Perception, 1992, volume 21, pages 627-636
Amodal completion versus induced inhomogeneities in the organization of illusory figures Marco Davi, Baingio Pinna, Marco Sambin Dipartimento di Psicologia Generale, Universita di Padova, Piazza Capitaniato 3, 35139 Padova, Italy Received 25 July 1990, in revised form 25 January 1992
Abstract. An analysis is presented of a phenomenological model of illusory contours. The model is based on amodal completion as the primary factor giving rise to the illusory figure. In the experiment, conducted by the method of paired comparisons, the same parameter was manipulated in two series of equivalent configurations. The first series yielded examples of amodal completion, the second examples of illusory figures. Three groups of subjects evaluated the magnitude of completion, the brightness contrast of the illusory figure, and the contour clarity of the illusory figure. A control experiment was conducted, which demonstrated that in these configurations amodal completion and amodal continuation behave in the same way. Line displacement did not influence the brightness or the contour clarity of the illusory figures, though it influenced the magnitude of amodal completion. These results are in agreement with the energetic model developed by Sambin. 1 Introduction One of the first models of the formation of illusory figures (IF, such as the illusory triangle shown in figure 1) was formulated by Kanizsa (1955); it is based on amodal completion/ 1 ) Arguments in support of this hypothesis have been repeatedly put forward by Kanizsa and his colleagues (Kanizsa 1955; Kanizsa and Gerbino 1 9 8 1 ; Minguzzi 1984; Gerbino and Kanizsa 1987); elsewhere a modified version of it has been proposed (Kanizsa 1974, 1975, 1980; Minguzzi 1984). A further modification of Kanizsa's model has been propounded by Minguzzi (1987). Kanizsa (1955) observed that in situations that give rise to the formation of an IF a specific condition is always present, namely the presence of elements which in themselves are not perfectly regular, and so require a certain completion in order to reach regularity. But completion, to have an amodal character, needs an opaque occluding
V V Figure 1. Kanizsa's triangle. This is a classical example of an illusory figure. W Perceptual completion is termed amodal when visual qualities (form and colour) are absent in the completed area.
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surface, which arises in the absence of any stimulus discontinuity. This surface is unitary and it segregates at a different depth level from the background, along subjective contours that are constrained by the given figural conditions. In Kanizsa's (1974) article there is a revision of the 1955 hypothesis. Originally Kanizsa (1955) suggested that a tendency to attain maximum regularity was the important factor in completion, whereas in the 1974 model the main factor is no longer the tendency to geometrical regularity, but rather it is the tendency to closure of open structures. It may be noted here that the 1974 model goes actually one step further than the 1955 model, in claiming that the incomplete structures are the open structures. An alternative explanation, which we want to juxtapose to Kanizsa's, is the energetic model of the induced inhomogeneities proposed by Sambin (1974, 1978, 1981, 1987). This model (for a more exhaustive presentation see Sambin 1987) hypothesizes that every object in the visual field would generate an activation orthogonal to the object contour; at the point where two contours meet, given the directionality of activations, a gap will be created, which corresponds to a zone without activations. This is the zone of the induced inhomogeneity. A single induced inhomogeneity is below threshold, but when several of them are close to each other and in such an arrangement that they can unify, they generate an IF. In the case of lines, the direction of the activations is orthogonal to the line direction, and the induced inhomogeneity will be at the end of the line. As an example, in figure 2 the model predicts the formation of sixteen induced inhomogeneities (one for each end of each line), but only the eight inward ones are near enough to each other to unify, crossing the threshold level and yielding an IF. Our main experiment is intended to test the completion hypothesis. Some examples of IFs without amodal completion have already been provided, such as illusory edges at the right-angle corners of black and white bars or of squares of diminishing size (Kennedy and Chattaway 1975; Kennedy 1978; Day 1987). Day and Kasperczyk (1983) have also shown experimentally that IFs, although of reduced strength, can occur with regular and complete cross-like elements. Although these demonstrations show that the presence of amodal completion is not a necessary condition for the formation of an IF, and hence cannot be its only cause, they do not directly deny a causal role of amodal completion in the great number of IF configurations in which it is present. Hence in the present experiment we used configurations in which amodal completion is present, with the aim of checking if it plays a causal role. To this end, we manipulated one variable that affects the magnitude of the tendency to completion in
/i\ Figure 2. The eight inward inhomogeneities are close enough to each other to generate an illusory figure. The eight outward ones are not.
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order to see if there is a parallel modification in the brightness contrast or in the contour clarity of the IF. If amodal completion is the cause of the IF in our stimuli, by varying the degree of amodal completion we should obtain a parallel modification of the brightness of the IF or of its contour clarity. In the energetic theory, on the other hand, amodal completion is not a causal factor. For this model requires only that the inducers have proximal spatial arrangements, and this is present in all the IF stimuli used in this experiment. Thus this model would not predict a variation in the IF conditions, given a significant variation in the amodal completion condition. However, it must be said that a result in which the IF does not vary would also be in agreement with models based on the interpolation of the ends of the inducing lines (Gregory 1970, 1972, 1987; Rock and Anson 1979; Rock 1987). In fact, in the stimuli of the present experiment the ends of the inducing lines on each side of the IF will also be aligned, and so they will also be equally easily interpolated by straight contours. 2 Experiment We modified the same parameter (the displacement of the lines on the right side of the figure) in two series of equivalent configurations. The first series gives rise to examples of amodal completion (figure 3), the second to examples of illusory figures (figure 4). In addition, in the second series judgments were made about the brightness of the IF and the clarity of its contour, by two different groups of subjects, to determine the influence of variations of amodal completion. 2.1 Method 2.1.1 Subjects. Sixty psychology students of the Padova University served as subjects; twenty in the condition in which judgements were made about amodal completion, twenty in the condition with judgement of the brightness of the IF, and twenty in the condition with judgement of the clarity of the contour of the IF. 2.1.2 Stimuli. For the amodal completion condition the stimuli were rectangles (height, 11 cm; width, 3.3 cm) with the longer sides vertical. There were three lines which were orthogonal to each of the longer sides. The lines to the left were always placed at the centre of the side, whereas those to the right could be either at the centre or displaced downwards at four different levels (in total, five levels: 0, 4, 8, 12, and 16 mm; see figures 3a and 3b for the extreme stimuli in the series).
(a) (b) Figure 3. Stimuli from the amodal completion condition.
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The IF condition stimuli were the same rectangles in which the two longer sides were not drawn (five levels; see figures 4a and 4b for the extreme stimuli in these two series). Stimuli were drawn in black India ink (0.4 mm thick) on white paper (30 cm x 21 cm).
(a)
(b)
Figure 4. Stimuli from the illusory figure conditions. 2.1.3 Procedure. Apart from the difference in the stimuli, the procedure was the same in all conditions. The method of paired comparisons was used; only the pairing of the same stimuli was excluded, so there were two judgments for each of the remaining pairs, in one of which a particular stimulus appeared on the left and in the other on the right. The subject was seated in a black experimental booth. Pairs of stimuli were presented by the experimenter one at a time in random sequence, placed on a reading-desk at a distance of about 90 cm. Within the booth there was diffuse lighting of about 150 lux. Before the experimental session the subjects were shown classical examples of amodal completion configurations (figures similar to figure 3, in which instead of the three lines, on each side of the central rectangle there were two small rectangles, at several different orientations) or of IFs (two figures similar to figure 2, one drawn with thick lines and one with thin lines), depending on the group to which they were assigned, in order to explain to them the nature of the judgements. The subjects were given the following instructions: (i) Amodal completion condition "In the example there are figures formed from a large central rectangle with two smaller rectangles at its sides. The two little rectangles can be seen as separated or joining. In each figure there is a larger or smaller tendency for the two rectangles to join. I shall show you figures in which there are some lines instead of the two little rectangles. The lines, however, as well as the rectangles in the example have a tendency to join, of different magnitude in the different cases. These figures will be shown in pairs and your task is to indicate (by saying 'left' or 'right') in which of the two elements in the pair the tendency of the lines to join is greater." (ii) IF brightness "Looking at the figures in the example (illusory figures) you can see that there is a difference between the white inside the disk and that of the background. Now I shall show you figures in which instead of the disk there are other figures. However, they will also be illusory figures. These figures will be shown in pairs and your task is to indicate (by saying 'left' or 'right') in which of the two elements in the pair the difference in brightness is greater."
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(iii) Clarity of the IF contours "Looking at the figures in the example (illusory figures) you can see two white disks covering a stellar figure. In one figure the contour is very sharp (figure with thick lines), while in the other it is less sharp (figure with thin lines). Now I shall show you figures in which instead of the disk there are other figures. However, they will also be illusory figures. These figures will be shown in pairs and your task is to indicate (by saying 'left' or 'right') in which of the two elements in the pair the contour is sharper." 2.2 Results T h e proportions in which figures were chosen were converted into scale values by the method of Thurstone (see Guilford 1971). T h e scale values are reported in table 1. Regressions for each series of data (on positive scale values) were estimated, and their significance was statistically evaluated. For the amodal completion and the brightness of the IF conditions the data were fitted with a linear equation; in these cases a confidence interval (p = 0.05) for the slopes of the lines is given. T h e data for the clarity of the IF contours are well described by a third-order equation. T h e results for the three conditions (see also figured) are as follows: (i) Amodal completion Regression line (r = 0.99): A = - 0 . 3 0 1 D + 5.042, where A is the tendency to amodal completion, and D is the displacement of lines. Table 1. Scale values for the amodal completion and the two IF conditions, for the different levels of line displacement. Line displacement, D/mm
Condition
0
Amodal completion IF brightness IF contour clarity
5.3 0.72 0.66
3.1 0.14 0
2.8 0.15 0.29
12
16
2.1 0.20 0.53
0 0 0.19
amodal completion IF brightness IF contour clarity
4 f
2 I
0
0
4 8 12 16 Displacement of lines/mm Figure 5. Regressions for the amodal completion condition and the two illusory figure conditions.
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Slope of line significant (p = 0.0085); confidence interval of the slope (p = 0.05) from-0.441 t o - 0 . 1 4 2 . (ii) IF brightness Regression line {r = 0.92): B = -0.036D + 0.533, where B is brightness contrast, and D is the displacement of lines. Slope of line not significant; confidence interval of the slope (p = 0.05) from -0.084 to +0.014. (iii) Clarity of the IF contours Regression equation (r = 0.99): C = -0.002£> 3 + 0.051£> 2 -0.328D + 0.654 where C is contour clarity, D is the displacement of lines; difference between values not significant. 2.3 Discussion From the analyses it can be seen that the factor D (displacement of lines) has a significant effect only on amodal completion. When the lines on each side are aligned, the tendency to completion is maximum, and the tendency diminishes as the displacement of lines increases. The subject can meaningfully distinguish different degrees of amodal completion. The displacement of lines has no effect on the brightness contrast of the IF, nor on its contour clarity. In short, the stimulus variations produced a variation in the magnitude of the tendency to completion, but had no effect on the brightness contrast of the IF or on the clarity of its contours. Given that a significant variation in the amount of amodal completion yielded no change in two parameters of the IF, a causal dependence of the IF on amodal completion seems unlikely. 3 Amodal continuation There is an hypothesis, formulated by Minguzzi (1984, 1987), which is an extension of Kanizsa's and which seems able to account for our results. This hypothesis can also account for IFs induced by lines, which are not treated by Kanizsa's model. For a definition of amodal continuation, we quote the author: "It is more suitable to speak of a tendency to continuation rather than a tendency to figural completion. This reformulation seems necessary for two reasons. First, the word completion implies the concepts incompleteness and gap. In the classical Kanizsa triangle, and in many other displays, the incompleteness of the inducing figures is obvious ... However, this does not always happen ... Second, the outcome of amodal presence behind the anomalous surface is not always a completion ... But what happens in every case is the continuation of the inducing figure beyond its physical edge, ie behind the anomalous figure. This continuation sometimes completes the inducing figure or unifies it with another, and sometimes it is only a figural spread, obviously amodal." (Minguzzi 1987, page 71). Hence, it is possible that in the case reported here there was a difference in the tendency to completion (related to the different likelihood that the lines on one side are unified with those on the other), but there was no difference in the amount of continuation in the lines behind the surface. In order to test this possibility the following control experiment was carried out.
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4 Control experiment Two conditions were used. The first was intended to test whether with the stimuli of the amodal completion condition of the preceding experiment there is also a variation in the magnitude of the tendency to amodal continuation of the lines orthogonal to the sides of the rectangle. In the second condition the stimuli of the IF condition of the preceding experiment were used (see figure 4); but now the subjects were asked for the amount of continuation of the lines orthogonal to the sides of the illusory rectangle. 4.1 Method 4.1.1 Subjects. Forty psychology students of the Padova University served as subjects, twenty in each condition. 4.1.2 Stimuli. For the first condition (continuation with modal rectangle) the stimuli were the same as in the amodal completion condition of the preceding experiment. In the second condition (continuation with illusory rectangle) the stimuli were the same as in the IF condition of the preceding experiment. 4.1.2 Procedure. The procedure was the same as in the preceding experiment. Before the experimental session the subjects were shown classical examples of amodal continuation configurations (rectangles with a rectangle of different width and length or with a single line of different length on one side), in order to explain to them the nature of the judgements. The instructions in the continuation with modal rectangle condition were the following: "In the example there are figures formed from a large rectangle and a line or a small rectangle. The lines and the small rectangles can be seen as terminating at the edge of the large rectangle or continuing behind it. Their tendency to continue is different in the different figures. Now I shall show figures which contain only lines. These figures will be shown in pairs and your task is to indicate (by saying 'left' or 'right') in which of the two elements in the pair the tendency of the lines to continue is greater." In the continuation with illusory rectangle condition the instructions were the same, except that it was added that the large rectangle was going to be an IF and that Kanizsa's triangle was shown as an example of an IF. 4.2 Results The proportions in which figures were chosen were converted into scale values by the method of Thurstone (see Guilford 1971). Scale values are reported in table 2. Linear regressions for each of the two series of data (on positive scale values) were estimated, and the significance of their slopes was statistically evaluated (versus the null hypothesis of a horizontal line); finally, a confidence interval (p = 0.05) for the slopes of the two lines was calculated. The results for the two conditions are as Table 2. Scale values for the amodal continuation conditions, with the modal rectangle and with the illusory rectangle. Amodal continuation condition
With modal rectangle With illusory rectangle
Line displacement, D/mm 0
4
8
12
16
3.1 1.5
1.8 0.63
1.4 0.59
0.90 0.35
0 0
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follows (see also figure 6): (a) Continuation with modal rectangle Regression line (r = 0.98): T = -0.178D +2.863, where T is the tendency to continuation, and D is the displacement of lines. Slope of line significant (p = 0.0044); confidence interval of the slope (p = 0.05) from -0.25 to -0.105. (b) Continuation with illusory rectangle Regression line (r = 0.93): T = -0.082D + 1.276. Slope of line significant {p = 0.0199); confidence interval of the slope (p = 0.05) from - 0 . 1 4 t o -0.025. Amodal continuation with modal rectangle with anomalous rectangle J2
2
co
1
0
|
~ ^
0 4 8 12 16 Displacement of lines/mm
Figure 6. Regression lines for the amodal continuation conditions, with the modal rectangle and with the illusory rectangle. 4.3 Discussion From the analyses it can be seen that the factor D (displacement of lines) has a significant effect on the tendency to continuation in both situations. Furthermore, the tendency to continuation decreases linearly as the displacement of lines increases, just as the tendency to completion did in the previous experiment. Hence, the distinction between amodal completion and amodal continuation, introduced by Minguzzi to extend Kanizsa's model, is just a distinction in terminology, at least as far as our conditions are concerned. Empirically, they behave exactly in the same way. Moreover, now it is clear that the variation in continuation that was present in the amodal completion condition of the preceding experiment is also present with the illusory rectangles with which we obtained the scaling of the brightness contrast of the IF. In short, all the data obtained in the second experiment support the conclusions drawn in the first one. 5 General discussion Before evaluating our data we wish to comment on two previous studies concerned with the role of completion in the formation of IFs. One study with the aim of testing Kanizsa's model is by Purghe (1989). Purghe points out two kinds of theoretical situations that could falsify the model: (a) complete figural inducers that give rise to an IF; and (b) incomplete figural inducers that do not give rise to an IF.
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Purghe did not find any examples of (a), but he did find examples of (b). However, the discovery of examples of type (b) is, in our opinion, irrelevant to the falsification of the model, for a logical reason. In fact, the causal relationship proposed by Kanizsa (completion => IF) has to be translated logically in the implication (IF ^ completion). Purghe (1989), instead, treats the relationship as if it were a bi-implication. It is obvious that, since the relationship is a simple implication, the only case that falsifies it is the case in which there is an IF without a completion [situation (a)]. Kanizsa (1955, 1974) avoided this problem; in fact, he claimed to have found completion in every case in which there was an IF, and not that where there was completion an IF should be present. Situation (a) on the other hand, as Purghe says, is difficult to assess. We agree with this opinion. Returning to Kanizsa's (1955, 1974) model, it could be asked why it is so hard to find a situation that directly falsifies the model, ie a case in which the figural conditions yield an IF without the presence of amodal completion of the inducers. In our opinion, this is because amodal completion is a co-present phenomenon in the perception of IFs. Reversing Kanizsa's argument, it can be said that, given the IF, the inducers have a certain tendency (sometimes, however, very small) to complete themselves behind it. Among other things, in this way amodal completion in the case of IFs can be considered to be the same thing as completion in the case of modal figures. This way of considering completion in IFs can also be found in Gregory (1970, 1972, 1987). We agree with this view of completion, but Gregory's model of IF, being probabilistic, is clearly different from our energetic model. Watanabe and Oyama (1988) tried to determine the causal flow in the process of the formation of the IF. They used as a stimulus Kanizsa's square, and the factors they varied were the luminance of the disks (the inducers) and the separation between the nearest disks. They used the causal inference method, which was originally proposed by Simon (1954) and developed by Blalock (1962); this method, in which partial correlation is used, is especially effective in classifying the causal flows between variables. They found that the output of the process responsible for illusory contour clarity has some effect on the processes responsible for the apparent depth and the brightness difference between the framed area and the surroundings. This result is contrary to Kanizsa's model because Kanizsa claimed that stratification gives rise to contours. Here, instead, it has been found that the output of the contour formation process is involved in the stratification process. The results obtained by us in the IF conditions can be well interpreted within the energetic theory of induced inhomogeneities (Sambin 1974, 1978, 1981, 1987) quoted above. In fact, given that this model does not refer to amodal completion nor to the alignment of the inducers, the model predicts an IF with the same brightness contrast and the same contour clarity in all the stimuli used in this work, and this is what actually happens. The only constraint required by the model in order to have an IF is a certain spatial proximity among inducers, and this has been demonstrated to be a major factor in the formation of IFs by other authors also (Dumais and Bradley 1976). Finally, we can state that this model can predict the data obtained in this work, and we think that it is, at present, a useful model for the available data on illusory figures. Acknowledgments: We thank Professor G Kanizsa for having suggested the first condition of the control experiment.
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References BlalockHM, 1962 "Four-variable causal models and partial correlations" American Journal of Sociology 68 182-194 Day R H , 1987 "Cues for edge and the origin of illusory contours: an alternative approach" in The Perception of Illusory Contours Eds S Petry, G E Meyer (New York: Springer-Verlag) pp 5 3 - 6 1 Day R H, Kasperczyk R T, 1983 "Amodal completion as a basis for illusory contours" Perception ScPsychophysics 3 3 3 5 5 - 3 6 4 DumaisST, Bradley D R, 1976 "The effects of illumination level and retinal size on the apparent strength of subjective contours" Perception &Psychophysics 19 339 - 345 Gerbino W, Kanizsa G, 1987 "Can we seen constructs?" in The Perception of Illusory Contours Eds S Petry, G E Meyer (New York: Springer-Verlag) pp 246 - 252 Gregory R L , 1970 The Intelligent Eye (London: Weidenfeld & Nicholson; New York: McGrawHill) Gregory R L, 1972 "Cognitive contours" Nature (London) 238 5 1 - 5 2 Gregory R L , 1987 "Illusory contours and occluding surfaces" in The Perception of Illusory Contours Eds S Petry, G E Meyer (New York: Springer-Verlag) pp 81 - 89 Guilford J P, 1971 Psychometric Methods (New York: McGraw-Hill) Kanizsa G, 1955 "Margini quasi-percettivi in campi con stimolazione omogenea" Rivista di Psicologia 49 7 - 30 Kanizsa G, 1974 "Contours without gradients or cognitive contours?" Italian Journal of Psychology 1 9 3 - 1 1 3 Kanizsa G, 1975 "The role of regularity in perceptual organization" in Studies in Perception: Festschrift for Fabio Metelli Ed. G Flores d'Arcais (Milano: Martello-Giunti) pp 48 - 66 Kanizsa G, 1980 Grammatica del Vedere (Bologna: II Mulino) Kanizsa G, Gerbino W, 1981 "II completamento amodale tra vedere e pensare" Giornale Italiano di Psicologia 8 297-307 Kennedy J M, 1978 "Illusory contours not due to completion" Perception 7 1 8 7 - 1 8 9 Kennedy J M, ChattawayLD, 1975 "Subjective contours, binocular and movement phenomena" Italian Journal of Psychology 2 3 5 3 - 3 6 7 Minguzzi G, 1984 "La percezione di superfici anomale" in Fenomenologia sperimentale della visione Ed. G Kanizsa (Milano: Franco Angeli) pp 97 -118 Minguzzi G, 1987 "Anomalous figures and the tendency to continuation" in The Perception of Illusory Contours Eds S Petry, G E Meyer (New York: Springer-Verlag) pp 71 - 75 PurgheF, 1989 "II ruolo della completezza figurale e del completamento amodale nella formazione di superfici anomale" Giornale Italiano di Psicologia 16 101-118 Rock I, 1987 "A problem-solving approach to illusory contours" in The Perception of Illusory Contours Eds S Petry, G E Meyer (New York: Springer-Verlag) pp 62 - 70 Rock I, Anson R, 1979 "Illusory contours as the solution to a problem" Perception 8 125 -134 Sambin M, 1974 "Angular margins without gradient" Italian Journal of Psychology 1 355-361 Sambin M, 1978 "II contrasto di chiarezza nelle figure anomale" Giornale Italiano di Psicologia 3 543-564 Sambin M, 1981 On the threshold measurement of anomalous figures (Padova: Istituto di Psicologia, Universita di Padova, Report No. 30) pp 1-16 Sambin M, 1987 "A dynamic model of anomalous figures" in The Perception of Illusory Contours Eds S Petry, G E Meyer (New York: Springer-Verlag) pp 131 -142 Simon HA, 1954 "Spurious correlation: A causal interpretation" Journal of the American Statistical Association 49 467 - 479 Watanabe T, Oyama T, 1988 "Are illusory contours a cause or a consequence of apparent differences in brightness and depth in the Kanizsa's square?" Perception 1 7 5 1 3 - 5 2 1
© 1992 a Pion publication printed in Great Britain
Amodal completion versus induced inhomogeneities in the organization of illusory figures Marco Davi, Baingio Pinna, Marco Sambin Dipartimento di Psicologia Generale, Universita di Padova, Piazza Capitaniato 3, 35139 Padova, Italy Received 25 July 1990, in revised form 25 January 1992
Abstract. An analysis is presented of a phenomenological model of illusory contours. The model is based on amodal completion as the primary factor giving rise to the illusory figure. In the experiment, conducted by the method of paired comparisons, the same parameter was manipulated in two series of equivalent configurations. The first series yielded examples of amodal completion, the second examples of illusory figures. Three groups of subjects evaluated the magnitude of completion, the brightness contrast of the illusory figure, and the contour clarity of the illusory figure. A control experiment was conducted, which demonstrated that in these configurations amodal completion and amodal continuation behave in the same way. Line displacement did not influence the brightness or the contour clarity of the illusory figures, though it influenced the magnitude of amodal completion. These results are in agreement with the energetic model developed by Sambin. 1 Introduction One of the first models of the formation of illusory figures (IF, such as the illusory triangle shown in figure 1) was formulated by Kanizsa (1955); it is based on amodal completion/ 1 ) Arguments in support of this hypothesis have been repeatedly put forward by Kanizsa and his colleagues (Kanizsa 1955; Kanizsa and Gerbino 1 9 8 1 ; Minguzzi 1984; Gerbino and Kanizsa 1987); elsewhere a modified version of it has been proposed (Kanizsa 1974, 1975, 1980; Minguzzi 1984). A further modification of Kanizsa's model has been propounded by Minguzzi (1987). Kanizsa (1955) observed that in situations that give rise to the formation of an IF a specific condition is always present, namely the presence of elements which in themselves are not perfectly regular, and so require a certain completion in order to reach regularity. But completion, to have an amodal character, needs an opaque occluding
V V Figure 1. Kanizsa's triangle. This is a classical example of an illusory figure. W Perceptual completion is termed amodal when visual qualities (form and colour) are absent in the completed area.
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surface, which arises in the absence of any stimulus discontinuity. This surface is unitary and it segregates at a different depth level from the background, along subjective contours that are constrained by the given figural conditions. In Kanizsa's (1974) article there is a revision of the 1955 hypothesis. Originally Kanizsa (1955) suggested that a tendency to attain maximum regularity was the important factor in completion, whereas in the 1974 model the main factor is no longer the tendency to geometrical regularity, but rather it is the tendency to closure of open structures. It may be noted here that the 1974 model goes actually one step further than the 1955 model, in claiming that the incomplete structures are the open structures. An alternative explanation, which we want to juxtapose to Kanizsa's, is the energetic model of the induced inhomogeneities proposed by Sambin (1974, 1978, 1981, 1987). This model (for a more exhaustive presentation see Sambin 1987) hypothesizes that every object in the visual field would generate an activation orthogonal to the object contour; at the point where two contours meet, given the directionality of activations, a gap will be created, which corresponds to a zone without activations. This is the zone of the induced inhomogeneity. A single induced inhomogeneity is below threshold, but when several of them are close to each other and in such an arrangement that they can unify, they generate an IF. In the case of lines, the direction of the activations is orthogonal to the line direction, and the induced inhomogeneity will be at the end of the line. As an example, in figure 2 the model predicts the formation of sixteen induced inhomogeneities (one for each end of each line), but only the eight inward ones are near enough to each other to unify, crossing the threshold level and yielding an IF. Our main experiment is intended to test the completion hypothesis. Some examples of IFs without amodal completion have already been provided, such as illusory edges at the right-angle corners of black and white bars or of squares of diminishing size (Kennedy and Chattaway 1975; Kennedy 1978; Day 1987). Day and Kasperczyk (1983) have also shown experimentally that IFs, although of reduced strength, can occur with regular and complete cross-like elements. Although these demonstrations show that the presence of amodal completion is not a necessary condition for the formation of an IF, and hence cannot be its only cause, they do not directly deny a causal role of amodal completion in the great number of IF configurations in which it is present. Hence in the present experiment we used configurations in which amodal completion is present, with the aim of checking if it plays a causal role. To this end, we manipulated one variable that affects the magnitude of the tendency to completion in
/i\ Figure 2. The eight inward inhomogeneities are close enough to each other to generate an illusory figure. The eight outward ones are not.
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order to see if there is a parallel modification in the brightness contrast or in the contour clarity of the IF. If amodal completion is the cause of the IF in our stimuli, by varying the degree of amodal completion we should obtain a parallel modification of the brightness of the IF or of its contour clarity. In the energetic theory, on the other hand, amodal completion is not a causal factor. For this model requires only that the inducers have proximal spatial arrangements, and this is present in all the IF stimuli used in this experiment. Thus this model would not predict a variation in the IF conditions, given a significant variation in the amodal completion condition. However, it must be said that a result in which the IF does not vary would also be in agreement with models based on the interpolation of the ends of the inducing lines (Gregory 1970, 1972, 1987; Rock and Anson 1979; Rock 1987). In fact, in the stimuli of the present experiment the ends of the inducing lines on each side of the IF will also be aligned, and so they will also be equally easily interpolated by straight contours. 2 Experiment We modified the same parameter (the displacement of the lines on the right side of the figure) in two series of equivalent configurations. The first series gives rise to examples of amodal completion (figure 3), the second to examples of illusory figures (figure 4). In addition, in the second series judgments were made about the brightness of the IF and the clarity of its contour, by two different groups of subjects, to determine the influence of variations of amodal completion. 2.1 Method 2.1.1 Subjects. Sixty psychology students of the Padova University served as subjects; twenty in the condition in which judgements were made about amodal completion, twenty in the condition with judgement of the brightness of the IF, and twenty in the condition with judgement of the clarity of the contour of the IF. 2.1.2 Stimuli. For the amodal completion condition the stimuli were rectangles (height, 11 cm; width, 3.3 cm) with the longer sides vertical. There were three lines which were orthogonal to each of the longer sides. The lines to the left were always placed at the centre of the side, whereas those to the right could be either at the centre or displaced downwards at four different levels (in total, five levels: 0, 4, 8, 12, and 16 mm; see figures 3a and 3b for the extreme stimuli in the series).
(a) (b) Figure 3. Stimuli from the amodal completion condition.
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The IF condition stimuli were the same rectangles in which the two longer sides were not drawn (five levels; see figures 4a and 4b for the extreme stimuli in these two series). Stimuli were drawn in black India ink (0.4 mm thick) on white paper (30 cm x 21 cm).
(a)
(b)
Figure 4. Stimuli from the illusory figure conditions. 2.1.3 Procedure. Apart from the difference in the stimuli, the procedure was the same in all conditions. The method of paired comparisons was used; only the pairing of the same stimuli was excluded, so there were two judgments for each of the remaining pairs, in one of which a particular stimulus appeared on the left and in the other on the right. The subject was seated in a black experimental booth. Pairs of stimuli were presented by the experimenter one at a time in random sequence, placed on a reading-desk at a distance of about 90 cm. Within the booth there was diffuse lighting of about 150 lux. Before the experimental session the subjects were shown classical examples of amodal completion configurations (figures similar to figure 3, in which instead of the three lines, on each side of the central rectangle there were two small rectangles, at several different orientations) or of IFs (two figures similar to figure 2, one drawn with thick lines and one with thin lines), depending on the group to which they were assigned, in order to explain to them the nature of the judgements. The subjects were given the following instructions: (i) Amodal completion condition "In the example there are figures formed from a large central rectangle with two smaller rectangles at its sides. The two little rectangles can be seen as separated or joining. In each figure there is a larger or smaller tendency for the two rectangles to join. I shall show you figures in which there are some lines instead of the two little rectangles. The lines, however, as well as the rectangles in the example have a tendency to join, of different magnitude in the different cases. These figures will be shown in pairs and your task is to indicate (by saying 'left' or 'right') in which of the two elements in the pair the tendency of the lines to join is greater." (ii) IF brightness "Looking at the figures in the example (illusory figures) you can see that there is a difference between the white inside the disk and that of the background. Now I shall show you figures in which instead of the disk there are other figures. However, they will also be illusory figures. These figures will be shown in pairs and your task is to indicate (by saying 'left' or 'right') in which of the two elements in the pair the difference in brightness is greater."
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(iii) Clarity of the IF contours "Looking at the figures in the example (illusory figures) you can see two white disks covering a stellar figure. In one figure the contour is very sharp (figure with thick lines), while in the other it is less sharp (figure with thin lines). Now I shall show you figures in which instead of the disk there are other figures. However, they will also be illusory figures. These figures will be shown in pairs and your task is to indicate (by saying 'left' or 'right') in which of the two elements in the pair the contour is sharper." 2.2 Results T h e proportions in which figures were chosen were converted into scale values by the method of Thurstone (see Guilford 1971). T h e scale values are reported in table 1. Regressions for each series of data (on positive scale values) were estimated, and their significance was statistically evaluated. For the amodal completion and the brightness of the IF conditions the data were fitted with a linear equation; in these cases a confidence interval (p = 0.05) for the slopes of the lines is given. T h e data for the clarity of the IF contours are well described by a third-order equation. T h e results for the three conditions (see also figured) are as follows: (i) Amodal completion Regression line (r = 0.99): A = - 0 . 3 0 1 D + 5.042, where A is the tendency to amodal completion, and D is the displacement of lines. Table 1. Scale values for the amodal completion and the two IF conditions, for the different levels of line displacement. Line displacement, D/mm
Condition
0
Amodal completion IF brightness IF contour clarity
5.3 0.72 0.66
3.1 0.14 0
2.8 0.15 0.29
12
16
2.1 0.20 0.53
0 0 0.19
amodal completion IF brightness IF contour clarity
4 f
2 I
0
0
4 8 12 16 Displacement of lines/mm Figure 5. Regressions for the amodal completion condition and the two illusory figure conditions.
M Davi, B Pinna, M Sambin
Slope of line significant (p = 0.0085); confidence interval of the slope (p = 0.05) from-0.441 t o - 0 . 1 4 2 . (ii) IF brightness Regression line {r = 0.92): B = -0.036D + 0.533, where B is brightness contrast, and D is the displacement of lines. Slope of line not significant; confidence interval of the slope (p = 0.05) from -0.084 to +0.014. (iii) Clarity of the IF contours Regression equation (r = 0.99): C = -0.002£> 3 + 0.051£> 2 -0.328D + 0.654 where C is contour clarity, D is the displacement of lines; difference between values not significant. 2.3 Discussion From the analyses it can be seen that the factor D (displacement of lines) has a significant effect only on amodal completion. When the lines on each side are aligned, the tendency to completion is maximum, and the tendency diminishes as the displacement of lines increases. The subject can meaningfully distinguish different degrees of amodal completion. The displacement of lines has no effect on the brightness contrast of the IF, nor on its contour clarity. In short, the stimulus variations produced a variation in the magnitude of the tendency to completion, but had no effect on the brightness contrast of the IF or on the clarity of its contours. Given that a significant variation in the amount of amodal completion yielded no change in two parameters of the IF, a causal dependence of the IF on amodal completion seems unlikely. 3 Amodal continuation There is an hypothesis, formulated by Minguzzi (1984, 1987), which is an extension of Kanizsa's and which seems able to account for our results. This hypothesis can also account for IFs induced by lines, which are not treated by Kanizsa's model. For a definition of amodal continuation, we quote the author: "It is more suitable to speak of a tendency to continuation rather than a tendency to figural completion. This reformulation seems necessary for two reasons. First, the word completion implies the concepts incompleteness and gap. In the classical Kanizsa triangle, and in many other displays, the incompleteness of the inducing figures is obvious ... However, this does not always happen ... Second, the outcome of amodal presence behind the anomalous surface is not always a completion ... But what happens in every case is the continuation of the inducing figure beyond its physical edge, ie behind the anomalous figure. This continuation sometimes completes the inducing figure or unifies it with another, and sometimes it is only a figural spread, obviously amodal." (Minguzzi 1987, page 71). Hence, it is possible that in the case reported here there was a difference in the tendency to completion (related to the different likelihood that the lines on one side are unified with those on the other), but there was no difference in the amount of continuation in the lines behind the surface. In order to test this possibility the following control experiment was carried out.
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4 Control experiment Two conditions were used. The first was intended to test whether with the stimuli of the amodal completion condition of the preceding experiment there is also a variation in the magnitude of the tendency to amodal continuation of the lines orthogonal to the sides of the rectangle. In the second condition the stimuli of the IF condition of the preceding experiment were used (see figure 4); but now the subjects were asked for the amount of continuation of the lines orthogonal to the sides of the illusory rectangle. 4.1 Method 4.1.1 Subjects. Forty psychology students of the Padova University served as subjects, twenty in each condition. 4.1.2 Stimuli. For the first condition (continuation with modal rectangle) the stimuli were the same as in the amodal completion condition of the preceding experiment. In the second condition (continuation with illusory rectangle) the stimuli were the same as in the IF condition of the preceding experiment. 4.1.2 Procedure. The procedure was the same as in the preceding experiment. Before the experimental session the subjects were shown classical examples of amodal continuation configurations (rectangles with a rectangle of different width and length or with a single line of different length on one side), in order to explain to them the nature of the judgements. The instructions in the continuation with modal rectangle condition were the following: "In the example there are figures formed from a large rectangle and a line or a small rectangle. The lines and the small rectangles can be seen as terminating at the edge of the large rectangle or continuing behind it. Their tendency to continue is different in the different figures. Now I shall show figures which contain only lines. These figures will be shown in pairs and your task is to indicate (by saying 'left' or 'right') in which of the two elements in the pair the tendency of the lines to continue is greater." In the continuation with illusory rectangle condition the instructions were the same, except that it was added that the large rectangle was going to be an IF and that Kanizsa's triangle was shown as an example of an IF. 4.2 Results The proportions in which figures were chosen were converted into scale values by the method of Thurstone (see Guilford 1971). Scale values are reported in table 2. Linear regressions for each of the two series of data (on positive scale values) were estimated, and the significance of their slopes was statistically evaluated (versus the null hypothesis of a horizontal line); finally, a confidence interval (p = 0.05) for the slopes of the two lines was calculated. The results for the two conditions are as Table 2. Scale values for the amodal continuation conditions, with the modal rectangle and with the illusory rectangle. Amodal continuation condition
With modal rectangle With illusory rectangle
Line displacement, D/mm 0
4
8
12
16
3.1 1.5
1.8 0.63
1.4 0.59
0.90 0.35
0 0
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follows (see also figure 6): (a) Continuation with modal rectangle Regression line (r = 0.98): T = -0.178D +2.863, where T is the tendency to continuation, and D is the displacement of lines. Slope of line significant (p = 0.0044); confidence interval of the slope (p = 0.05) from -0.25 to -0.105. (b) Continuation with illusory rectangle Regression line (r = 0.93): T = -0.082D + 1.276. Slope of line significant {p = 0.0199); confidence interval of the slope (p = 0.05) from - 0 . 1 4 t o -0.025. Amodal continuation with modal rectangle with anomalous rectangle J2
2
co
1
0
|
~ ^
0 4 8 12 16 Displacement of lines/mm
Figure 6. Regression lines for the amodal continuation conditions, with the modal rectangle and with the illusory rectangle. 4.3 Discussion From the analyses it can be seen that the factor D (displacement of lines) has a significant effect on the tendency to continuation in both situations. Furthermore, the tendency to continuation decreases linearly as the displacement of lines increases, just as the tendency to completion did in the previous experiment. Hence, the distinction between amodal completion and amodal continuation, introduced by Minguzzi to extend Kanizsa's model, is just a distinction in terminology, at least as far as our conditions are concerned. Empirically, they behave exactly in the same way. Moreover, now it is clear that the variation in continuation that was present in the amodal completion condition of the preceding experiment is also present with the illusory rectangles with which we obtained the scaling of the brightness contrast of the IF. In short, all the data obtained in the second experiment support the conclusions drawn in the first one. 5 General discussion Before evaluating our data we wish to comment on two previous studies concerned with the role of completion in the formation of IFs. One study with the aim of testing Kanizsa's model is by Purghe (1989). Purghe points out two kinds of theoretical situations that could falsify the model: (a) complete figural inducers that give rise to an IF; and (b) incomplete figural inducers that do not give rise to an IF.
Amodal completion in illusory figures
635
Purghe did not find any examples of (a), but he did find examples of (b). However, the discovery of examples of type (b) is, in our opinion, irrelevant to the falsification of the model, for a logical reason. In fact, the causal relationship proposed by Kanizsa (completion => IF) has to be translated logically in the implication (IF ^ completion). Purghe (1989), instead, treats the relationship as if it were a bi-implication. It is obvious that, since the relationship is a simple implication, the only case that falsifies it is the case in which there is an IF without a completion [situation (a)]. Kanizsa (1955, 1974) avoided this problem; in fact, he claimed to have found completion in every case in which there was an IF, and not that where there was completion an IF should be present. Situation (a) on the other hand, as Purghe says, is difficult to assess. We agree with this opinion. Returning to Kanizsa's (1955, 1974) model, it could be asked why it is so hard to find a situation that directly falsifies the model, ie a case in which the figural conditions yield an IF without the presence of amodal completion of the inducers. In our opinion, this is because amodal completion is a co-present phenomenon in the perception of IFs. Reversing Kanizsa's argument, it can be said that, given the IF, the inducers have a certain tendency (sometimes, however, very small) to complete themselves behind it. Among other things, in this way amodal completion in the case of IFs can be considered to be the same thing as completion in the case of modal figures. This way of considering completion in IFs can also be found in Gregory (1970, 1972, 1987). We agree with this view of completion, but Gregory's model of IF, being probabilistic, is clearly different from our energetic model. Watanabe and Oyama (1988) tried to determine the causal flow in the process of the formation of the IF. They used as a stimulus Kanizsa's square, and the factors they varied were the luminance of the disks (the inducers) and the separation between the nearest disks. They used the causal inference method, which was originally proposed by Simon (1954) and developed by Blalock (1962); this method, in which partial correlation is used, is especially effective in classifying the causal flows between variables. They found that the output of the process responsible for illusory contour clarity has some effect on the processes responsible for the apparent depth and the brightness difference between the framed area and the surroundings. This result is contrary to Kanizsa's model because Kanizsa claimed that stratification gives rise to contours. Here, instead, it has been found that the output of the contour formation process is involved in the stratification process. The results obtained by us in the IF conditions can be well interpreted within the energetic theory of induced inhomogeneities (Sambin 1974, 1978, 1981, 1987) quoted above. In fact, given that this model does not refer to amodal completion nor to the alignment of the inducers, the model predicts an IF with the same brightness contrast and the same contour clarity in all the stimuli used in this work, and this is what actually happens. The only constraint required by the model in order to have an IF is a certain spatial proximity among inducers, and this has been demonstrated to be a major factor in the formation of IFs by other authors also (Dumais and Bradley 1976). Finally, we can state that this model can predict the data obtained in this work, and we think that it is, at present, a useful model for the available data on illusory figures. Acknowledgments: We thank Professor G Kanizsa for having suggested the first condition of the control experiment.
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References BlalockHM, 1962 "Four-variable causal models and partial correlations" American Journal of Sociology 68 182-194 Day R H , 1987 "Cues for edge and the origin of illusory contours: an alternative approach" in The Perception of Illusory Contours Eds S Petry, G E Meyer (New York: Springer-Verlag) pp 5 3 - 6 1 Day R H, Kasperczyk R T, 1983 "Amodal completion as a basis for illusory contours" Perception ScPsychophysics 3 3 3 5 5 - 3 6 4 DumaisST, Bradley D R, 1976 "The effects of illumination level and retinal size on the apparent strength of subjective contours" Perception &Psychophysics 19 339 - 345 Gerbino W, Kanizsa G, 1987 "Can we seen constructs?" in The Perception of Illusory Contours Eds S Petry, G E Meyer (New York: Springer-Verlag) pp 246 - 252 Gregory R L , 1970 The Intelligent Eye (London: Weidenfeld & Nicholson; New York: McGrawHill) Gregory R L, 1972 "Cognitive contours" Nature (London) 238 5 1 - 5 2 Gregory R L , 1987 "Illusory contours and occluding surfaces" in The Perception of Illusory Contours Eds S Petry, G E Meyer (New York: Springer-Verlag) pp 81 - 89 Guilford J P, 1971 Psychometric Methods (New York: McGraw-Hill) Kanizsa G, 1955 "Margini quasi-percettivi in campi con stimolazione omogenea" Rivista di Psicologia 49 7 - 30 Kanizsa G, 1974 "Contours without gradients or cognitive contours?" Italian Journal of Psychology 1 9 3 - 1 1 3 Kanizsa G, 1975 "The role of regularity in perceptual organization" in Studies in Perception: Festschrift for Fabio Metelli Ed. G Flores d'Arcais (Milano: Martello-Giunti) pp 48 - 66 Kanizsa G, 1980 Grammatica del Vedere (Bologna: II Mulino) Kanizsa G, Gerbino W, 1981 "II completamento amodale tra vedere e pensare" Giornale Italiano di Psicologia 8 297-307 Kennedy J M, 1978 "Illusory contours not due to completion" Perception 7 1 8 7 - 1 8 9 Kennedy J M, ChattawayLD, 1975 "Subjective contours, binocular and movement phenomena" Italian Journal of Psychology 2 3 5 3 - 3 6 7 Minguzzi G, 1984 "La percezione di superfici anomale" in Fenomenologia sperimentale della visione Ed. G Kanizsa (Milano: Franco Angeli) pp 97 -118 Minguzzi G, 1987 "Anomalous figures and the tendency to continuation" in The Perception of Illusory Contours Eds S Petry, G E Meyer (New York: Springer-Verlag) pp 71 - 75 PurgheF, 1989 "II ruolo della completezza figurale e del completamento amodale nella formazione di superfici anomale" Giornale Italiano di Psicologia 16 101-118 Rock I, 1987 "A problem-solving approach to illusory contours" in The Perception of Illusory Contours Eds S Petry, G E Meyer (New York: Springer-Verlag) pp 62 - 70 Rock I, Anson R, 1979 "Illusory contours as the solution to a problem" Perception 8 125 -134 Sambin M, 1974 "Angular margins without gradient" Italian Journal of Psychology 1 355-361 Sambin M, 1978 "II contrasto di chiarezza nelle figure anomale" Giornale Italiano di Psicologia 3 543-564 Sambin M, 1981 On the threshold measurement of anomalous figures (Padova: Istituto di Psicologia, Universita di Padova, Report No. 30) pp 1-16 Sambin M, 1987 "A dynamic model of anomalous figures" in The Perception of Illusory Contours Eds S Petry, G E Meyer (New York: Springer-Verlag) pp 131 -142 Simon HA, 1954 "Spurious correlation: A causal interpretation" Journal of the American Statistical Association 49 467 - 479 Watanabe T, Oyama T, 1988 "Are illusory contours a cause or a consequence of apparent differences in brightness and depth in the Kanizsa's square?" Perception 1 7 5 1 3 - 5 2 1
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