Illusory form with inducers of opposite contrast polarity: Evidence for multistage integration

The perception of brightness differences in Ehrenstein figures and of illusory contours in phaseshifted line gratings was investigated as a function of the contrast polarity of the inducing elements. We presented either continuous lines or line-like arrangements composed of aligned dashes or dots whose spacing was varied. Ayes/no procedure was used in which naive observers had to decide whether or not they perceived a brightness difference in a given Ehrenstein figure or an illusory contour in a phase-shifted line grating. The results show that brightness differences are perceived to some extent in Ehrenstein figures with inducers of opposite polarity of contrast; however, the percentage ofyes responses was systematically lower and response times were longer than for figures with inducers of the same polarity. Phase-shifted line gratings with lines of opposite polarity of contrast yielded stronger illusory contours and shorter response times than those with lines of the same polarity. When the sign of contrast was not the same within a given line of induction, neither differences in brightness nor illusory contours were perceived. The results suggest that the mechanisms that lead to apparent differences in brightness are more sensitive to input of the same contrast polarity, the mechanisms generating illusory contours more sensitive to input of opposite polarity. The data are discussed in the light of a multistage approach to illusory form perception and some implications for cortical models of illusory contour integration are discussed.     

Subjective contours independent of subjective brightness

Two theories of subjective contours are distinguished according to the interrelationship of subjective contours and subjective brightness effects. In one view, subjective contours are illusory brightness gradients generated from grouped local brightness effects. In another view, subjective contours are the edges of subjective forms created on the basis of gestalt factors; subjective brightness is a secondary consequence of form perception. Two experiments which use rating scales to separate judgments of subjective contour and subjective brightness are presented. The first shows that subjects may judge contour to be strong when there is no subjective brightness gradient. In the second, gestalt grouping factors are shown to be more important than factors which should influence brightness according to local effects theories. Both experiments support the view that subjective brightness occurs through interactions at the level of form perception.     

Directional harmonic theory: a computational Gestalt model to account for illusory contour and vertex formation

Visual illusions and perceptual grouping phenomena offer an invaluable tool for probing the computational mechanism of low-level visual processing. Some illusions, like the Kanizsa figure, reveal illusory contours that form edges collinear with the inducing stimulus. This kind of illusory contour has been modeled by neural network models by way of cells equipped with elongated spatial receptive fields designed to detect and complete the collinear alignment. There are, however, other illusory groupings which are not so easy to account for in neural network terms. The Ehrenstein illusion exhibits an illusory contour that forms a contour orthogonal to the stimulus instead of collinear with it. Other perceptual grouping effects reveal illusory contours that exhibit a sharp corner or vertex, and still others take the form of vertices defined by the intersection of three, four, or more illusory contours that meet at a point. A direct extension of the collinear completion models to account for these phenomena tends towards a combinatorial explosion, because it would suggest cells with specialized receptive fields configured to perform each of those completion types, each of which would have to be replicated at every location and every orientation across the visual field. These phenomena therefore challenge the adequacy of the neural network approach to account for these diverse perceptual phenomena. I have proposed elsewhere an alternative paradigm of neurocomputation in the harmonic resonance theory (Lehar 1999, see website), whereby pattern recognition and completion are performed by spatial standing waves across the neural substrate. The standing waves perform a computational function analogous to that of the spatial receptive fields of the neural network approach, except that, unlike that paradigm, a single resonance mechanism performs a function equivalent to a whole array of spatial receptive fields of different spatial configurations and of different orientations, and thereby avoids the combinatorial explosion inherent in the older paradigm. The present paper presents the directional harmonic model, a more specific development of the harmonic resonance theory, designed to account for specific perceptual grouping phenomena. Computer simulations of the directional harmonic model show that it can account for collinear contours as observed in the Kanizsa figure, orthogonal contours as seen in the Ehrenstein illusion, and a number of illusory vertex percepts composed of two, three, or more illusory contours that meet in a variety of configurations.     

The illusion of transparency and chromatic subjective contours

Subjective contours can be produced that include an illusion of edge and an extension of color throughout the area of the illusion. The phenomenological appearance is of a transparent colored shape in front of the background. Two explanations of this illusion are proposed. The first is that there is an assimilation of color analogous to brightness assimilation. The second is a variant of the stratification of depth theory of subjective contours. In it, the pattern elements lead to the illusion of a surface in front of the pattern elements. We thus predicted that an illusion of transparency would enhance the subjective contour, Metelli’s model of transparency was used to quantify our prediction, and it was found that the possibility of transparency was a powerful predictor of the chromatic subjective contour.     

The perception of moving subjective contours by 4-month-old infants

We investigated whether 4-month-old infants are capable of perceiving illusory contours produced by the Kanizsa-square display, first introduced by Prazdny (1983, Perception & Psychophysics 34 403-404), which tests whether a viewer perceives the illusory contour in the absence of brightness contrast (illusory brightness). Because the illusory square appears to move across the computer screen and infants are attracted to motion, this display holds their interest. In experiment 1, 4-month-old infants were tested for their ability to distinguish between a continuously moving illusory square and a continuously moving control display in which the pacman elements were rotated so that the perception of subjective contours did not occur. Data analysis revealed a significant preference for the subjective contour display. In experiment 2, habituation-dishabituation was used with 4-month-old infants. They were tested for their ability to discriminate between the illusory Kanizsa square that continuously moved back and forth and an illusory square which changed positions randomly. Although the infants did not show differences in dishabituation as a function of the habituation display, they looked significantly longer at the continuously moving display.     

When figure-ground segmentation modulates brightness: the case of phantom illumination

In the phantom illumination illusion, luminance ramps ranging from black to white induce a brightness enhancement on an otherwise homogeneous dark background. The strength of the illusion was tested with regard to the extension of the brightness inducing perimeter, surrounding the target area by manipulating the number of inducers (exp. 1) and the size of the inducers (exp. 2). Participants' task was to rate the difference in brightness between the target area and the background. Results show that the illusion occurs only when the target area is not completely segregated from the background by luminance ramps; vice versa, when the target area is delimited by a continuous gradient, it appears darker than the background. These findings suggest a major role of figure-ground organization in the appearance of the illusion. This hypothesis was tested in a rating task experiment with three types of target area shapes circumscribed by four types of edges: luminance contours, illusory contours, no contours, and ambiguous contours. Illusory contours, just as luminance contours, hinder the illusion and produce a darkening of the target area. A control experiment measured the brightness of the previous stimuli without luminance ramps: all configurations resulted in a darkening of the target area. Results from all experiments suggest that figure-ground segmentation plays a major role in the determination of both illumination and lightness in stimuli with luminance gradients.     

The relationship between brightness contrast and illusory contours.

One group of subjects rated differences in brightness and another the clarity of illusory contours for eight figure-ground combinations of the Kanizsa and Ehrenstein patterns made from Munsell papers. For four combinations there was a difference in Munsell value (brightness) between figure and ground and for another four no difference. For the latter the pattern was derived from differences in hue or colour quality. For the combinations with a Munsell value difference the ratings of both brightness difference and contour clarity were high and for those of uniform value both were low. The results are interpreted as supporting the argument that illusory contours derive primarily from contrast-induced differences in brightness and possibly in colour between contiguous, physically uniform regions.     

Apparent brightness enhancement in the Kanizsa square with and without illusory contour formation

The perceived strength of darkness enhancement in the centre of surfaces surrounded or not surrounded by illusory contours was investigated as a function of proximity of the constituent elements of the display and their angular size. Magnitude estimation was used to measure the perception of the darkness phenomenon in white-on-grey stimuli. Darkness enhancement was perceived in both types of the stimuli used, but more strongly in the presence of illusory contours. In both cases, perceived darkness enhancement increased with increasing proximity of the constituent parts of the display and with their angular size. These results suggest that the occurrence of darkness (or brightness) enhancement phenomena in the centre of the displays is not directly related to illusory contour formation.     

Amodal completion versus induced inhomogeneities in the organization of illusory figures.

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.     

Can subthreshold summation be observed with the Ehrenstein illusion?

Subthreshold summation between physical target lines and illusory contours induced by edges such as those produced in the Kanizsa illusion has been reported in previous studies. Here, we investigated the ability of line-induced illusory contours, using Ehrenstein figures, to produce similar subthreshold summation. In the first experiment, three stimulus conditions were presented. The target line was superimposed on the illusory contour of a four-arm Ehrenstein figure, or the target was presented between two dots (which replaced the arms of the Ehrenstein figure), or the target was presented on an otherwise blank screen (control). Detection of the target line was significantly worse when presented on the illusory contour (on the Ehrenstein figure) than when presented between two dots. This result was consistent for both curved and straight target lines, as well as for a 100 ms presentation duration and unlimited presentation duration. Performance was worst in the control condition. The results for the three stimulus conditions were replicated in a second experiment in which an eight-arm Ehrenstein figure was used to produce a stronger and less ambiguous illusory contour. In the third experiment, the target was either superimposed on the illusory contour, or was located across the central gap (illusory surface) of the Ehrenstein figure, collinear with two arms of the figure. As in the first two experiments, the target was either presented on the Ehrenstein figure, or between dots, or on a blank screen. Detection was better in the dot condition than in the Ehrenstein condition, regardless of whether the target was presented on the illusory contour or collinear with the arms of the Ehrenstein figure. These three experiments demonstrate the ability of reduced spatial uncertainty to facilitate the detection of a target line, but do not provide any evidence for subthreshold summation between a physical target line and the illusory contours produced by an Ehrenstein figure. The incongruence of these results with previous findings on Kanizsa figures is discussed.     

Figure-background segregation and the formation of illusory figures

Three experiments were carried out to test the relationship between figure-background segregation and illusory contours. Illusory figures are believed to arise as byproducts of figure-background segregation. When, in a scene, part of what should be the background becomes an illusory figure, a mechanism of contour attribution favoring the area in which the illusory figure appears takes place. This mechanism is prevented from operating when the attribution of the contour is inhibited by the presence of "groupable" (connectable) contours. Spatial proximity is one of the factors affecting such grouping: the closer the connectable contours, the more likely is their grouping in a single unit and the less likely is the emergence of an illusory figure. Experimental results showed that the illusory effect was established when contours were prevented from being connected. This outcome is interpreted as evidence that a mechanism of contour attribution is effective in the formation of illusory figures.     

Contextual illusions reveal the limit of unconscious visual processing

The perception of even the most elementary features of the visual environment depends strongly on their spatial context. In the study reported here, we asked at what level of abstraction such effects require conscious processing of the context. We compared two visual illusions that alter subjective judgments of brightness: the simultaneous brightness contrast illusion, in which two circles of identical physical brightness appear different because of different surround luminance, and the Kanizsa triangle illusion, which occurs when the visual system extrapolates a surface without actual physical stimulation. We used a novel interocular masking technique that allowed us to selectively render only the context invisible. Simultaneous brightness contrast persisted even when the surround was masked from awareness. In contrast, participants did not experience illusory contours when the inducing context was masked. Our findings show that invisible context is resolvable by low-level processes involved in surface-brightness perception, but not by high-level processes that assign surface borders through perceptual completion.     

The perceived strength of illusory contours.

Illusory contours are not well understood, partially because a lack of physical substance complicates their specification via physical standards. One solution is to gauge illusory contours with respect to luminance-defined contours, which are easily quantified physically. Accordingly, we chose a metric (perceived contrast) that expresses illusory contour strength in terms of the physical contrast of luminance-defined contours. Using this metric, adult observers adjusted the contrast of a luminance-defined contour until it matched the perceived contrast of an illusory contour. Illusory contour length, inducer size, and inducer contrast all influenced illusory contour strength. The results are adequately explained via low-level visual processes. It appears that matching paradigms can be beneficial in quantitative studies of illusory contours.     

The perceived strength of illusory contours

Illusory contours are not well understood, partially because a lack of physical substance complicates their specification via physical standards. One solution is to gauge illusory contours with respect to luminance-defined contours, which are easily quantified physically. Accordingly, we chose a metric (perceived contrast) that expresses illusory contour strength in terms of the physical contrast of luminance-defined contours. Using this metric, adult observers adjusted the contrast of a luminance-defined contour until it matched the perceived contrast of an illusory contour. Illusory contour length, inducer size, and inducer contrast all influenced illusory contour strength.. The results are adequately explained via low-level visual processes. It appears that matching paradigms can be beneficial in quantitative studies of illusory contours.     

Visual illusory productions with or without amodal completion.

A new type of illusory contour is presented whose appearance is generated by the graphic representation of groups of human figures interacting in a coordinated manner with external reality. When numerous pictorial indicators of cause-effect relationships are provided, and appropriate techniques and sufficiently ambiguous observation conditions are used, hallucinatory objects congruent with expectations linked to the meaning of the configurations appear. There is thus a high-level semantic component that is active in the formation of visual illusory contours and is even capable of interacting with other known factors: brightness contrast, the number of elements, the degree of alignment of the elements, etc. This new type of illusory contour fits current definitions and can be experimentally modified. The variations in subjective clarity scores are presented for a study in which twenty subjects observed nineteen experimental figures, certain variables of which were manipulated. The issue is worthy of further experimental investigation.     

Surface contours, Glass patterns, and a slant illusion

A surface contour pattern constructed from continuous sine waves is subject to several visual interpretations, whereby the separate regions containing the maxima and the minima of the sine waves may be seen as representing either convex or concave areas of a three-dimensional surface. In a pattern of segments of contours comprising only the regions containing the maxima and minima of the sine waves, a set of surfaces is perceived, each of which tends to be seen as convex, and which possesses an illusory slant which is different for columns of contour segments containing maxima as compared with columns containing minima. It is conjectured that the slant illusion is a manifestation of the processes by which depth is derived from surface contour information. It is demonstrated that corresponding figures constructed from sinusoidal Glass patterns produce similar effects. From this it is concluded that the structure of Glass patterns provides a sufficient input representation for the processes by which surface shape is recovered from surface contours.     

Boundary completion in illusory contours: interpolation or extrapolation?

Most computational and neural-style models of contour completion (ie illusory and occluded contours) are based on interpolation: the filling in of an edge between two visible edges. The results of three experiments suggest an alternative conception, that units are formed as a result of extrapolation from visible edges. In three experiments, subjects reported illusory contours between standard illusory-contour inducing elements and forms that do not, by themselves, induce illusory contours. We suggest that these forms are not a special case of inducing elements but that they represent a different class--receiving elements. Receiving elements are forms that can receive an illusory contour but cannot generate one, and they can alter contour formation. In experiment 1, receiving elements increased the judged clarity of illusory contours. In experiment 2, illusory edges were seen to connect to corners, line ends, and even the edges of circles. Boundary formation in motion displays also appears to be based on extrapolation. In experiment 3, subjects reported that small moving dots altered the formation of spatiotemporally defined boundaries. Implications for higher-order operator and network models of boundary formation are discussed.     

Are illusory contours a cause or a consequence of apparent differences in brightness and depth in the Kanizsa square?

The causal flows between the processes responsible for illusory contour clarity, brightness, and apparent depth in the Kanizsa square were examined. The sixty-four stimuli used consisted of all possible combinations of eight disk luminances and eight centre-to-centre separations between nearest disks. Ten subjects were instructed to rate the clarity of the illusory contour and the brightness and apparent depth differences between the Kanizsa square and its surround in each stimulus. On the basis of results obtained with the causal inference method, using partial correlations and path analysis, it is suggested that clarity of illusory contour can be influenced directly by disk separation, and that the output from the process responsible for illusory contour clarity has some effect on the processes responsible for the apparent depth and brightness differences.     

Neon flank and illusory contour: interaction between the two processes leads to color filling-in.

Two aspects of neon color spreading, local color spreading (neon flank) and illusory contour, were investigated by dichoptic viewing. Neon flank was not observed under appropriate dichoptic stimulation, suggesting that input to the process for local color spreading is based on monocular configuration. However, illusory contours were formed according to the interocularly combined configuration rather than according to each monocular configuration, suggesting that input to the process responsible for illusory contours should be ocularly-nonselective and binocular, rather than monocular. The possibilities of artifacts such as those arising from interocular rivalry were appropriately eliminated, and thus, it is tentatively concluded that the process underlying local color spreading is monocularly driven, whereas the process underlying illusory contours is binocularly driven. Furthermore, a new demonstration is presented that indicates that interocularly-induced illusory contours 'capture' and extend the monocularly-induced local color spreading, resulting in global color spreading (neon color spreading). These results support our hypotheses that neon color spreading involves two separable processes in the early visual processing, the feature detection process (for local color spreading) and the illusory contour process, and that these two processes interact with each other at later stages of cortical processing. The relation of local color spreading and illusory contours to surface separation is also discussed.     

Infants' perception of illusory contours in static and moving figures

We investigated 3-8-month-olds' (N=62) perception of illusory contours in a Kanizsa figure by using a preferential looking technique. Previous studies suggest that this ability develops around 8 months of age. However, we hypothesized that even 3-4-month-olds could perceive illusory contours in a moving figure. To check our hypothesis, we created an illusory contour figure in which the illusory square underwent lateral movement. By rotating the elements of this figure, we created non-illusory contour figures. We found that: (1) infants preferred moving illusory contours to non-illusory contours by 3-4 months of age, and (2) only 7-8-month-olds preferred static illusory contours. Our findings demonstrate that motion information promotes infants' perception of illusory contours. Our results parallel those reported in the study of partly occluded objects ().