume that receptive fields of end-stopped cells in Area V1 which are aligned along the same vertical (bottom left) signal the
l l0
M A N U E L SORIANO et al.
nearby ends of lines for each of the two gratings. They further assume that at least two end points in each grating are necessary to define an illusory contour by activating a gating mechanism in the cells labelled X. These cells in Area V2 are hypothesized to multiply the individual signals and send them to a higher-order neuron (E), where the inputs from the two gratings are summed. The result in perception would be an illusory line for which there is no physical equivalence. Since the same neuron also responds to a real line oriented at right angles (top left), it cannot distinguish between the two kinds of stimuli. Receptive fields for the edge detecting path (No.l) and response fields for the grouping path (No.2) are assumed to overlap on the same patch of retina. In our study we asked the following questions: which parameters govern the strength of the illusory line? Under which conditions does the illusory line disappear? Is there a correlation between perceived strength in human observers and the magnitude of single cell responses in the monkey? METHODS
To determine the boundary conditions under which the illusion occurs, we varied eight parameters: number of lines, length of lines, phase angle between gratings, spacing of lines, lateral alignment relative to the vertical, tilt angle of one grating relative to the other, line width, and overall orientation of both gratings. The pattern shown in Fig. 1 served as a standard. Only one parameter was varied at a time, while the others remained constant. Experimental stimuli were produced on a Macintosh computer and printed with high contrast on a laser printer. The luminance of the white background was 9 5 c d / m z. The task of the subject was to judge the subjective strength (salience) of the illusory line for each
Standard pattern Number of lines: 26
(I)(~-- \ (2)
F I G U R E 2. Diagram of the hypothetical contour mechanism. Endstopped receptive fields activated by the ends of opposing grating lines (left) feed their signals into a gating mechanism (cells X, right). A higher-order neuron (E) sums the inputs from the two gratings and produces a neural representation of an illusory line oriented at right angles to the grating lines (No. 2, "grouping path"). The same neuron also responds to a vertically oriented, real line (No. l, "edge detecting path"). (After Peterhans, yon der Heydt & Baumgartner, 1986.)
condition. Magnitude estimation was used. To establish a criterion, two anchor stimuli were presented for reference: one, identical to Fig. 1, elicited the strongest illusion (modulus 10), whereas the other had a gap of 0.22 deg in the middle between the two gratings and elicited no illusion at all (modulus 1). Both stimuli had been selected in a pilot study and were presented continuously throughout the experiment. In contrast, experimental stimuli were shown only once to avoid the risk of the same response being given again (from memory). This would have introduced a bias which would have reflected the fidelity of the subjects' recall rather than the judged magnitude for a given stimulus. There was a total of 62 stimuli presented individually and randomized for each subject. Fifteen subjects viewed the stimulus patterns binocularly from a distance of 40 cm. In the following graphs, results are combined for all subjects. Rating strength is given for each parameter by the median (thick curve). In addition, the 25 and 75% percentiles are shown as an estimate of response variability (thin curves). Insets illustrate the parametric variation of stimulus under consideration.
Line length: 5.7 deg Phase angle: 180 deg Line spacing: 1.1 deg Lateral alignment: 0 deg Tilt angle: 0 deg Line width: 0.13 deg Orientation: 0 deg
F I G U R E 1. The shifted grating pattern. Note the illusory line along the vertical between the two gratings. The numbers behind each parameter refer to the standard pattern used.
RESULTS Figure 3 plots rating strength as a function of the total number of grating lines (cumulated over both gratings). A weak illusory contour is already present for four lines, the curve then rises steeply, reaches a peak at 10 grating lines and thereafter declines slightly. For comparison, yon der Heydt and Peterhans (1989a) found that, in the monkey, the neuronal response curves saturated at 7-13 grating lines (indicated by the thick horizontal bar above the abscissa). In the cat, orientation discrimination for an illusory line was optimal for 4 10 lines (DeWeerd et al., 1990). Thus, there is fair agreement between the psychophysical, neurophysiological, and behavioral data.
THE ABUTTING GRATING ILLUSION
111
10
9 8
8
7
7
~6
~:~ 6 e-
rr
5 4
4
3
3
2
2
1
•
•
.
•
|
•
•
5
,
,
,
•
•
,
.
10
|
,
•
15
,
u
]
i
20
•
-
0
45
N u m b e r of lines
90
Figure 4 shows rating strength plotted as a function of the length of the grating lines. The illusory contour first emerges at a line length of approx. 1.5 deg, thereafter the curve increases rapidly and peaks at a line length of 6 deg. For longer lines the curve declines. No comparable data are available in the monkey. In Fig. 5, rating strength is plotted against the phase angle between the two gratings. An illusory line is first noticed at a phase shift of 30 deg, the curve then rises and reaches a peak at 180 deg. This result indicates that the opposing' grating lines need not be in counterphase
180
angle [degrees]
Phase
F I G U R E 3. Rating strength as a function of number of grating lines. The thick line represents the median, whereas the upper and lower thin lines represent the 75 and 25% percentiles, respectively. The thick bar above the abscissa illustrates the optimal range for single cell responses in the monkey (from v o n d e r Heydt & Peterhans, 1989a).
135
F I G U R E 5. Rating strength as a function of the phase shift between the two gratings. A value of 0 deg corresponds to collinearity, a value of 180 deg to a phase shift of one half cycle.
to elicit an illusion, but may assume a wide range of phase angles. Figure 6 gives rating strength as a function of the spacing between individual lines within a grating. The number of lines was kept constant. When the vertical distance between the lines is small (up to 1.08 deg), rating strength is maximal. For larger separations, the curve decreases rapidly and reaches the abscissa at a spacing of 3 deg. Von der Heydt and Peterhans (1989a) found that, in the monkey, cells responded best to line spacings of 0.4-0.8 deg (thick horizontal bar above X-axis). In the cat, the shape of the curve is similar,
109 lO 9
8
8
7
7
.~: rr"
6
rr
5
5
4
4
3
3
2
2
1 0
1
. . . .
i
i
|
|
i
4
6
8
10
12
Line length [degrees] F I G U R E 4. Rating strength as a function of the length of the grating lines.
1
2
3
Line
4
5
6
7
spacing [degrees]
F I G U R E 6. Rating strength as a function of spacing between the individual grating lines. The thick bar above the abscissa illustrates the optimal range for single cell responses in the monkey (from yon der Heydt & Peterhans, 1989a).
112
M A N U E L S O R I A N O et al.
-@
@ 10-
lO
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
C
1
o
-0.3
-0.2
0.0
0.1
1
|
I
-0.1
0.2
0.3
o.o
|
|
u
0.1
0.2
0,3
n
n
0.4
n
0.5
0.6
Line width [degrees]
Alignment [degrees] F I G U R E 7. Rating strength as a function of the amount of lateral misalignment for gratings presented either with a gap (right) or an overlap (left).
although optimal line separations are larger (Redies et al., 1986). Figure 7 plots rating strength for positive and negative misalignments. Normally, the end points of the two gratings are perfectly aligned at the same vertical. However, when a small lateral misalignment is introduced at the midline, perceived strength of the illusion decreases quickly. Results on the right refer to a gap between the gratings, whereas results on the left refer to an overlap. The curve is mirror-symmetric. It shows that separating or interlacing the two gratings by an amount of only _+0.14deg is sufficient to abolish perception of the illusory line. Von der Heydt and Peterhans (1989a)
F I G U R E 9. Rating strength as a function of grating line width.
reported no consistent neuronal response pattern in Area V2 of the monkey for misalignments ranging from 0.5 to - 0 . 5 deg. When one of the gratings was tilted relative to the other (Fig. 8), rating strength remained largely unchanged up to a tilt angle of 20deg and thereafter decreased steadily to reach an asymptote at 45 deg. Von der Heydt and Peterhans (1989a) did not use this kind of pattern in the monkey. When the width of the lines and thus the duty cycle was varied, rating strength behaved somewhat irregularly (Fig. 9). On average, there was a slight decrease from thin to thick grating lines.
r
lO
10 9
e-
8
8
7
7 ~6
6
5
5
4
4
3
3
2
2
1 0
n
u
n
|
n
10
20
30
40
50
m
60
Tilt angle [degrees] F I G U R E 8. Rating strength as a function of tilt angle of one grating relative to the other,
1
m
0
,
m
15
•
,
m
30
m
45
m
,
~
60
,
,
|
75
•
,
u
90
Orientation [degrees] F I G U R E 10. Rating strength as a function of the overall orientation of the two gratings.
THE ABUTTING GRATING ILLUSION TABLE 1. Summary of psychophysical results (maximal rating strength) in 15 human observers and neuronal responses in the monkey Parameter
Maximum
vdH & P
(A) Illusion increases with increasing value of the parameter Number of lines 10 lines 7 13 lines Line length 6 deg Phase angle 165-180 deg (B) Illusion decreases with increasing value of the parameter Line spacing 0.38-1.08 deg 0.4-0.8 deg Lateral misalignment 0 deg - 0 . 5 +0.5 deg Tilt angle 0 20 deg Width of lines 0.084).43 deg Orientation of pattern 90, 0 deg (C) Illusion persists with Mixed polarities of the grating lines Low contract of the grating lines ( ~ 5 % ) The monkey data are from von der Heydt & Peterhans (1989a).
Finally, when the grating pattern was rotated as a whole (Fig. 10), vertical patterns elicited stronger effects than horizontal patterns and ratings for both were higher than for intermediate orientations. The lowest rating was given for the diagonal gratings (i.e. oblique effect). Table 1 summarizes the results: (A) refers to an increase of the strength of the illusion; (B) to a decrease. For comparison with the psychophysical values, data from single cell responses in the monkey are added where available (from v o n d e r Heydt & Peterhans, 1989a).
DISCUSSION From the results of our experiment, several predictions follow for the model proposed by Peterhans, von der Heydt and Baumgartner (see Fig. 2). First, the length of the end-stopped receptive fields activated by individual grating lines may be in the order of 6 deg. This value derives from the peak of Fig. 4 and disregards the slight decrease of the curve for longer lines. Second, the width of the end-stopped fields appears to be approx. 2 deg. This value obtains if one assumes that a grating line of 6 deg length may be rotated by 20 deg before the strength of the illusion declines (Figs 4 and 8). Third, the length of the response fields of the orthogonal grouping mechanism integrating across line ends is given by a total of 10 grating lines, five on either side (Fig. 3). Based on a line spacing of 1.1 deg and a phase angle of 180 deg, this number would correspond to a length of approx. 5 deg. Fourth, the width of the grouping mechanism as derived from the misalignment experiment (Fig. 7) is about 0.15deg. Interactions between parameters were not tested. A response field with a length-to-width ratio of 30 for the grouping mechanism is "skinny" indeed. To reconcile this large ratio with data from single cell recordings remains a challenge for future work. In our experiment, lateral misalignment between the two gratings was the most destructive parameter to the perception of the illusory line: a small gap or overlap immediately abol-
113
ished the illusion. In the monkey, lateral misalignment appears to be a less critical factor than in human observers, although responses for only four cells have been documented (Peterhans et al., 1986; von der Heydt & Peterhans, 1989a). However, with a different stimulus cells in V2 were shown to be highly sensitive to deviations from collinearity. Using rows of spaced dots, Peterhans and v o n d e r Heydt (1989b, 1991b) found that the neuronal response was reduced to half when one dot was misaligned by as little as _ 2 min arc relative to the other dots. With larger displacements there was no response. Such a mechanism could potentially play a role in the breakdown of the illusory line in human vision if the end points of two abutting gratings are not strictly aligned. When we asked our subjects why they had judged the illusion to be absent in such stimuli, they were not even aware that the two sets of grating lines had been slightly spaced apart or interleaved. In this context, it might be mentioned that the shape of the tip of the grating lines is important. Squared-off terminals produce stronger subjective contours than rounded tips, whereas tapered and bevelled line ends do not elicit an illusory edge at all (Kennedy, 1978, 1988). Similarly, when small figural stops, such as short orthogonal lines, are attached to the grating lines, the illusion breaks down (Minguzzi, 1987; for a neuronal correlate see von der Heydt et al., 1984). Finally, if the continuous grating lines are replaced by short dashes or rows of dots, the illusory line is largely absent (Dresp, Spillmann & Bonnet, 1993; for neurophysiological and computational correlates see Redies et al., 1986 and Zucker & Davis, 1988). Compared to the grouping mechanism, the endstopped receptive fields responding to the individual grating lines exhibit a remarkable latitude. The finding that the two abutting gratings need not be parallel, but may differ in orientation by a tilt angle of up to 20 deg (Fig. 8), suggests that end-stopped cells with different orientation preferences may interact with one other; and that the illusory line must not necessarily be oriented orthogonally to the inducing gratings. Gillam (1987) has shown that the abutting grating illusion may be quite strong when elicited by scrambled grating lines, and the same applies to inducing stimuli where the illusory lines are curved or slanted (Kanizsa, 1974, 1976, 1979; Parks, 1980; Wade, 1982; Wilson & Richards, 1992). The eventual decrease in strength with increasing tilt angle is consistent with neurophysiological results by v o n d e r Heydt and Peterhans (1989a, b), who found weaker responses in the monkey for grating stimuli abutting one another at an angle. O t h e r models
Our experiment was originally conceived as a psychophysical test of the model by Peterhans et al. (1986). Alternative models have been advanced by a number of authors to account for the occurrence of illusory contours in Kanisza-type figures (Grossberg & Mingolla, 1985, 1987; Finkel & Edelman, 1989; Morgan & Hotopf, 1989; Kellman & Shipley, 1991; Shipley &
l l4
MANUEL SORIANO et al.
Kellman, 1990, 1992;. Wilson & Richards, 1992). These models are based on a c o m p u t a t i o n a l a p p r o a c h to vision. Regarding line spacing, the majority o f these models predict a m o n o t o n i c decrease o f strength o f the illusion with increasing line separation; this has indeed been observed (Fig. 6). On the other hand, Lesher and Mingolla (1993) reported that "clarity" or salience varied with "line density" according to an inverted U-shaped function. This behavior would be compatible with the model by Grossberg and Mingolla (1985). A fall-off with decreasing line spacing is consistent with the small trough in Fig. 6, if one attributes the subsequent upswing o f the curve to the physical c o n t o u r formed by the very dense line ends. A rating o f 10 was obtained only once in this study and m a y be based on the fact that opposing lines almost touched each other. With regard to tilt angle, we f o u n d only a small effect on the strength o f the illusion for the first 20 deg (Fig. 8). This finding is not predicted by Peterhans et al. (1986), as they assumed the illusory c o n t o u r to extend orthogonally to the preferred orientation o f the end-stopped units. Kellman and Shipley (1991), in their rendition o f the model, o v e r c o m e this problem by pooling across neighboring orientations. As for orientation, the p r o n o u n c e d oblique effect (Appelle, 1972) observed when the entire inducing pattern was rotated (Fig. 8) is not predicted by any o f these models and is not supported by an anisotropic distribution o f orientation selectivity in cells mediating illusory c o n t o u r s ( v o n d e r H e y d t & Peterhans, 1989a; E. Peterhans, personal communication). A n o t h e r model that extracts illusory c o n t o u r s is the one b y Wilson and Richards (1992). The first stage o f the model consists o f simple cell-like filtering, whereas in the second stage the response is squared and subjected to low-pass filtering. A n advantage o f this model is that it does not need pre-wired connections for c o n t o u r detection and thus can readily deal with tilt angle and curved boundaries. However, the model does not predict the symmetric results obtained with lateral misalignment (Fig. 7). Whereas it is true that with interlaced grating lines, illusory c o n t o u r strength would be expected to decrease, the fall-off would not nearly be as steep as shown by our data. In contrast, when the two gratings are separated by a gap, the Wilson Richards model does not predict a fall-off.
P a r v o vs m a g n o s t r e a m processing
In cursory observations, we have f o u n d that the shifted grating illusion persists with mixed polarity o f the inducing lines (Dresp et al., 1993). This observation correlates with neurophysiological findings showing that neurons in Area V1 o f the m o n k e y respond to illusoryc o n t o u r stimuli independently o f the contrast polarity o f the inducers ( G r o s o f et al., 1993). The illusion is also visible with low contrast (approx. 5%) and with different colours o f the stimulus. However, it does not occur at equiluminance (Ejima & Takahashi, 1988; G r e g o r y &
Heard, 1989; W a t a n a b e & Sato, 1989). Findings are summarized in Table 1C). These psychophysical results point in the direction of a magnocellular mechanism underlying the occurrence o f an illusory c o n t o u r in abutting gratings. Cells signalling illusory lines or edges have indeed been found within the pale and thick stripes, but not the thin stripes, o f the c y t o c h r o m e oxidase pattern o f Area V2 (Baumgartner, 1990; Peterhans & v o n der Heydt, 1991b, 1993). A neuronal origin o f the illusory contours in the " c o l o r blind", orientation selective interblob and magnocellular processing streams is also supported by the finding that spectral sensitivity curves for the abutting grating illusion are n o n - o p p o n e n t (Takahashi, Kaihara, T a k e m o t o , Ido & Ejima, 1992). In conclusion, we have defined a framework o f boundary conditions under which the abutting grating illusion will occur in h u m a n perception. A l t h o u g h comparable data from single cells exist for only three parameters, a c o m p a r i s o n between the psychophysical observations and the neurophysiological results suggests that the two kinds o f approaches complement each other and may ultimately lead to a better understand of illusory contours.
REFERENCES
Appetle, S. (1972). Perception and discrimination as a function of stimulus orientation: the "oblique effect' in men and animals. Psychological Bulletin, 78, 266 278. Baumgartner, G. (1990). Where do visual signals become a perception? In Eccles, J. C. & Creutzfeldt, O. (Eds), The principles ¢~fdesign and operation ~[' the brain (pp. 77 114). Pontificiae Academiae Scientiarum Scripta Varia, 78. Ex Aedibus Academicis in Civitate Vaticana. Baumgartner, G., vonder Heydt, R. & Peterhans, E. (1984). Anomalous contours: A tool in studying the neurophysiology of vision. Experimental Brain Research (Suppl), 9, 413~.419. Bertenthal, B. I., Campos, J. & Haith, M. M. (1980). Development of visual organization: The perception of subjective contours. Child Development, 51, 1072 1080. Bravo, M., Blake, R. & Morrison, S. (1988). Cats see subjective contours. Vision Research, 28, 861 865. Coren, S. (1972). Subjective contours and apparent depth. Psychological Review, 79, 359- 367. DeWeerd, P., Vandenbussehe, E., DeBruyn, B. & Orban, G. A.. (1990). Illusory contour orientation discrimination in the cat. Behavioural Brain Research, 39, 1 17. Dresp, B., Spillmann, L. & Bonnet, C. (1993). Collector units and illusory form perception: evidence for cooperative mechanisms in the Ehrenstein illusion. Perception 22 (Suppl.), 3, (Abstr.). Ejima, Y. & Takahashi, S. (1988). Illusory contours induced by chromatic patterns. Vision Research, 28, 1367 1377. Finkel, L. H. & Edelman, G. M. (1989). Integration of distributed cortical systems by reentry: a computer simulation of interactive functionally segregated visual areas. Journal i~f Neuroscience, 9, 3188 3208. Ghim, H. R. (1990). Evidence for perceptual organization in infants: perception of subjective contours by young infants. Infant Behavior and Development, 13, 221 248. Gibson, J. J. (1950). The perception of the visual world (Fig. 41). Boston: Houghton Mifflin. Gillam, B. (1987). Perceptual grouping and subjective contours. In Perry, S. & Meyer, G. E. (Eds), The perception of illusory contours (pp. 268 273). New York: Springer-Verlag.
THE ABUTTING GRATING ILLUSION Gregory, R. & Heard, P. (1989). Some phenomena and implications of isoluminance. In Kulikowski, J. J., Dickinson, C. M. & Murray, I. J. (Eds), Seeing contours and colour (pp. 725 728). Oxford: Pergamon Press. Grosof, D. H., Shapley, R. M. & Hawken, M. J. (1993). Macaque V1 neurons can signal illusory contours. Nature, 365, 550 552. Grossberg, S. & Mingolla, E. (1985). Neural dynamics of form perception: Boundary completion, illusory figures, and neon color spreading. Psychological Review, 92, 173-211. Grossberg, S. & Mingolla, E. (1987). The role of illusory contours in visual segmentation. In Petry, S. & Meyer, G. E. (Eds), The perception of illusory contours (pp. 116 125). New York: SpringerVerlag. Gurnsey, R., Humphrey, G. K. & Kapitan, P. (1992). Parallel discrimination of subjective contours defined by offset gratings. Perception & Psychophysics, 52, 263-276.' Hateren, J. H., Srinivasan, M. V. & Wait, P. B. (1990). Pattern recognition in bees: orientation discrimination. Journal of Comparative Physiology, 167, 649 654. Horridge, G. A., Zhang, S.-W. & O'Carroll, D. (1992). Insect perception of illusory contours. Philosophical Transactions of the Royal Society B, 337, 59 64. Kanizsa, G. (1974). Contours without gradients or cognitive contours? Italian Journal of Psychology, I, 93 112. Kanizsa, G. (1976). Subjective contours. Scientific American, 234, 48-52. Kanizsa, G. ( 1979). Organization in vision: Essays on Gestalt perception New York: Praeger. Kellman, P. J. & Shipley, T. F. (1991). A theory of visual interpolation in object perception. Cognitive Psychology, 23, 141 221. Kennedy, J: M. (1975). Depth at an edge, coplanarity, slant depth, change in direction and change in brightness in the production of subjective contours. Italian Journal o f Psychology, 2, 107-123. Kennedy, J. M. (1978). Illusory contours and the ends of lines. Perception, 7, 605 607. Kennedy, J. M. (1988). Line endings and subjective contours. Spatial Vision, 3, 151 158. Lesher, G. W. & Mingolla, E. (1993). The role of edges and lineends in illusory contour formation. Vision Research, 33, 22532270. Minguzzi, G. F. (1987). Anomalous figures and the tendency to continuation. In Petry, S. & Meyer, G. E. (Eds), The perception of illusory contours (pp. 71 75). New York: Springer-Verlag. Morgan, M. J. & Hotopf, W. H. N. (1989). Perceived diagonals in grids and lattices. Vision Research, 29, 1005-1015. Paradisco, M. A., Shimojo, S. & Nakayama, K. (1989). Subjective contours, tilt aftereffects, and visual cortical organization. Vision Research, 29, 1205 1213. Parks, T. E. (1980). Letter to the Editor. Perception, 9, 723. Perona, P. & Kooi, F. (1990). Illusory contour motion. Investigative Ophthalmology & Visual Sciences, 31, 531. (Abstr.) Peterhans, E. & von der Heydt, R. (1982). Cortical neuron responses and 'illusory' contours. Perception, 11, A19 (Abstr.). Peterhans, E. & von der Heydt, R. (1987). The role of end-stopped receptive fields in contour perception. In Eisner, J. & Creutzfeldt, O. (Eds), New .frontiers in brain research (p. 29). Stuttgart: Thieme (Abstr.). Peterhans, E. & v o n der Heydt, R. (1989a). Mechanisms of contour perception in monkey visual cortex. II. Contours bridging gaps. Journal of Neuroscienee, 9, 1749-1763. Peterhans, E. & v o n der Heydt, R. (1989b). The whole and the pieces---cortical neuron responses to bars and rows Of moving dots. In Kulikowski, J. J., Dickinson, C. M. & Murray, I. J. (Eds), Seeing contours and colour (pp. 125-130). Oxford: Pergamon Press. Peterhans, E. & v o n der Heydt, R. (1991a). Subjective contours-bridging the gap between psychophysics and physiology. Trends in Neuroscience, 14, 112 119. Peterhans, E. & yon der Heydt, R. (1991b). Elements of form perception in monkey prestriate cortex. In Gorea, A., Fr6gnac, Y., Kapoula, Z. & Findlay, J. (Eds), Representations o f vision: Trends and tacit assumptions in vision research (pp. 111-124),. Cambridge: Cambridge University Press:
115
Peterhans, E. & v o n der Heydt, R. (1993). Functional organization of Area V2 in the alert monkey. European Journal of Neuroscience, 5, 509-524. Peterhans, E., vonder Heydt, R. & Baumgartner, G. (1986). Neuronal responses to illusory contour stimuli reveal stages of visual cortical processing. In Pettigrew, J. D., Sanderson, K. J. & Levick, W. R. (Eds), Visual neuroscience (pp. 343-351. Cambridge: Cambridge University Press. Prazdny, K. (1983). Illusory contours are not caused by simultaneous rightness contrast. Perception & Psychophysics, 34, 403404. Redies, C. (1989). Discontinuities along lines: Psychophysics and neurophysiology. Neuroscience & Biobehavioral Reviews, 13, 17 22. Redies, C., Crook, J. M. & Creutzfeldt, O. D. (1986). Neuronal responses to borders with and without luminance gradients in cat visual cortex and dorsal lateral geniculate nucleus. Experimental Brain Research, 61, 469 481. Richardson, B. L. & Wuillemin, D. B. (1981). Illusory contours not accompanied by a brightness gradient. Italian Journal o f Psychology, 8, 201~07. Rieth, C. & Sireteanu, R. (1993). How do infants perceive subjective contours? Poster at the 4th Meeting of the Child Vision Research Society, Lyon, July 11-13, 1993. Sambin, M. (1974). Angular margins without gradients. Italian Journal of Psychology, 1, 355 361. Sambin, M. (1975). The rule of terminal tensions in th~ organization of margins without gradients. Italian Journal of Psychology, 6, 239-257. Sambin, M. (1977). Contouzs without gradient with different phenomenal evidence. Italian Journal of Psychology, 6, 121 147. Sambin, M. (1985). Figure anomale: La misura dell'ampiezza di una disomogeneitfi indotta. In Gerbino, W. (Ed.), Conoscenza e struttura: Festsehrift per Gaetano Kanizsa (pp. 437-452). Bologna: Ie Mulino. Sambin, M. (1987). A dynamic model of anomalous figures. In Petry, S. & Meyer, G. E. (Eds), The perception of illusory contours (pp. 131 142). New York: Springer-Verlag. Shipley, T. F. & Kellman, P. J. (1990). The role of discontinuities in the perception of subjective figures. Perception & Psychophysics, 48, 259-270. Shipley, T. F. & Kellman, P. J. (1992). Strength of visual interpolation depends on the ratio of physically specified to total edge length. Perception & Psychophysies, 52, 97 106. Takahashi, S., Kaihara, T., Takemoto, A., Ido, K. & Ejima, Y. (1992). Spectral sensitivities for illusory contour perception: A manifold linkage of chromatic and achromatic cues with the generation of contours. Vision Research, 32, 1709-1718. Vogels, R. & Orban, G. A. (1987). Illusory contour orientation discrimination. Vision Research, 27, 453 467. v o n d e r Heydt, R. & Peterhans, E. (1989a). Mechanisms of contour perception in monkey visual cortex. I. Lines of pattern discontinuity. Journal of Neuroscience, 9, 1731 1748. yon der Heydt, R. & Peterhans, E. (1989b). Cortical contour mechanisms and geometrical illusions. In Lain, D. M. & Gilbert, C. D. (Eds), Neural mechanisms of visual perception (pp. 157 170). The Woodlands: Portfolio Publishers. von der Heydt, R. & Peterhans, E. (1989c). Ehrenstein and Z611ner illusions in a neuronal theory of contour processing. In Kulikowski, J. J., Dickinson, C. M. & Murray, I. J. (Eds), Seeing contour and colour (pp. 729-734). Oxford: Pergamon Press. von der Heydt, R., Peterhans, E. & Baumgartner, G. (1984). Illusory contours and cortical neuron responses. Science, NY, 224, 1260-1262. Wade, N. (1982). The art and science of visual illusions (Figs 1.4.3 1.4.4; also Figs 1.2.17 1.2.22, 1.3.26, 1.3.29). London: Routledge & Kegan Paul. Another good example is Vasarely's Altair (1957-58). Ware, C. (1981). Subjective contours independent of subjective brightness. Perception & Psychophysics, 29, 500 504. Ware, C. & Kennedy, J. M. (1977). Illusory line linking solid rods. Perception, 6, 601 602.
116
MANUEL SORIANO et al.
Watanabe, T. & Sato, T. (1989). Effects of luminance contrast on color spreading and illusory contour in the neon color spreading effect. Perception & Psychophysics, 45, 427-430. Wilson, W. R. & Richards, W. A. (1992). Curvature and separation discrimination at texture boundaries. Journal of the Optical Society of America, A9, 1653-1662. Zucker, S. W. & Davis, S. (1988). Points and endpoints: A size/spacing constraint for dot grouping. Perception, 17, 229 247.
Acknowledgements~his manuscript was supported, in part, by Grants SFB 325, B3 and B4, from the Deutsche Forschungsgemeinschaft. S. Menees improved the English in the manuscript, B. Dresp
provided new data on the Ehrenstein illusion, and M. Teuber drew the authors' attention to related op-art phenomena. P. Bressan, W. Ehrenstein, E. Peterhans and C. Redies commented on an earlier draft. We thank them all.
APPENDIX For further studies of the abutting-grating illusion see Gibson (1950); Paradiso, Shimojo and Nakayama (1989); Perona and Kooi (1990); Prazdny (1983); Richardson and Wuillemin (1981); Sambin (1974, 1975, 1977, 1985, 1987); Ware (1981); Ware and Kennedy (1977); and Vogels and Orban (1987).
Pergamon
0042-6989(95)00107-7
Copyright (c) 1995 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0042-6989/96 $9.50 + 0.00
The Abutting Grating Illusion* M A N U E L SORIANO,t L O T H A R SPILLMANN,$§ M I C H A E L BACH? Received 22 November 1993; in revised form 20 March 1995
Two line gratings abutting each other with a phase shift of half a cycle elicit the perception of an illusory line running orthogonany between the two sets of grating lines. We found that rating strength increases with increasing number of lines, line length, and phase angle. In contrast, rating strength decreases with increasing spacing of lines, lateral misalignment, rotation of one grating relative to the other, and line width. There is a pronounced oblique effect at 45 deg when the orientation of the abutting gratings is changed from horizontal through diagonal to vertical. Findings are interpreted in terms of a neurophysiological model. We conclude that the end-stopped receptive fields activated by the grating lines are about 6 deg long and 2 deg wide. On the other hand, the "response fields" of the cells, integrating orthogonally across line ends, are assumed to be 5 deg long and less than 1 deg wide. The psyehophysical data compare favorably with available neurophysiological data in Area V2 of the macaque suggesting that the perception of illusory contours in human observers may be based on cortical cell properties similar to those found in the monkey.
Abutting grating illusion
Illusory contour End-stopped cells
INTRODUCTION We have studied an illusion first described by Kanizsa (1974). Figure 1 shows the stimulus pattern used. It consists of two horizontal line gratings shifted in phase and juxtaposed at the vertical. When this pattern is freely viewed, one perceives a straight illusory line where the two gratings meet. Alternatively, one may also perceive an apparent edge between two texture planes located at different depths (Coren, 1972; Kennedy, 1975). Free viewing is recommended. If one fixates at the region of the illusory line, the illusion becomes weak or disappears. (For further studies of this illusion see Appendix.) Neurophysiological experiments have shown that illusory contours arising from stimuli such as used here may be represented at relatively early stages in the visual system. Baumgartner and collaborators (Peterhans & yon der Heydt, 1982; Baumgartner, von der Heydt & Peterhans, 1984; v o n d e r Heydt, Peterhans & Baumgartner, 1984), recording from Area V2 of the awake rhesus monkey, found that over 30% of the cells responding to a real bar, or edge, also responded to a partially occluded bar, or a pair of abutting gratings eliciting perception of an illusory contour. Occasionally, the response to an illusory contour stimulus was even *Dedicated to the memory of Professor Gaetano Kanizsa, deceased 14 March, 1993. tUniversit/its-Augenklinik, Freiburg im Breisgau, Germany. ++Neurologische Klinik, Freiburg im Breisgau, Germany. §To whom reprint requests should be addressed at: lnstitut ffir Biophysik und Strahlenbiologie, Hansastrasse 9, D-79104 Freiburg, Germany. 109
stronger than to a real contour of the same orientation (Baumgartner et al., 1984). Similar results were obtained by Redies, Crook and Creutzfeldt (1986) and Redies (1989) who found responses in Areas 17 and 18 of the anesthetized cat. More recently, Grosof, Shapley and Hawken (1993) have reported neuronal responses to abutting gratings also in Area VI of the macaque monkey. From these findings it appears that bottom-up processing is sufficient to explain the occurrence of subjective contours and that a higher cognitive function (i.e. top-down processing) is not warranted. Several observations support this conclusion: (i) subjective contours may arise pre-attentively (Gurnsey, Humphrey & Kapitan, 1992). (ii) In a preferential looking test, young infants look at an abutting grating edge longer and more often than at continuous gratings (Rieth & Sireteanu, 1993; see also Bertenthal, Campos & Haith, 1980; Ghim, 1990). (iii) Cats likewise appear to respond to illusory contours in abutting grating patterns (Bravo, Blake & Morrison, 1988; DeWeerd, Vandenbussche, DeBruyn & Orban, 1990). (iv) Even insects behave as though they react to such stimuli (Hateren, Srinivasan & Wait, 1990; Horridge, Zhang & O'Carroll, 1992). A hypothesis which plausibly accounts for the emergence of the illusory line between abutting gratings has been advanced by Peterhans, von der Heydt and Baumgartner (1986) (see also Peterhans & von der Heydt, 1987, 1989a, 1991a; v o n d e r Heydt & Peterhans, 1989b, c). Figure 2 shows schematically the hypothetical contour mechanism proposed. The authors assume that receptive fields of end-stopped cells in Area V1 which are aligned along the same vertical (bottom left) signal the
l l0
M A N U E L SORIANO et al.
nearby ends of lines for each of the two gratings. They further assume that at least two end points in each grating are necessary to define an illusory contour by activating a gating mechanism in the cells labelled X. These cells in Area V2 are hypothesized to multiply the individual signals and send them to a higher-order neuron (E), where the inputs from the two gratings are summed. The result in perception would be an illusory line for which there is no physical equivalence. Since the same neuron also responds to a real line oriented at right angles (top left), it cannot distinguish between the two kinds of stimuli. Receptive fields for the edge detecting path (No.l) and response fields for the grouping path (No.2) are assumed to overlap on the same patch of retina. In our study we asked the following questions: which parameters govern the strength of the illusory line? Under which conditions does the illusory line disappear? Is there a correlation between perceived strength in human observers and the magnitude of single cell responses in the monkey? METHODS
To determine the boundary conditions under which the illusion occurs, we varied eight parameters: number of lines, length of lines, phase angle between gratings, spacing of lines, lateral alignment relative to the vertical, tilt angle of one grating relative to the other, line width, and overall orientation of both gratings. The pattern shown in Fig. 1 served as a standard. Only one parameter was varied at a time, while the others remained constant. Experimental stimuli were produced on a Macintosh computer and printed with high contrast on a laser printer. The luminance of the white background was 9 5 c d / m z. The task of the subject was to judge the subjective strength (salience) of the illusory line for each
Standard pattern Number of lines: 26
(I)(~-- \ (2)
F I G U R E 2. Diagram of the hypothetical contour mechanism. Endstopped receptive fields activated by the ends of opposing grating lines (left) feed their signals into a gating mechanism (cells X, right). A higher-order neuron (E) sums the inputs from the two gratings and produces a neural representation of an illusory line oriented at right angles to the grating lines (No. 2, "grouping path"). The same neuron also responds to a vertically oriented, real line (No. l, "edge detecting path"). (After Peterhans, yon der Heydt & Baumgartner, 1986.)
condition. Magnitude estimation was used. To establish a criterion, two anchor stimuli were presented for reference: one, identical to Fig. 1, elicited the strongest illusion (modulus 10), whereas the other had a gap of 0.22 deg in the middle between the two gratings and elicited no illusion at all (modulus 1). Both stimuli had been selected in a pilot study and were presented continuously throughout the experiment. In contrast, experimental stimuli were shown only once to avoid the risk of the same response being given again (from memory). This would have introduced a bias which would have reflected the fidelity of the subjects' recall rather than the judged magnitude for a given stimulus. There was a total of 62 stimuli presented individually and randomized for each subject. Fifteen subjects viewed the stimulus patterns binocularly from a distance of 40 cm. In the following graphs, results are combined for all subjects. Rating strength is given for each parameter by the median (thick curve). In addition, the 25 and 75% percentiles are shown as an estimate of response variability (thin curves). Insets illustrate the parametric variation of stimulus under consideration.
Line length: 5.7 deg Phase angle: 180 deg Line spacing: 1.1 deg Lateral alignment: 0 deg Tilt angle: 0 deg Line width: 0.13 deg Orientation: 0 deg
F I G U R E 1. The shifted grating pattern. Note the illusory line along the vertical between the two gratings. The numbers behind each parameter refer to the standard pattern used.
RESULTS Figure 3 plots rating strength as a function of the total number of grating lines (cumulated over both gratings). A weak illusory contour is already present for four lines, the curve then rises steeply, reaches a peak at 10 grating lines and thereafter declines slightly. For comparison, yon der Heydt and Peterhans (1989a) found that, in the monkey, the neuronal response curves saturated at 7-13 grating lines (indicated by the thick horizontal bar above the abscissa). In the cat, orientation discrimination for an illusory line was optimal for 4 10 lines (DeWeerd et al., 1990). Thus, there is fair agreement between the psychophysical, neurophysiological, and behavioral data.
THE ABUTTING GRATING ILLUSION
111
10
9 8
8
7
7
~6
~:~ 6 e-
rr
5 4
4
3
3
2
2
1
•
•
.
•
|
•
•
5
,
,
,
•
•
,
.
10
|
,
•
15
,
u
]
i
20
•
-
0
45
N u m b e r of lines
90
Figure 4 shows rating strength plotted as a function of the length of the grating lines. The illusory contour first emerges at a line length of approx. 1.5 deg, thereafter the curve increases rapidly and peaks at a line length of 6 deg. For longer lines the curve declines. No comparable data are available in the monkey. In Fig. 5, rating strength is plotted against the phase angle between the two gratings. An illusory line is first noticed at a phase shift of 30 deg, the curve then rises and reaches a peak at 180 deg. This result indicates that the opposing' grating lines need not be in counterphase
180
angle [degrees]
Phase
F I G U R E 3. Rating strength as a function of number of grating lines. The thick line represents the median, whereas the upper and lower thin lines represent the 75 and 25% percentiles, respectively. The thick bar above the abscissa illustrates the optimal range for single cell responses in the monkey (from v o n d e r Heydt & Peterhans, 1989a).
135
F I G U R E 5. Rating strength as a function of the phase shift between the two gratings. A value of 0 deg corresponds to collinearity, a value of 180 deg to a phase shift of one half cycle.
to elicit an illusion, but may assume a wide range of phase angles. Figure 6 gives rating strength as a function of the spacing between individual lines within a grating. The number of lines was kept constant. When the vertical distance between the lines is small (up to 1.08 deg), rating strength is maximal. For larger separations, the curve decreases rapidly and reaches the abscissa at a spacing of 3 deg. Von der Heydt and Peterhans (1989a) found that, in the monkey, cells responded best to line spacings of 0.4-0.8 deg (thick horizontal bar above X-axis). In the cat, the shape of the curve is similar,
109 lO 9
8
8
7
7
.~: rr"
6
rr
5
5
4
4
3
3
2
2
1 0
1
. . . .
i
i
|
|
i
4
6
8
10
12
Line length [degrees] F I G U R E 4. Rating strength as a function of the length of the grating lines.
1
2
3
Line
4
5
6
7
spacing [degrees]
F I G U R E 6. Rating strength as a function of spacing between the individual grating lines. The thick bar above the abscissa illustrates the optimal range for single cell responses in the monkey (from yon der Heydt & Peterhans, 1989a).
112
M A N U E L S O R I A N O et al.
-@
@ 10-
lO
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
C
1
o
-0.3
-0.2
0.0
0.1
1
|
I
-0.1
0.2
0.3
o.o
|
|
u
0.1
0.2
0,3
n
n
0.4
n
0.5
0.6
Line width [degrees]
Alignment [degrees] F I G U R E 7. Rating strength as a function of the amount of lateral misalignment for gratings presented either with a gap (right) or an overlap (left).
although optimal line separations are larger (Redies et al., 1986). Figure 7 plots rating strength for positive and negative misalignments. Normally, the end points of the two gratings are perfectly aligned at the same vertical. However, when a small lateral misalignment is introduced at the midline, perceived strength of the illusion decreases quickly. Results on the right refer to a gap between the gratings, whereas results on the left refer to an overlap. The curve is mirror-symmetric. It shows that separating or interlacing the two gratings by an amount of only _+0.14deg is sufficient to abolish perception of the illusory line. Von der Heydt and Peterhans (1989a)
F I G U R E 9. Rating strength as a function of grating line width.
reported no consistent neuronal response pattern in Area V2 of the monkey for misalignments ranging from 0.5 to - 0 . 5 deg. When one of the gratings was tilted relative to the other (Fig. 8), rating strength remained largely unchanged up to a tilt angle of 20deg and thereafter decreased steadily to reach an asymptote at 45 deg. Von der Heydt and Peterhans (1989a) did not use this kind of pattern in the monkey. When the width of the lines and thus the duty cycle was varied, rating strength behaved somewhat irregularly (Fig. 9). On average, there was a slight decrease from thin to thick grating lines.
r
lO
10 9
e-
8
8
7
7 ~6
6
5
5
4
4
3
3
2
2
1 0
n
u
n
|
n
10
20
30
40
50
m
60
Tilt angle [degrees] F I G U R E 8. Rating strength as a function of tilt angle of one grating relative to the other,
1
m
0
,
m
15
•
,
m
30
m
45
m
,
~
60
,
,
|
75
•
,
u
90
Orientation [degrees] F I G U R E 10. Rating strength as a function of the overall orientation of the two gratings.
THE ABUTTING GRATING ILLUSION TABLE 1. Summary of psychophysical results (maximal rating strength) in 15 human observers and neuronal responses in the monkey Parameter
Maximum
vdH & P
(A) Illusion increases with increasing value of the parameter Number of lines 10 lines 7 13 lines Line length 6 deg Phase angle 165-180 deg (B) Illusion decreases with increasing value of the parameter Line spacing 0.38-1.08 deg 0.4-0.8 deg Lateral misalignment 0 deg - 0 . 5 +0.5 deg Tilt angle 0 20 deg Width of lines 0.084).43 deg Orientation of pattern 90, 0 deg (C) Illusion persists with Mixed polarities of the grating lines Low contract of the grating lines ( ~ 5 % ) The monkey data are from von der Heydt & Peterhans (1989a).
Finally, when the grating pattern was rotated as a whole (Fig. 10), vertical patterns elicited stronger effects than horizontal patterns and ratings for both were higher than for intermediate orientations. The lowest rating was given for the diagonal gratings (i.e. oblique effect). Table 1 summarizes the results: (A) refers to an increase of the strength of the illusion; (B) to a decrease. For comparison with the psychophysical values, data from single cell responses in the monkey are added where available (from v o n d e r Heydt & Peterhans, 1989a).
DISCUSSION From the results of our experiment, several predictions follow for the model proposed by Peterhans, von der Heydt and Baumgartner (see Fig. 2). First, the length of the end-stopped receptive fields activated by individual grating lines may be in the order of 6 deg. This value derives from the peak of Fig. 4 and disregards the slight decrease of the curve for longer lines. Second, the width of the end-stopped fields appears to be approx. 2 deg. This value obtains if one assumes that a grating line of 6 deg length may be rotated by 20 deg before the strength of the illusion declines (Figs 4 and 8). Third, the length of the response fields of the orthogonal grouping mechanism integrating across line ends is given by a total of 10 grating lines, five on either side (Fig. 3). Based on a line spacing of 1.1 deg and a phase angle of 180 deg, this number would correspond to a length of approx. 5 deg. Fourth, the width of the grouping mechanism as derived from the misalignment experiment (Fig. 7) is about 0.15deg. Interactions between parameters were not tested. A response field with a length-to-width ratio of 30 for the grouping mechanism is "skinny" indeed. To reconcile this large ratio with data from single cell recordings remains a challenge for future work. In our experiment, lateral misalignment between the two gratings was the most destructive parameter to the perception of the illusory line: a small gap or overlap immediately abol-
113
ished the illusion. In the monkey, lateral misalignment appears to be a less critical factor than in human observers, although responses for only four cells have been documented (Peterhans et al., 1986; von der Heydt & Peterhans, 1989a). However, with a different stimulus cells in V2 were shown to be highly sensitive to deviations from collinearity. Using rows of spaced dots, Peterhans and v o n d e r Heydt (1989b, 1991b) found that the neuronal response was reduced to half when one dot was misaligned by as little as _ 2 min arc relative to the other dots. With larger displacements there was no response. Such a mechanism could potentially play a role in the breakdown of the illusory line in human vision if the end points of two abutting gratings are not strictly aligned. When we asked our subjects why they had judged the illusion to be absent in such stimuli, they were not even aware that the two sets of grating lines had been slightly spaced apart or interleaved. In this context, it might be mentioned that the shape of the tip of the grating lines is important. Squared-off terminals produce stronger subjective contours than rounded tips, whereas tapered and bevelled line ends do not elicit an illusory edge at all (Kennedy, 1978, 1988). Similarly, when small figural stops, such as short orthogonal lines, are attached to the grating lines, the illusion breaks down (Minguzzi, 1987; for a neuronal correlate see von der Heydt et al., 1984). Finally, if the continuous grating lines are replaced by short dashes or rows of dots, the illusory line is largely absent (Dresp, Spillmann & Bonnet, 1993; for neurophysiological and computational correlates see Redies et al., 1986 and Zucker & Davis, 1988). Compared to the grouping mechanism, the endstopped receptive fields responding to the individual grating lines exhibit a remarkable latitude. The finding that the two abutting gratings need not be parallel, but may differ in orientation by a tilt angle of up to 20 deg (Fig. 8), suggests that end-stopped cells with different orientation preferences may interact with one other; and that the illusory line must not necessarily be oriented orthogonally to the inducing gratings. Gillam (1987) has shown that the abutting grating illusion may be quite strong when elicited by scrambled grating lines, and the same applies to inducing stimuli where the illusory lines are curved or slanted (Kanizsa, 1974, 1976, 1979; Parks, 1980; Wade, 1982; Wilson & Richards, 1992). The eventual decrease in strength with increasing tilt angle is consistent with neurophysiological results by v o n d e r Heydt and Peterhans (1989a, b), who found weaker responses in the monkey for grating stimuli abutting one another at an angle. O t h e r models
Our experiment was originally conceived as a psychophysical test of the model by Peterhans et al. (1986). Alternative models have been advanced by a number of authors to account for the occurrence of illusory contours in Kanisza-type figures (Grossberg & Mingolla, 1985, 1987; Finkel & Edelman, 1989; Morgan & Hotopf, 1989; Kellman & Shipley, 1991; Shipley &
l l4
MANUEL SORIANO et al.
Kellman, 1990, 1992;. Wilson & Richards, 1992). These models are based on a c o m p u t a t i o n a l a p p r o a c h to vision. Regarding line spacing, the majority o f these models predict a m o n o t o n i c decrease o f strength o f the illusion with increasing line separation; this has indeed been observed (Fig. 6). On the other hand, Lesher and Mingolla (1993) reported that "clarity" or salience varied with "line density" according to an inverted U-shaped function. This behavior would be compatible with the model by Grossberg and Mingolla (1985). A fall-off with decreasing line spacing is consistent with the small trough in Fig. 6, if one attributes the subsequent upswing o f the curve to the physical c o n t o u r formed by the very dense line ends. A rating o f 10 was obtained only once in this study and m a y be based on the fact that opposing lines almost touched each other. With regard to tilt angle, we f o u n d only a small effect on the strength o f the illusion for the first 20 deg (Fig. 8). This finding is not predicted by Peterhans et al. (1986), as they assumed the illusory c o n t o u r to extend orthogonally to the preferred orientation o f the end-stopped units. Kellman and Shipley (1991), in their rendition o f the model, o v e r c o m e this problem by pooling across neighboring orientations. As for orientation, the p r o n o u n c e d oblique effect (Appelle, 1972) observed when the entire inducing pattern was rotated (Fig. 8) is not predicted by any o f these models and is not supported by an anisotropic distribution o f orientation selectivity in cells mediating illusory c o n t o u r s ( v o n d e r H e y d t & Peterhans, 1989a; E. Peterhans, personal communication). A n o t h e r model that extracts illusory c o n t o u r s is the one b y Wilson and Richards (1992). The first stage o f the model consists o f simple cell-like filtering, whereas in the second stage the response is squared and subjected to low-pass filtering. A n advantage o f this model is that it does not need pre-wired connections for c o n t o u r detection and thus can readily deal with tilt angle and curved boundaries. However, the model does not predict the symmetric results obtained with lateral misalignment (Fig. 7). Whereas it is true that with interlaced grating lines, illusory c o n t o u r strength would be expected to decrease, the fall-off would not nearly be as steep as shown by our data. In contrast, when the two gratings are separated by a gap, the Wilson Richards model does not predict a fall-off.
P a r v o vs m a g n o s t r e a m processing
In cursory observations, we have f o u n d that the shifted grating illusion persists with mixed polarity o f the inducing lines (Dresp et al., 1993). This observation correlates with neurophysiological findings showing that neurons in Area V1 o f the m o n k e y respond to illusoryc o n t o u r stimuli independently o f the contrast polarity o f the inducers ( G r o s o f et al., 1993). The illusion is also visible with low contrast (approx. 5%) and with different colours o f the stimulus. However, it does not occur at equiluminance (Ejima & Takahashi, 1988; G r e g o r y &
Heard, 1989; W a t a n a b e & Sato, 1989). Findings are summarized in Table 1C). These psychophysical results point in the direction of a magnocellular mechanism underlying the occurrence o f an illusory c o n t o u r in abutting gratings. Cells signalling illusory lines or edges have indeed been found within the pale and thick stripes, but not the thin stripes, o f the c y t o c h r o m e oxidase pattern o f Area V2 (Baumgartner, 1990; Peterhans & v o n der Heydt, 1991b, 1993). A neuronal origin o f the illusory contours in the " c o l o r blind", orientation selective interblob and magnocellular processing streams is also supported by the finding that spectral sensitivity curves for the abutting grating illusion are n o n - o p p o n e n t (Takahashi, Kaihara, T a k e m o t o , Ido & Ejima, 1992). In conclusion, we have defined a framework o f boundary conditions under which the abutting grating illusion will occur in h u m a n perception. A l t h o u g h comparable data from single cells exist for only three parameters, a c o m p a r i s o n between the psychophysical observations and the neurophysiological results suggests that the two kinds o f approaches complement each other and may ultimately lead to a better understand of illusory contours.
REFERENCES
Appetle, S. (1972). Perception and discrimination as a function of stimulus orientation: the "oblique effect' in men and animals. Psychological Bulletin, 78, 266 278. Baumgartner, G. (1990). Where do visual signals become a perception? In Eccles, J. C. & Creutzfeldt, O. (Eds), The principles ¢~fdesign and operation ~[' the brain (pp. 77 114). Pontificiae Academiae Scientiarum Scripta Varia, 78. Ex Aedibus Academicis in Civitate Vaticana. Baumgartner, G., vonder Heydt, R. & Peterhans, E. (1984). Anomalous contours: A tool in studying the neurophysiology of vision. Experimental Brain Research (Suppl), 9, 413~.419. Bertenthal, B. I., Campos, J. & Haith, M. M. (1980). Development of visual organization: The perception of subjective contours. Child Development, 51, 1072 1080. Bravo, M., Blake, R. & Morrison, S. (1988). Cats see subjective contours. Vision Research, 28, 861 865. Coren, S. (1972). Subjective contours and apparent depth. Psychological Review, 79, 359- 367. DeWeerd, P., Vandenbussehe, E., DeBruyn, B. & Orban, G. A.. (1990). Illusory contour orientation discrimination in the cat. Behavioural Brain Research, 39, 1 17. Dresp, B., Spillmann, L. & Bonnet, C. (1993). Collector units and illusory form perception: evidence for cooperative mechanisms in the Ehrenstein illusion. Perception 22 (Suppl.), 3, (Abstr.). Ejima, Y. & Takahashi, S. (1988). Illusory contours induced by chromatic patterns. Vision Research, 28, 1367 1377. Finkel, L. H. & Edelman, G. M. (1989). Integration of distributed cortical systems by reentry: a computer simulation of interactive functionally segregated visual areas. Journal i~f Neuroscience, 9, 3188 3208. Ghim, H. R. (1990). Evidence for perceptual organization in infants: perception of subjective contours by young infants. Infant Behavior and Development, 13, 221 248. Gibson, J. J. (1950). The perception of the visual world (Fig. 41). Boston: Houghton Mifflin. Gillam, B. (1987). Perceptual grouping and subjective contours. In Perry, S. & Meyer, G. E. (Eds), The perception of illusory contours (pp. 268 273). New York: Springer-Verlag.
THE ABUTTING GRATING ILLUSION Gregory, R. & Heard, P. (1989). Some phenomena and implications of isoluminance. In Kulikowski, J. J., Dickinson, C. M. & Murray, I. J. (Eds), Seeing contours and colour (pp. 725 728). Oxford: Pergamon Press. Grosof, D. H., Shapley, R. M. & Hawken, M. J. (1993). Macaque V1 neurons can signal illusory contours. Nature, 365, 550 552. Grossberg, S. & Mingolla, E. (1985). Neural dynamics of form perception: Boundary completion, illusory figures, and neon color spreading. Psychological Review, 92, 173-211. Grossberg, S. & Mingolla, E. (1987). The role of illusory contours in visual segmentation. In Petry, S. & Meyer, G. E. (Eds), The perception of illusory contours (pp. 116 125). New York: SpringerVerlag. Gurnsey, R., Humphrey, G. K. & Kapitan, P. (1992). Parallel discrimination of subjective contours defined by offset gratings. Perception & Psychophysics, 52, 263-276.' Hateren, J. H., Srinivasan, M. V. & Wait, P. B. (1990). Pattern recognition in bees: orientation discrimination. Journal of Comparative Physiology, 167, 649 654. Horridge, G. A., Zhang, S.-W. & O'Carroll, D. (1992). Insect perception of illusory contours. Philosophical Transactions of the Royal Society B, 337, 59 64. Kanizsa, G. (1974). Contours without gradients or cognitive contours? Italian Journal of Psychology, I, 93 112. Kanizsa, G. (1976). Subjective contours. Scientific American, 234, 48-52. Kanizsa, G. ( 1979). Organization in vision: Essays on Gestalt perception New York: Praeger. Kellman, P. J. & Shipley, T. F. (1991). A theory of visual interpolation in object perception. Cognitive Psychology, 23, 141 221. Kennedy, J: M. (1975). Depth at an edge, coplanarity, slant depth, change in direction and change in brightness in the production of subjective contours. Italian Journal o f Psychology, 2, 107-123. Kennedy, J. M. (1978). Illusory contours and the ends of lines. Perception, 7, 605 607. Kennedy, J. M. (1988). Line endings and subjective contours. Spatial Vision, 3, 151 158. Lesher, G. W. & Mingolla, E. (1993). The role of edges and lineends in illusory contour formation. Vision Research, 33, 22532270. Minguzzi, G. F. (1987). Anomalous figures and the tendency to continuation. In Petry, S. & Meyer, G. E. (Eds), The perception of illusory contours (pp. 71 75). New York: Springer-Verlag. Morgan, M. J. & Hotopf, W. H. N. (1989). Perceived diagonals in grids and lattices. Vision Research, 29, 1005-1015. Paradisco, M. A., Shimojo, S. & Nakayama, K. (1989). Subjective contours, tilt aftereffects, and visual cortical organization. Vision Research, 29, 1205 1213. Parks, T. E. (1980). Letter to the Editor. Perception, 9, 723. Perona, P. & Kooi, F. (1990). Illusory contour motion. Investigative Ophthalmology & Visual Sciences, 31, 531. (Abstr.) Peterhans, E. & von der Heydt, R. (1982). Cortical neuron responses and 'illusory' contours. Perception, 11, A19 (Abstr.). Peterhans, E. & von der Heydt, R. (1987). The role of end-stopped receptive fields in contour perception. In Eisner, J. & Creutzfeldt, O. (Eds), New .frontiers in brain research (p. 29). Stuttgart: Thieme (Abstr.). Peterhans, E. & v o n der Heydt, R. (1989a). Mechanisms of contour perception in monkey visual cortex. II. Contours bridging gaps. Journal of Neuroscienee, 9, 1749-1763. Peterhans, E. & v o n der Heydt, R. (1989b). The whole and the pieces---cortical neuron responses to bars and rows Of moving dots. In Kulikowski, J. J., Dickinson, C. M. & Murray, I. J. (Eds), Seeing contours and colour (pp. 125-130). Oxford: Pergamon Press. Peterhans, E. & v o n der Heydt, R. (1991a). Subjective contours-bridging the gap between psychophysics and physiology. Trends in Neuroscience, 14, 112 119. Peterhans, E. & yon der Heydt, R. (1991b). Elements of form perception in monkey prestriate cortex. In Gorea, A., Fr6gnac, Y., Kapoula, Z. & Findlay, J. (Eds), Representations o f vision: Trends and tacit assumptions in vision research (pp. 111-124),. Cambridge: Cambridge University Press:
115
Peterhans, E. & v o n der Heydt, R. (1993). Functional organization of Area V2 in the alert monkey. European Journal of Neuroscience, 5, 509-524. Peterhans, E., vonder Heydt, R. & Baumgartner, G. (1986). Neuronal responses to illusory contour stimuli reveal stages of visual cortical processing. In Pettigrew, J. D., Sanderson, K. J. & Levick, W. R. (Eds), Visual neuroscience (pp. 343-351. Cambridge: Cambridge University Press. Prazdny, K. (1983). Illusory contours are not caused by simultaneous rightness contrast. Perception & Psychophysics, 34, 403404. Redies, C. (1989). Discontinuities along lines: Psychophysics and neurophysiology. Neuroscience & Biobehavioral Reviews, 13, 17 22. Redies, C., Crook, J. M. & Creutzfeldt, O. D. (1986). Neuronal responses to borders with and without luminance gradients in cat visual cortex and dorsal lateral geniculate nucleus. Experimental Brain Research, 61, 469 481. Richardson, B. L. & Wuillemin, D. B. (1981). Illusory contours not accompanied by a brightness gradient. Italian Journal o f Psychology, 8, 201~07. Rieth, C. & Sireteanu, R. (1993). How do infants perceive subjective contours? Poster at the 4th Meeting of the Child Vision Research Society, Lyon, July 11-13, 1993. Sambin, M. (1974). Angular margins without gradients. Italian Journal of Psychology, 1, 355 361. Sambin, M. (1975). The rule of terminal tensions in th~ organization of margins without gradients. Italian Journal of Psychology, 6, 239-257. Sambin, M. (1977). Contouzs without gradient with different phenomenal evidence. Italian Journal of Psychology, 6, 121 147. Sambin, M. (1985). Figure anomale: La misura dell'ampiezza di una disomogeneitfi indotta. In Gerbino, W. (Ed.), Conoscenza e struttura: Festsehrift per Gaetano Kanizsa (pp. 437-452). Bologna: Ie Mulino. Sambin, M. (1987). A dynamic model of anomalous figures. In Petry, S. & Meyer, G. E. (Eds), The perception of illusory contours (pp. 131 142). New York: Springer-Verlag. Shipley, T. F. & Kellman, P. J. (1990). The role of discontinuities in the perception of subjective figures. Perception & Psychophysics, 48, 259-270. Shipley, T. F. & Kellman, P. J. (1992). Strength of visual interpolation depends on the ratio of physically specified to total edge length. Perception & Psychophysies, 52, 97 106. Takahashi, S., Kaihara, T., Takemoto, A., Ido, K. & Ejima, Y. (1992). Spectral sensitivities for illusory contour perception: A manifold linkage of chromatic and achromatic cues with the generation of contours. Vision Research, 32, 1709-1718. Vogels, R. & Orban, G. A. (1987). Illusory contour orientation discrimination. Vision Research, 27, 453 467. v o n d e r Heydt, R. & Peterhans, E. (1989a). Mechanisms of contour perception in monkey visual cortex. I. Lines of pattern discontinuity. Journal of Neuroscience, 9, 1731 1748. yon der Heydt, R. & Peterhans, E. (1989b). Cortical contour mechanisms and geometrical illusions. In Lain, D. M. & Gilbert, C. D. (Eds), Neural mechanisms of visual perception (pp. 157 170). The Woodlands: Portfolio Publishers. von der Heydt, R. & Peterhans, E. (1989c). Ehrenstein and Z611ner illusions in a neuronal theory of contour processing. In Kulikowski, J. J., Dickinson, C. M. & Murray, I. J. (Eds), Seeing contour and colour (pp. 729-734). Oxford: Pergamon Press. von der Heydt, R., Peterhans, E. & Baumgartner, G. (1984). Illusory contours and cortical neuron responses. Science, NY, 224, 1260-1262. Wade, N. (1982). The art and science of visual illusions (Figs 1.4.3 1.4.4; also Figs 1.2.17 1.2.22, 1.3.26, 1.3.29). London: Routledge & Kegan Paul. Another good example is Vasarely's Altair (1957-58). Ware, C. (1981). Subjective contours independent of subjective brightness. Perception & Psychophysics, 29, 500 504. Ware, C. & Kennedy, J. M. (1977). Illusory line linking solid rods. Perception, 6, 601 602.
116
MANUEL SORIANO et al.
Watanabe, T. & Sato, T. (1989). Effects of luminance contrast on color spreading and illusory contour in the neon color spreading effect. Perception & Psychophysics, 45, 427-430. Wilson, W. R. & Richards, W. A. (1992). Curvature and separation discrimination at texture boundaries. Journal of the Optical Society of America, A9, 1653-1662. Zucker, S. W. & Davis, S. (1988). Points and endpoints: A size/spacing constraint for dot grouping. Perception, 17, 229 247.
Acknowledgements~his manuscript was supported, in part, by Grants SFB 325, B3 and B4, from the Deutsche Forschungsgemeinschaft. S. Menees improved the English in the manuscript, B. Dresp
provided new data on the Ehrenstein illusion, and M. Teuber drew the authors' attention to related op-art phenomena. P. Bressan, W. Ehrenstein, E. Peterhans and C. Redies commented on an earlier draft. We thank them all.
APPENDIX For further studies of the abutting-grating illusion see Gibson (1950); Paradiso, Shimojo and Nakayama (1989); Perona and Kooi (1990); Prazdny (1983); Richardson and Wuillemin (1981); Sambin (1974, 1975, 1977, 1985, 1987); Ware (1981); Ware and Kennedy (1977); and Vogels and Orban (1987).