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Perceptual grouping appears both as organized forms of real figural units and as illusory or “phantom” figures. The phenomenon is visible in the Hermann grid and in configurations which generate color spreading, e.g., “neon effects.” These configurations, generally regular repetitive patterns, appear to be crossed by illusory bands filled with a brighter shade or a colored tinge connecting the various loci of illusory effects. In this work, we explore a particular new illusion showing a grouping effect. It manifests as illusory streaks irradiating from the vertexes of angular contours and connecting pairs of figures nearby. It is only clearly visible when more than one figure is shown, and takes the shape of a net crossing their corners. Although the grouping effect is vivid, the local source of the illusion is completely hidden. Theories explaining this effect as due to the irradiation of illusory streaks (mainly that of
Since the analyses of the early Gestaltists (e.g.,
Vision research on figural grouping, and more specifically approaches based on phenomenological accounts of visual perception, have revealed the role played by several factors in perceptual grouping, such as the well-known gestalt rules of orientation, closure, and symmetry. However, the role of photometric variables such as stimulus luminance, processed during earlier stages of the visual system, are still difficult to understand, probably due to our still incomplete understanding both of what light is and of the psychophysiology of early vision processes.
Study of early processes in perceptual grouping has mainly focused on the role of contrast polarity, with a wide variety of tasks and stimuli: contour formation in Glass patterns (
The role of luminance contrast may be better understood by distinguishing two kinds of phenomenally important grouping processes: (1) a new perceptual unit results from the combination of differing elements (e.g., a square made of four different segments); (2) the grouping of elements is mediated by the generation of additional elements connecting various figures, such as a lattice made of neon light spreading through the elements and connecting them (
In explaining both these grouping effects,
To explain a phenomenon like that shown in
“The lattice of diagonal boundary contours enables gray featural quality to flow out of the squares and fill in the positions bounded by the lattice within the FC System” (
Some simple manipulations of these patterns show that the alternation of light and dark components is not a necessary condition for the effect to arise. In
This new configuration is suitable for testing further manipulations.
Grouping of the inducing figures seems to be necessary for illusory lines to emerge.
To conclude, illusory lines appear to join the vertexes of angular perimeters, provided that these corners are
The grouping effect related to perceptual illusions involving elements of various brightness levels is well-known (see
The phenomenon shown in
The phenomenon of perceptual grouping shown in
The experimental stimuli were variations of a general pattern, in which a series of filled polygons were placed over the X-junctions of a checkerboard (see
The illusory effects perceived in
The experiment reported in the following section was conducted to test the effect of these two variables systematically. We concentrated on the angular regions of the contour of the figure, to demonstrate that systematic variations of the geometric variable (angle amplitude) and photometric factors (contrasts at borders) affect the visibility of illusory streaks.
The experiment aimed at measuring the vividness of illusory streaks and how it is affected by geometric and photometric variables. The stimuli used were the same as those shown in
The effects of the following parameters were tested:
The participants in the experiment were one of the authors and 19 psychology students of the University of Siena (12 women, aged 20–25 years) who were unaware of the aim of the experiment. All participants had normal or corrected-to-normal visual acuity. All gave their written informed consent in accordance with the Declaration of Helsinki, and were debriefed at the end of the experiment about the purpose of the study.
The stimuli were generated by manipulating two variables: the geometrical shape of the inducers, and the luminance of their borders and inner surfaces.
Four types of inducers were used:
Star-like (acute): 46° of acute angle amplitude (
Star-like (acute): 62° acute angle amplitude (
Squares: 90° amplitude (
Octagons: alternation of 110 and 160° angles (
The luminance magnitudes of the inducer surfaces and the contours were combined, to create an inducer-contour-background ramp both increasing and decreasing in luminance.
Six combinations of contour/inner surface luminance in inducers (cd/m2) and corresponding Michelson contrast.
Photometric condition | Inner luminance (cd/m2) | Contour luminance (cd/m2) | Michelson contrast | Contrast magnitude class | Contrast polarity |
---|---|---|---|---|---|
1 | 10,00 | 24,00 | -0,41 | High | Negative (dark→light) |
2 | 4,40 | 7,60 | -0,27 | Intermediate | |
3 | 10,4 | 14,7 | -0,17 | Low | |
4 | 16,50 | 6,20 | 0,45 | High | Positive (light→dark) |
5 | 25,00 | 12,60 | 0,32 | Intermediate | |
6 | 37,50 | 25,20 | 0,19 | Low |
Twenty-four inducers were generated by combining the photometric variable (six levels) with the geometrical variable (four levels). These were drawn on two checkerboards, one the “negative” reproduction of the other. The introduction of these two sets of stimuli allowed us to monitor the same illusory effect, both in one direction (clockwise inclination) and in the mirror one (anti-clockwise inclination), for a total of 48 stimuli.
A series of variations for each of these stimuli was generated by gradually changing the luminance of the checkerboard tiles, from lighter to darker and vice versa. The creation of each series of stimuli followed two steps. In the basic starting configuration, the dark and light tiles were very different in luminance, care being taken that no streaking line was perceived. A second stimulus was then depicted, varying the luminance of the tiles where the inducers formed a luminance ramp. The operation was replicated, with a further variation in shade, to obtain a third stimulus, and so on until the luminance gradient was replaced by a luminance step. The luminance varied in regular steps of magnitude in the descending (white-to-black) and ascending (black-to-white) ramps (from the inside of the inducer to the squares of the checkerboard, passing through the contour). In the black-to-white ramp, the variable surface increased/decreased in luminance in steps of 2.0 ± 0.2 cd/m2; in the white-to-black ramp, the variation was in steps of 0.6 ± 0.3 cd/m2. The 48 series of stimuli were reproduced in slides shown to the observers twice in fixed order: once in ascending (darkest to lightest shades) and once in descending order (Supplementary Material).
The stimuli were presented on a 17″ CRT NEC MultiSync 95F monitor with 1280 × 1024 pixel resolution (mean luminance, 26.9 cd/m2, horizontal refresh rate 96 Hz, vertical refresh rate 160 Hz), powered by a PC. Viewing distance was 80 cm. Overall, the stimulus subtended 12.8° of visual angle, both horizontally and vertically. The sides of the checkerboard squares were 1.8 cm long and subtended a visual angle of 1.29°. The inducers were inscribed in a circle subtending 1° of visual angle. The contour was 1.4 mm thick.
The method of limits was used to determine the luminance of the corner surrounds required to perceive illusory streaks. After each stimulus presentation, subjects were asked to say whether they perceived diagonal streaks and, if so, to indicate the direction of their inclination by saying “left” or “right,” and reporting polarity (lighter or darker than the background). For each of the 96 trials (each corresponding to one series), two luminance magnitudes were calculated: one in which the illusion began to appear (T1), and one coinciding with the illusion vanishing (T2). The difference between T1 and T2 corresponds to the range of luminance variation during which the illusion persisted, and was considered as a measure of its vividness. The experiment was divided into two sessions over two successive days, and subjects were told that they could stop participation at any time during the sessions without giving any reason.
At the beginning of the experiment, participants were presented with a stimulus and given the following instructions: “The figure displayed here is made up of a checkerboard and some regular figures overlapping the corners. After the gray shades change, some streaks may appear, crossing the checkerboard diagonally.” The experimenter then showed some examples until the observers convincingly reported seeing light or dark gray streaks, and then continued: “Each trial starts with the presentation of a figure. Please say whether you perceive the streaks and, if so, indicate their polarity (lighter or darker than the background) and inclination, clockwise or anti-clockwise. After this first experiment, a second one with a different checkerboard will follow.”
Some practice trials were carried out. Subjects were instructed to indicate both polarity and inclination as soon as they perceived the illusory effect and, if it persisted in the following stimuli, then only the direction. The experimenter recorded the “right” or “left” response and interrupted the trial following two consecutive reports with no diagonal perceived.
The figures were displayed on a CRT monitor and lasted for 1 s. Immediately after the presentation of each configuration, a mask stimulus composed of randomly arranged geometrical figures and lines was displayed for 1 s. Observers were asked to give their responses within this 2-s interval. The stimuli were presented by MS Powerpoint, and both responses and thresholds were manually recorded by the experimenter. Not all the programmed trials were run. Conditions in which the inducers were octagons with obtuse angles did not elicit any illusory streaking effects. The experimenter only tested six of the planned series of 24 stimuli.
There was total agreement among subjects’ judgments: the illusory lines were seen to cross the checkerboard diagonally, and appeared as prolongations of the corners formed by the contours of intermediate luminance (i.e., a luminance ramp).
The illusory streaks appeared to be lighter than the background when the inducer surfaces were the palest figural units in the configuration. Polarity was reversed when this surface was the darkest. Therefore, the direction of the luminance gradient predicted the polarity of the illusion.
Both geometric and photometric factors thus seemed to play a role in creating the illusion. With acute angles, all observers reported the appearance of streaks in all luminance conditions. With 90° angles, illusory effects were recorded in four luminance combinations out of six. In addition, in these cases, judgments did not converge. With obtuse angles, the impression of streaks was very rarely evoked, and was totally absent for most observers. A first conclusion can thus be drawn: only corners having amplitudes of 90° or less are sources of illusory streaks. Data for inducers with obtuse angles were therefore excluded from further analyses.
For each of the six conditions,
Experimental results for three of four angular conditions, when orientation of streaks was from bottom-left to top-right.
Direction: |
Geometric conditions | ||||||
---|---|---|---|---|---|---|---|
Photometric conditions |
Acute angles I (46°) |
Acute angles II (62°) |
Square angles (90°) |
||||
Negative | High | 25.8–34.6 | 8.8 | 26.8–37.3 | 10.5 | – | – |
Intermediate | 8.0–15.9 | 7.9 | 8.6–16.0 | 7.4 | 8.6–13.3 | 4.7 | |
Low | 15–27.1 | 12.2 | 15.4–27.6 | 12.2 | 15.9–24.5 | 8.6 | |
Positive | High | 1.7–5.8 | 4.0 | 1.5–5.4 | 3.9 | 2.5–5.0 | 2.5 |
Intermediate | 6.5–12.8 | 6.3 | 5.7–12.1 | 6.4 | 7.9–10.8 | 2.9 | |
Low | 17.2–24.4 | 7.1 | 15.3–23.5 | 8.2 |
Experimental results for three of four angular conditions, when orientation of streaks was from top-left to bottom-right.
Direction: |
Geometric conditions | ||||||
---|---|---|---|---|---|---|---|
Photometric conditions |
Acute angle (46°) |
Acute angle (62°) |
Square angle (90°) |
||||
Negative | High | 27.7–36.9 | 9.2 | 27.1–36.5 | 9.4 | – | – |
Intermediate | 7.9–14.8 | 6.9 | 8.7–16.9 | 8.2 | 8.6–11.7 | 3.1 | |
Low | 15.2–25.6 | 10.5 | 15.3–25.8 | 10.5 | 15.9–23.4 | 7.4 | |
Positive | High | 1.8–5.6 | 3.9 | 1.9–5.3 | 3.3 | 2.9–4.5 | 1.6 |
Intermediate | 5.8–12.2 | 6.4 | 5.1–12.6 | 7.5 | 7.2–10.5 | 3.3 | |
Low | 17.4–24.5 | 7.2 | 17.1–24.1 | 6.9 |
Although, these findings indicate the weaker persistence of illusory streaks in the 90° condition, the average range in this condition could not be formally compared with the average ranges recorded for the star-like inducers, because there was only partial agreement in observers’ estimates. Also, a complete set of judgments could only be gathered when the inducers had acute corners. Consequently, only data for acute angle conditions were further analyzed.
Data on the range of visibility of the effect were analyzed in a four-way, repeated-measures ANOVA including
The interaction between streak polarity and contrast magnitude was also significant [
It is important to note that, in 36.8% of the trials, phantom streaks were seen even when the contour was isoluminant with the background (i.e., one of the two thresholds coincided with a starting or ending point of the series). This means that the luminance gradient is not a necessary condition for the creation of the illusion. Interestingly, participants reported this effect in the presence of a luminance step (the edges separating the inside of the inducers and the square, given the isoluminance of square and contour) only when the contrast at this edge was low (
Frequency of trials in which effect was perceived, even when contour was isoluminant with square in which streak was seen.
Negative contrast polarity |
Positive contrast polarity | |||||
---|---|---|---|---|---|---|
Angle amplitude (°) | High contrast | Intermediate contrast | Low contrast | High contrast | Intermediate contrast | Low contrast |
46 | 5 | 25 | 33 | 15 | 27 | 21 |
62 | 0 | 16 | 29 | 10 | 23 | 12 |
0,0625 | 0,5125 | 0,775 | 0,3125 | 0,625 | 0,4125 |
The experiment reported here was conducted to examine a novel grouping effect occurring in a repetitive pattern, which takes the form of illusory bands connecting the corners of oriented inducers. Our test results confirm that the luminance contrast at the corners and their amplitude are relevant to the appearance of streaking lines and affect the luminance range of visibility of the illusion. Our main findings may be summarized as follows:
Illusory streaks are seen to join angles of 90° or less. The phenomenon is always recorded when the angles are acute, although when the stimulus contour is a square, the illusion occurs in most cases but with discordant judgments on the part of subjects. Wider angles eliminate this effect.
The range of visibility of the illusion is not linearly related to angle amplitude. However, the weakest manifestations were recorded with square inducers.
The streaks have the same contrast polarity as the corner surfaces.
A luminance ramp at corners strengthens the illusion, as the highest intensities are attained when smooth gradients (surface-contour-surround) are shown. However, even in the case of isoluminance between contour and surround, illusions were perceived.
The darker streaks persist over a larger range of variations of the background.
First, these findings help to clarify the geometric and photometric conditions in which illusory streaks arise, although uncertainty still persists regarding their causes and origin. Why does a sharp, low-contrast corner behave like a geyser spouting featural qualities of the shape it defines? If color spreading occurs, why does it concentrate in the vertexes but is absent in the straight edges of the inducers? We believe this phenomenon may be explained by examining both local and global processes, as shown in
Two main phenomena seem to be locally at play at the inducer corners:
A boundary gap at the corner vertex (
Color spreading. The dotted arrow in
The far right figure (
We now examine the implications of this theory as related to the processes of
The authors assume that “In order to work properly, boundary contour responses need to be sensitive to the amount of contrast in scenic edges” (
To our knowledge, the illusory alteration in brightness in the space outside the vertex has not been previously recorded. Brightness alterations at corners were previously documented by
Illusory phenomena of color induction and/or bright ness/color assimilation have frequently been observed in the photometric conditions which appear to be crucial for illusory streaks to appear, i.e., low luminance contrast between an outline contour, or
Therefore, according to the reviewed literature, we cannot predict the appearance of phantom streaking lines connecting the inducer corners in
In our view, illusory diagonals are the result of a global effect arising from local phenomena. Two suggestions may be made.
The diagonal strikes documented here are probably a manifestation of the ease with which regions of brightness alteration merge to give rise to illusory “streets” in visual space. Several of the related illusory phenomena which we have illustrated, such as the Van Tujil, Ehrenstein, and Vasarely Arcturus configurations (
However, mere summation seems insufficient to account for our illusion. Illusory streaks are in fact not only not seen in a corner in isolation (
The illusory effects explored here may also be related to another grouping factor, reported by
Further research is certainly required to test the role of Gestalt grouping factors (e.g., “good continuation”) and other unexplored merging factors, in our illusion and in other similar effects involving phantom “streets” or lines, such as the Ehrenstein, Van Tujil, and Kitaoka configurations. Two sets of factors, as we have seen, are probably involved in the appearance of phantom diagonals, but both their relative effect and their precise role in the emergence of the streaks is still unclear. We are currently designing and planning some experiments aimed at investigating further the role of good continuation and proximity in this illusory phenomenon, which may shed more light on it and its determinants in the visual system. Further insights may come from studies of end-stopping processes. In any event, we believe that this and other illusory effects should be analyzed in depth before we can reach full understanding of perceptual grouping, as they may reveal still unexplored aspects of visual organization, eventually leading to revisions or extensions of current models.
SR: contributed to designing the experiment, analyzing the data, and writing the paper; SG: contributed to writing the paper and analyzing the data; OP: contributed to writing the paper; LB: contributed to conducting the experiment.
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
The Supplementary Material for this article can be found online at: