a NEW LOOK at NEW REALISM

5 When Is an Illusion an Illusion? An Examination of Contrast Information in Grouping and Grid Phenomena

Arthur G. Shapiro and Kai Hamburger

Edwin Holt was an early proponent of a form of realism that holds that the perceptual world corresponds to invariant aspects of the physical world. This view is at odds with theories that argue that our perception depends upon unconscious inferences (Helmholtz, 1867) or that our visual system creates the perceptual world based on internal rules of simplicity, as suggested by the Gestalt principles (proximity, similarity, good continuation, etc.; e.g., Metzger, 1936). Many arguments against Holt’s (and, later, Gibson’s) view are based on visual illusions: how can there be a “direct representation” of the world when an object looks bright against one background and dark against another? Or, how can there be a direct representation of the world when the addition of other objects changes how the viewer organizes the visual scene? In this chapter, we set out an intermediate path: we do not argue that the visual system does not infer properties of the scene based on prior experience or that the visual system does not rely to some extent on principles of organization; rather, we argue that such theories often do not consider all the information available in the environment. We will demonstrate our claim with reference to the simple properties of physical contrast and how physical contrast affects visual grouping.

It is generally agreed that contrast is fundamental for describing the response of neurons in the early visual system; that is to say, many neurons in the retina and in the lateral geniculate nucleus respond to relative changes in stimulation rather than to absolute stimulation (Whittle, 2003). Expressed in this way, contrast may seem a relatively intuitive concept, but in actuality, contrast is surprisingly difficult to define. The difficulty arises for two reasons: (a) The visual system extracts information from the environment at a variety of spatial and temporal scales (i.e., contrast can exist between two neighboring objects or between objects distant in both time and space). So, while a single physical quantity may express absolute stimulus values (luminance, color, etc.), there may be an infinite number of values to express contrast. (b) Contrast seems to be psychologically salient along a remarkable range of stimulus dimensions. For instance, “orientation contrast” could be considered a comparison between the orientation of a line at one location and the orientation of a line at another location; “motion contrast” could represent differences between the physical speed of two different objects. Each stimulus dimension (e.g., orientation, motion) seems to require both the specification of the stimulus itself and the contrast (or the change) along that dimension.

To encode contrast, then, the visual system must make relative comparisons along many stimulus dimensions and at many different spatial and temporal scales.

To simplify the nomenclature, we refer to the relative stimulus dimensions (like luminance contrast, orientation contrast, and motion-direction contrast) as second-order dimensions, and we refer to absolute stimulus dimensions (like luminance, orientation, and motion direction) as first-order dimensions. Over the past 20 years, a number of laboratories have proposed that the visual system is capable of responding separately to both first- and second-order information along many different stimulus dimensions. The separation of responses to first- and second-order information has been shown for motion (Chubb & Sperling, 1989; Lu & Sperling, 1999), orientation (Zhan & Baker, 2006), brightness (Shapiro, Charles, & Shear-Heyman, 2005; Shapiro et al., 2004), texture (Landy & Oruç, 2002; Oruç, Landy, & Pelli, 2006; Song & Baker, 2007), and color/color contrast (Shapiro, 2008). Separate first- and second-order representations (or higher; Smith, Greenlee, Singh, Kraemer, & Hennig, 1998) may occur even for more “complex” visual stimuli, such as human faces (Webster, 2004). Other researchers have shown that classic visual illusions can occur for strictly second-order stimuli (e.g., simultaneous contrast, Chubb, Sperling, & Solomon, 1989; D’Zmura & Singer, 1996; Mach bands and Cornsweet edges, Lu & Sperling, 1996; and variants of Hermann grids, Hamburger & Shapiro, 2009).

What are the implications of separate first- and second-order representations for understanding “visual illusions”? A visual illusion is often defined as a phenomenon in which the perception deviates dramatically from the physical world (Gregory, 1980). We contend that before classifying a phenomenon as a visual illusion (according to the usual definition), it is important to understand the informational content available in the physical stimulus. This may seem like an obvious approach, but in some research programs, the actual stimulus information is often marginalized. For instance, the psychologists who developed the Gestalt school were not interested in different types of information that composed the stimuli (Spillmann & Ehrenstein, 2004). Their stated objective was to find meaningful organizations of visual information; consequently, a reduction of perception to stimulus components was anathema to their agenda. Thus, when Wertheimer (1923) introduced the Gestalt law of similarity, he merely presented rows of white and black dots, showed how the dots were perceptually segregated, and defined the rule as “the tendency of like parts to band together.” He and the Gestalt psychologists were primarily interested in the perception of the objects in relation to the background (Rubin, 1921); they did not consider contrast (or second-order) information to be of fundamental interest.

In a previous chapter in this book, Charles hints at the importance of considering the informational content of images before reaching for hypotheses based on cognitive or organizational strategies. The example that he uses as a demonstration is that of “contrast asynchrony,” a technique that juxtaposes the temporal phase of luminance and contrast information (developed in the Shapiro laboratory). Contrast asynchronies illustrate that the visual system is sensitive to both first-order information (i.e., brightness or color) and second-order information (brightness contrast or color contrast) from a visual stimulus, even though we usually describe the world only in terms of something corresponding to the first-order information. That is, the contrast asynchrony demonstrates that people often report a sensitivity to the first-order information when they are really demonstrating sensitivity to the second-order information (i.e., they report that luminance is alternating between two locations, when it is really the contrast that is alternating).

In this chapter, we expand upon this idea by introducing many variants of the contrast asynchrony principle. The primary idea to be gleaned from these visual displays is that perceived grouping can be determined by second-order information in the image even though the elements of the image have a similar first-order appearance. We will contrast our interpretation of these displays with examples from Gestalt psychology, since Gestalt theory is one of the most prominent examples of a theoretical construction that goes beyond the stimulus—indeed, the one central premise of Gestalt psychology, “the whole is more than the sum of its parts,” seems to be a direct contradiction of the need for representing stimulus variables such as contrast. We will show that in many of our displays the Gestalt principle of similarity applies not only to the similarity of visual objects, but also to the similarity of contrast information—an invariant in the environment that is not captured by typical stimulus descriptions. The implication is that the visual response to second-order information may be just as valuable for visual grouping as the objects themselves (see also Shapiro & Hamburger, 2007; Sutter, et al., 1989). Such an idea may be difficult to integrate with standard Gestalt ideas because the second-order information cuts across the figure/ground border.

As an example of the importance of analyzing the information available in displays, we include our analysis of the Hermann grid, a well-known illusion in which spots appear at intersections; the spots are often referred to as illusory because they are thought to be absent from the stimulus. Hamburger and Shapiro (2009) showed that if one considers the grid at different spatial scales (i.e., in terms of the image’s spectral energy content), then the spots are actually physically present in the image. Our analysis poses a question that would be familiar to followers of Holt: Why do we perceive only some of the physical information in a visual display?

Grouping Effects With “Weaves”

We begin by examining the contrast and spatial scale in “weaves,” a variant of the Hermann Grid illusion (Brewster, 1844; Hermann, 1870) that consists of intertwined light horizontal bars and dark vertical bars (Hamburger & Shapiro, 2009). At some intersections, the light bars cross over the dark bars (the light-over-dark intersections), and vice versa at the others (the dark-over-light intersections).

Two rules govern the location of the “illusory” smudges in the weave patterns: (a) the smudges appear at the intersections at which the bar with the lower contrast relative to the background crosses over the bar with the higher contrast, and (b) smudges appear only if the background luminance is higher than the luminance of the light gray bars or is lower than that of the dark gray bars. For instance, in Figures 5.1a–c, the same (i.e., physically identical) weave is placed against three different backgrounds. On a white background, faint white smudges appear at light-over-dark intersections but not at dark-over-light intersections (Figure 5.1a). On a black background, faint dark smudges appear at dark-over-light intersections but not at light-over-dark intersections (Figure 5.1b). On a gradient background, the effects disappear completely in the middle section, where the background is a range of shades of gray (Figure 5.1c).

If the bars are equiluminant, the smudges are perceived at all intersections when the bars are placed against a light or dark background (a pattern similar to the standard Hermann grid), but the smudges do not appear when the bars are placed against a gray background. Hamburger and Shapiro (2009) suggested that in the equiluminant weaves, unlike the Hermann grid illusion, the perceptual smudges are also present with foveal fixation. Therefore, weave smudges are reminiscent of a phenomenon known as grating induction (Foley & McCourt, 1985; McCourt, 1982).

Figure-ground Segregation and Grouping in “Weaves”

The intersections were important for determining the appearance of the weaves. To this end, we added diamond shapes to each of the intersections; the diamonds increase the grouping within the weaves but remove the appearance of the perceptual smudges (also note that smudges in the weaves do not correspond to receptive field sizes, as is the case in Hermann grids). In Figures 5.2a and b, the diamonds are presented at the luminance level and depth of the lower bar (i.e., as if the diamonds are part of the lower bar). The formerly equally salient grid (Figures 5.1a and b) has split into salient vertical columns and horizontal stripes. On a white background with dark diamonds, a strong vertical grouping effect occurs (vertical columns), whereas on a dark background with light diamonds, a strong horizontal grouping emerges (horizontal columns).

The strong vertical/horizontal grouping effects persist even if diamonds are added to all intersections (Figures 5.3a and b), although with this pattern the grouping can be more dynamic. For instance, it is possible to see the background as a series of holes punched through a light gray/dark gray lattice. However, even with other perceptual interpretations, the vertical and horizontal striping persists. Thus, the grouping effects in Figures 5.2a and b are not simply due to the addition of diamonds to one class of bars (either vertical or horizontal).

Figure 5.1 In “weaves,” one perceives a change in subjective lightness (“smudges”) at the intersections, where one bar crosses in front of the other. (a) With a white background, light intersections are perceived, (b) whereas the other intersections appear dark on a black background. (c) With a luminance gradient in the background, light smudges are perceived in the top section, there are no effects in the middle section (intermediate gray), and dark smudges are perceived in the bottom section. In Figure 5.1c, vertical bar grouping is enhanced in the top section, and horizontal bar grouping in the bottom section. Note that the spatial frequency and the luminance of the bars are physically identical. Thus, the different grouping effects (orientation) result from the background luminance.

Figure 5.2 (a) Adding dark gray diamond shapes to the intersections where the light gray bars cross in front of the dark gray bars leads to a perception of vertical columns. Thus, the formerly equally salient grid splits up into the more salient vertical columns and the now less salient horizontal bars. The horizontal bars seem to become a part of the background. (b) The opposite effect occurs if light gray diamonds are added to the rest of the intersections. Now, horizontal columns become salient and the dark gray vertical bars become less salient. Dynamic versions of the illusion can be viewed at www.shapirolab.net/holt.

The effects can be made stronger by changing the background dynamically from light to dark at 1 Hz. In this case, the percept flips in synchrony with the modulation.

Figure 5.4 presents a different grouping effect, which is also due to changes in background luminance. The vertical bars consist of a luminance gradient. With a white background, the darker parts of the vertical bars are perceptually closer to each other (grouped), whereas with a black background, the lighter parts of the vertical bars seem to be closer to each other. The classical Gestalt law in this case would be grouping due to proximity, but the physical distance remains constant. Again, this effect is most striking when viewed with a temporally modulated background, which produces the perception that vertical lines move toward and away from each other (apparent sliding motion). The motion phenomenon and gradient stripes have been reported by Shapiro et al. (2004, 2005) and have the same basis as other motion effects (Gregory & Heard, 1983). For our purposes, it is important to note that the factor of common fate is determined by the interaction of the object with the background. Thus, the grouping is determined by the contrast of the object with the surround, not by elements within the object itself.

Figure 5.3 The same effects as in Figure 5.2 occur even if diamonds are added to all intersections. Again, (a) dark gray vertical columns or (b) light gray horizontal columns occur. These effects are due to variations in background luminance. Dynamic versions of the illusion can be viewed at www.shapirolab.net/holt.

The grouping effects can be enhanced by presenting the horizontal bars as gradients as well (Figure 5.5). In this case, the grouping follows the same rules as described before, but the apparent motion results in the expansion and contraction of the tiles. As a side note, when looking at static images of Figures 5.4 and 5.5 (bigger than in the printed version here) and moving one’s gaze all over the image, slight horizontal movements of the vertical bars (Figure 5.4) and horizontal movements of the vertical bars plus vertical movements of the horizontal bars (Figure 5.5) occur perceptually, which is reminiscent of Kitaoka’s various static motion illusions (Kitaoka, 2003; http://www.ritsumei.ac.jp/~akitaoka/index-e.html).

Figure 5.4 (a) If the vertical bars of the weaves are not shown as a homogeneous gray but rather as a luminance gradient, the vertical bars will be perceptually grouped together due to the perceived proximity of the black vertical bar parts. The Gestalt factor of proximity does not exist physically but only perceptually due to the white background. (b) Opposite effects occur with a black background. Here, the light parts of the bars are perceptually close together. The effect is strongest when viewed in an animation, where the background luminance is frequently modulated. Additionally, in the movie clip, the grouping effects become more vivid because of perceived apparent sliding (horizontal) motion of the vertical lines. Here, the factor of common fate can be taken into account. The black and white arrows (right images) schematically indicate the direction in which grouping and sliding motions are perceived. If the patterns (stronger for the black background) are looked at without fixation (moving the gaze over the whole pattern), sliding motion can be perceived as well, although much weaker than in the modulated background animation. Dynamic versions of the illusion can be viewed at www.shapirolab.net/holt.

Weaves, Hermann Grids, and High-pass Filters

Hamburger and Shapiro (2009) showed that the information contained in the weaves differs at different spatial scales. A high-pass filtered version of a weave and two Hermann grids are presented in Figure 5.6. They were created with the Adobe Photoshop high-pass filter set to a radius of 15.0 pixels (about the size in pixels of the width of the bars). As can be seen, the intersections contain physical increases or decreases in luminance level.

For the luminance-mismatched weaves (Figure 5.6a), there are physical luminance increases against the white background when the white bar is in front of the dark bar, and physical luminance decreases against a dark background when the white bar is behind the dark bar. For the Hermann grid, there are physical luminance decreases (Figure 5.6b) or luminance increases (Figure 5.6c) at all intersections.

Figure 5.6 (a) High-pass filtered version of a weave with three different background luminances (top white, middle gray, bottom black) and (b) two Hermann grids with a white background, and (c) a black background.

Why should the spots arise in the high-pass version of the images? A high-pass image can be considered the original image minus the low-pass image. In the low-pass image (where nothing happens for the weave, but a scintillating grid occurs for the Hermann grid; Schrauf, Lingelbach, & Wist, 1997), a bar is the average of a bar and the background in the original image, whereas an intersection is the average of two bars and the background. When the low-pass content is removed from the original image to create a high-pass image, the difference between these two averages will create a luminance overshoot at the intersections. The finding suggests that any process that removes low spatial frequency content (like that used to suppress motion blur; see, for instance, Barlow & Olshausen, 2004) can also create spots like those seen in the Hermann grid.

The implication is that spots correspond to some form of physical energy present in the display, which suggests that the spots are not entirely illusory and that perhaps the key to understanding Hermann spots is not to investigate why they arise, but rather why they do not arise under some conditions. The spots are present in the high spatial frequency representation of both the weaves and the grids; any neural system sensitive to the high spatial frequency information should therefore always produce something akin to the spots, even if the displays are viewed foveally. The observation is consistent with Shapiro, et al. (2007) and Shapiro and Knight (2008), who showed that the direction of change in most brightness illusions can be accounted for by the removal of low spatial frequency content from the images. (This approach can be considered a one-parameter version of a McCourt and Blakeslee ODOG model; Blakeslee & McCourt, 1999.) This finding suggests that the presence of the spots in both weaves and grids is related to standard brightness illusions.

Grouping Effects with “Dot Lattices”

The effect of examining contrast can be shown in an extension of the contrast asynchrony paradigm composed of dots lattices. We examined perceptual grouping within a 10 × 10 array of identical disks whose luminance levels modulate in time. The array is depicted in Figure 5.7 (but can also be viewed in the online interactive demonstration). The Gestalt principle of similarity predicts that the disks should always group together; and indeed, when the background is a uniform gray, as in Figure 5.7, the disks appear as a grid; all 100 disks modulate synchronously between light and dark.

We can investigate whether contrast can be used to drive grouping by placing the disks on different backgrounds. For instance, in Figure 5.8a, we place the modulating disks on a background that is split vertically down the middle, so that the left half of the background is white and the right half is black. In this condition, the luminances of the disks still modulate in phase with each other, but the contrasts of the disks on the right part of the background modulate in antiphase with the contrasts of the disks on the left part of the background. The Gestalt principle of similarity might predict that the background should not affect the perceptual grouping of the disks: The disks are all identical in luminance, and all become light and dark at the same time. However, as can be seen by examining the demonstration, the disks appear to group along the left and right halves of the display as if they are grouping according to the contrast information.

Figure 5.7 Dot lattice in front of a medium-gray background. The dot lattice modulates from light to dark and back to light (sine wave modulation; in phase). No motion is perceived in this configuration. Dynamic versions of the illusion at www.shapirolab.net/holt.

Figure 5.8a The dot lattice modulates from light to dark and back to light (sine wave modulation; in phase; 0°). The background remains static, and its luminance profile goes from light (upper left) to dark (lower right) in the left part of the image and in the opposite direction in the right part of the image. Again, two dim phantom-like bars can be perceived where luminance contrasts are minimal. Due to the modulation of the dot lattice, motion is perceived in opposite directions on the different backgrounds. Dynamic versions of the illusion can be viewed at www.shapirolab.net/holt.

One possible objection to a contrast interpretation of Figure 5.8a is that the split background creates two different frameworks, each of which works as a separate perceptual unit. To counter this objection, we have placed the disks on gradient backgrounds that would be interpreted as a single unit. Figure 5.8b shows a luminance gradient background that is shaded from upper left to lower right. As the disks modulate from light to dark, there is the appearance of second-order motion that tracks the point of zero contrast. As a result, the pattern of grouping divides the disks at oblique angles. The same effect can be shown with chromatic patterns in order to prevent the interpretation of this motion as simply the result of a “salience map” (not visualized here).

Figure 5.8b The dot lattice modulates from light to dark and back to light (sine wave modulation; in phase; 0°). The background remains static, and its luminance profile goes from light (upper left) to dark (lower right). In the static version, a phantom-like bar can be perceived (left image, upper left, and right image, lower right) where luminance contrasts are minimal. Due to the modulation of the dot lattice, this bar seems to move upward and downward. Dynamic versions of the illusion can be viewed at www.shapirolab.net/holt.

Figure 5.8c shows a similar condition with a radial background gradient. The second-order motion flows back and forth between the center and the edges of the disk array. In each of these conditions, the gradient backgrounds are not likely to be taken as separate perceptual frameworks. The grouping therefore follows the contrast information even though the disks are getting light and dark at the same time.

When the disks are modulating in antiphase on the gradient background of Figure 5.8b (this modulation is demonstrated in Figure 5.9a), we again obtain a coherent second-order motion that tracks the point of zero contrast on both backgrounds. A similar perceptual effect as in Figure 5.8a is obtained in Figure 5.9b, even though the background is not separated while the disks are modulating in antiphase.

Various other combinations can be tested with our interactive demonstrations. It is easy to create second-order motion and grouping that can be attributed to phase shifts in modulation over time and to manipulations of the background. The static versions of these backgrounds are presented in Figure 5.10.

Empirical Observations

We tested five naive observers (age ranged from 24 to 31) to verify that the effects described in Figures 5.7–5.10 could be perceived by observers other than the authors. All observers reported the perceptual effects as described above. The perceived direction of second-order motion is shown in the appropriate figure as “motion percept” (which represents the empirical data as well as our predictions). When observing the visual displays presented in static form in Figures 5.8b and 5.9a, observers reported a coherent (nondisrupted) “phantom bar” moving diagonally. (One participant described it as appearing like a rolling pin moving over the display.) This bar occurred where luminance contrast between disks and background was minimal. In contrast, for the visual displays presented in static form, observers reported two bars moving diagonally in opposite directions. For Figure 5.8a, observers were of the opinion that perceptual grouping into two columns was caused by the divided background. For Figure 5.9b, the same effect was said to result from the phase shift in the disk modulation. For Figure 5.9a, observers also reported two columns, left and right, but they could not state whether the percept was due to the dividedbackgroundor the phase shift. Additionally, they reported grouping to the sides of the perceived bar(s); in other words, disks to the left of the bar were perceived as a group, and disks to the right as another group (even though the disks were physically identical). Participants were able to switch between the different groupings consciously.

Figure 5.8c Here, the achromatic disks modulate in phase on a luminance-defined background. Expansion and contraction is perceived. This image is reminiscent of the Breathing Light Illusion (Gori & Stubbs, 2006). Dynamic versions of the illusion can be viewed at www.shapirolab.net/holt.

Figure 5.9a Here, the dot lattice again modulates out of phase (sine wave modulation; 180°) on the divided static background. Now, a coherent motion, as in Figure 5.8b, is perceived, even though the modulation and the background luminances are different. Thus, different luminance contrast combinations can lead to the same visual impression.

Figure 5.9b The left and the right parts of the dot lattice are modulating out of phase (sine wave modulation; 180°). The background remains static, and its luminance profile goes from light (upper left) to dark (lower right). Motion in opposite directions, as in Figure 5.8a, is perceived due to the out-of-phase modulation of the dot lattice. Dynamic versions of the illusion can be viewed at www.shapirolab.net/holt.

These latter observations speak against the aforementioned possible objection that the split background leads to two separate perceptual units, since coherent motion and grouping occur along the phantom bar on the split background.

Conclusion

Holt argued that one goal of the field of psychology was to determine what people responded to in various situations. Here we have presented evidence to support our claim that to understand many visual illusions—or, perhaps more accurately, to understand unexpected visual phenomena—a researcher should first try to understand the complexity of the physical stimulus before positing the existence of internal psychological rules. We contend that if a researcher describes the stimulus only in terms of objects that can be named, or even in terms of recordings from a simple spot photometer, then he or she may be missing crucial information for understanding how we see. Holt might have argued for a stronger “realist’s” point of view. We would advise against going too far in that direction, since, at the very least, the structure of the visual system certainly controls the information that can be extracted from the visual scene. Nonetheless, we do contend that Holt’s approach (i.e., to consider more deeply the information available in the environment) can lead to more informed theories of perception.

Figure 5.10 Further background variations provided by the interactive demonstration. With the interactive demonstration, the influence of contrast on second-order motion and perceptual grouping can easily be tested and modeled. Dynamic versions of the illusion can be viewed at www.shapirolab.net/holt.

We have shown two different types of effects whose appearance cannot be explained by simple measurements with a photometer. The first involved weaves, in which grouping and the location of the smudges are determined by the relative luminances of the bars and the background. The second involved dot lattices, in which an array of dots always has the same luminance, and grouping is determined by the relationship between the dots and the background. In order to determine principles underlying the organization of these displays, it would be possible to create inferences or to expand/apply Gestalt principles. An observer’s use of these inferences or principles, however, is not obvious; for instance, grouping in the dot lattice conditions seem to override the “laws” of similarity and common fate. More than that, though, the grouping principles seem to follow physical characteristics of the stimulus: in the weaves, the smudges are present in the high spatial frequency content of the images, and the grouping patterns of the lattices seem to correspond to the contrast of the dots relative to the background.

We suggest, therefore, that in order to understand the organization of the displays, a more sophisticated understanding of the physical stimulus is required, an idea not out of line with Holt’s general worldview. These ideas are not entirely absent from other schools of psychology and could possibly be integrated with contemporary takes on the field. For instance, according to Palmer (2002), the “principle of synchrony” says that elements changing at the same time tend to perceptually group together. In some ways, then, the contrast response in the dot lattices could be taken as the synchrony information that overrides rules of similarity and common fate.

Nonetheless, the addition of new rules is not the same as reconsidering the information in the display. For example, Koffka (1935) gave a demonstration in which a 5-cm hole was cut into a 50 × 50 cm screen. The white wall behind the screen was illuminated with a reddish-yellow light. If the observer perceived the hole as part of the wall, the hole appeared fairly white. If the observer perceived the hole as part of the screen, then the hole protruded from the screen and appeared yellowish. Koffka said the appearances were determined by which object (the screen or the wall) was determined to be ground. Such analysis, however, can also be cast in terms of multiple sources of information available in the image: for instance, light from the hole and the contrast of the light relative to the screen. Thus, in Koffka’s demonstration, a switch between the “screen as ground” and “wall as ground” constructions could also be construed as an alternation between sensitivity to contrast and sensitivity to luminance.

Bibliography

Barlow, H. B., & Olshausen, B. A. (2004). Convergent evidence for the visual analysis of optic flow through anisotropic attenuation of high spatial frequencies. Journal of Vision, 4, 415–426.

Blakeslee, B., & McCourt, M. E. (1999). A multiscale spatial filtering account of the White effect, simultaneous brightness contrast and grating induction. Vision Research, 39, 4361–4377.

Brewster, D. (1844). A notice explaining the cause of an optical phenomenon observed by the Rev. W. Selwyn. Report of the Meeting of the British Association for the Advancement of Science, 12, 8.

Chubb, C., & Sperling, G. (1989). Two motion perception mechanisms revealed through distance-driven reversal of apparent motion. Proceedings of the National Academy of Sciences, 86, 2985–2989.

Chubb, C., Sperling, G., & Solomon, J. A. (1989). Texture interactions determine perceived contrast. Proceedings of the National Academy of Sciences, 86, 9631–9635.

D’Zmura, M., & Singer, B. (1996). Spatial pooling of contrast in contrast gain control. Journal of the Optical Society of America A, 13, 2135–2140.

Foley, J. M., & McCourt, M. E. (1985). Visual grating induction. Journal of the Optical Society of America A, 2, 1220–1230.

Gori, S., & Stubbs, D. A. (2006). A new set of illusions—the dynamic luminance-gradient illusion and the breathing light illusion. Perception, 35, 1573–1577.

Gregory, R. L. (1980). The confounded eye. In R. L. Gregory & E. H. Gombrich (Eds.), Illusions in nature and art. London: Duckworth.

Gregory, R. L., & Heard, P. F. (1983). Visual dissociations of movement, position and stereo depth: Some phenomenal phenomena. Quarterly Journal of Experimental Psychology, 35A, 217–237.

Hamburger, K., & Shapiro, A. G. (2009). Spillmann’s weaves are more resilient than Hermann’s grid. Vision Research, 49, 2121–2130.

Helmholtz, H. (1867). Handbuch der Physiologischen Optik. Leipzig: Voss.

Hermann, L. (1870). Eine Erscheinung simultanen Contrastes. Pflügers Archiv für die gesamte Physiologie, 3, 13–15.

Kitaoka, A. (2003). Retrieved from http://www.ritsumei.ac.jp/~akitaoka/index-e.html

Koffka, K. (1935). Principles of Gestalt psychology. New York: Hardcourt, Brace.

Landy, M. S., & Oruç, I. (2002). Properties of second-order spatial frequency channels. Vision Research, 42, 2311–2329.

Lu, Z. L., & Sperling, G. (1996). Second-order illusions: Mach bands, Chevreul, and Craik—O’Brien—Cornsweet. Vision Research, 36, 559–572.

Lu, Z. L., & Sperling, G. (1999). Second-order reversed phi. Perception and Psychophysics, 61, 1075–1088.

McCourt, M. E. (1982). A spatial frequency dependent grating-induction effect. Vision Research, 22, 119–134.

Metzger, W. (1936). Gesetze des Sehens (Vol. VI Senckenberg-Buch). Frankfurt/Main: Kramer (Spillmann, L., Lehar, S., Stromeyer, M., & Wertheimer, M. (Trans.) (2006). Laws of seeing. Cambridge, MA: MIT Press).

Oruç, I., Landy, M. S., & Pelli, D. G. (2006). Noise masking reveals channels for second-order letters. Vision Research, 46, 1493–1506.

Palmer, S. E. (2002). Perceptual grouping: It’s later than you think. Current Directions in Psychological Science, 11, 101–106.

Rubin, E. (1921). Visuell wahrgenommene Figuren. Kobenhavn: Gyldendalske Boghandel.

Schrauf, M., Lingelbach, B., & Wist, E. R. (1997). The scintillating grid illusion. Vision Research, 37, 1033–1038.

Shapiro, A. G. (2008). Separating color from color contrast. Journal of Vision, 8(1), Article 8, 1–18.

Shapiro, A. G., Charles, J. P., & Shear-Heyman, M. (2005). Visual illusions based on single-field contrast asynchronies. Journal of Vision, 5, 764–782.

Shapiro, A. G., D’Antona, A. D., Charles, J. P., Belano, L. A., Smith, J. B., & Shear-Heyman, M. (2004). Induced contrast asynchronies. Journal of Vision, 4, 459–468.

Shapiro, A. G., & Hamburger, K. (2007). Grouping by contrast: Figure-ground segregation is not necessarily fundamental. Perception, 36, 1104–1107.

Shapiro, A. G., & Knight, E. (2008). Spatial and temporal influences on the contrast gauge. Vision Research, 48, 2642–2648.

Shapiro, A. G., Smith, J. B., & Knight, E. J. (2007). Spatial scale and simultaneous contrast phenomena [Abstract]. Journal of Vision, 7, 555a. Retrieved from http://journalofvision.org/7/9/555/, doi: 10.1167/7.9.555

Smith, A. T., Greenlee, M. W., Singh, K. D., Kraemer, F. M., & Hennig, J. (1998). The processing of first- and second-order motion in human visual cortex assessed by functional magnetic resonance imaging (fMRI). Journal of Neuroscience, 18, 3816–3830.

Song, Y., & Baker, C. L., Jr. (2007). Neuronal response to texture- and contrast-defined boundaries in early visual cortex. Visual Neuroscience, 24, 65–77.

Spillmann, L., & Ehrenstein, W. H. (2004). Gestalt factors in the visual neurosciences. In L. M. Chalupa & J. S. Werner (Eds.), The visual neurosciences (pp. 1573–1589). Cambridge, MA: MIT Press.

Sutter, A., Beck, J., & Graham, N. (1989). Contrast and spatial variables in texture segregation: Testing a simple spatial-frequency channels model. Perception & Psychophysics, 46, 312–332.

Wertheimer, M. (1923). Untersuchungen zur Lehre von der Gestalt II. Psychologische Forschung, 4, 301–350.

Zhan, C. A., & Baker, C. L., Jr. (2006). Boundary cue invariance in cortical orientation maps. Cerebral Cortex, 16, 896–906.