Watercolor spreading in Bridget Riley's and Piet Mondrian's op-art placed in the context of recent watercolor studies

Abstract

The watercolor effect (WCE) is a striking visual illusion elicited by a bichromatic double contour, such as a light orange and a dark purple, hugging each other on a white background. Color assimilation, emanating from the lighter contour, spreads onto the enclosed surface area, thereby tinting it with a chromatic veil, not unlike a weak but real color. Map makers in the 17th century utilized the WCE to better demarcate the shape of adjoining states, while 20th-century artist Bridget Riley created illusory watercolor as part of her op-art. Today's visual scientists study the WCE for its filling-in properties and strong figure–ground segregation. This review emphasizes the superior strength of the WCE for grouping and figure–ground organization vis-à-vis the classical Gestalt factors of Max Wertheimer (1923), thereby inspiring a notion of form from induced color. It also demonstrates that a thin chromatic line, flanking the inside of a black Mondrian-type pattern, induces the WCE across a large white surface area. Phenomenological, psychophysical, and neurophysiological approaches are reviewed.

Introduction

About 25 years ago, Baingio Pinna, from Sardegna, Italy, and the author introduced the watercolor effect (WCE) to the attendees of the meeting of the Vision Science Society in Sarasota, FL (Figure 1). Examples of Pinna's hand-drawn illustrations, showing subtle color emanating from the inner of two heterochromatic borders and filling in the enclosed surface area, were laid out on the conference floor. Many people were excited about the illusory veil of color and wondered whether they could take one of the illustrations back home. Others immediately attempted to reproduce the effect on a laptop, while Richard Gregory inspected one of the sheets from various angles to check whether the color was real or illusory. 

Figure 1.

 

Hand drawn. The yellowish lobes are physically identical to the white lobes. (Reprinted, by permission, from Pinna et al., 2001.)

At that time, we did not know that the WCE, first discovered by Pinna (1987) and later studied by Pinna, Brelstaff, and Spillmann (2001), was not entirely new. As it turned out, it had already been demonstrated in Renaissance maps of the 17th century, where it served to better demarcate neighboring countries in cartography (Bagrow & Skelton, 1985; Wollschläger, Rodriguez, & Hoffman, 2002; Spillmann, Pinna, & Werner, 2005; Pinna & Mariotti, 2006). Furthermore, there may be a relationship between watercolor spreading and the Renaissance technique of chiaroscuro (Pinna, 2005). 

The watercolor effect in Bridget Riley's paintings

More recently, Patrick Cavanagh (Dept. of Psychological and Brain Sciences, Dartmouth College), at the Frieze Masters 2015 exhibition in London, saw what appears to be a precursor of the WCE in art. Among the exhibited works (https://www.karstenschubert.com/exhibitions/183/) were two pieces by the noted British op-artist Bridget Riley. The first painting, about 2 m × 3 m, shows a field of slender, vertical lozenges delineated by green and purple and blue and yellow double contours (Figure 2A). As a result, the interspaces in between the contours appear uniformly filled with a reddish and greenish watercolor. In the second, similar painting (Figure 2B), the contours are composed of obliquely crisscrossing black lines, accompanied by red, green, or light-blue lines, thereby producing reddish, greenish, and bluish lozenges. All of these colors are illusory. 

Figure 2.

 

Note the subtle change of color among adjoining lozenges. The background in each painting is the same throughout. (A) Pasted graphic 15. (B) Pasted graphic 16. (Reprinted, by permission, from Kudielka, 2010.)

Assimilative color spreading is already evident in Riley's earlier paintings, such as Cataract 2 (1967), Orient 4 (1970), and Zing 2 (1971), reproduced in her collected writings (Kudielka, 2010). One of these paintings, Zing 2, is included here for comparison with the Pinna figures (Figure 3A). It consists of a series of red, blue, and green braided stripes adjoining each other in various combinations. The red, green, and blue bands extending horizontally across the striped pattern seem to fill the interspaces between the dark stripes uniformly with a reddish, greenish, or bluish haze; however, this is illusory. The innermost sections of the colored stripes are, in fact, white, or nearly so, as is shown by the magnified samples in Figure 3B. Differently from the Pinna figures, the edges of the vertical stripes are not sharp but ramped, decreasing in chroma from high to low and ultimately white. 

Figure 3.

 

(A) Zing 2 (1971). The red, green, and blue horizontal bands constitute an early demonstration of watercolor spreading (https://www.myartbroker.com/artist-bridget-riley/record-prices/bridget-riley-record-prices). (B) The magnified pattern shows that the colored stripes consist of four narrow steps varying from dark to light and high to low saturation at each of the juxtaposed edges. The wide bands in the middle are white or nearly so.

From her writings, it does not appear that Riley assigned any particular significance to the illusory coloration, although being an astute observer she must have been aware of it. Her paintings show that op-art was ahead of vision science in demonstrating the watercolor effect years before it was explained (Spillmann, 2007). 

The watercolor effect in visual science

Pinna's WCE, emanating from thin inducing lines, is unlike the assimilative coloration in the arabesques of Von Bezold (1874), which fill in the white interspaces between tangential lines. Whereas the area of illusory coloration in the arabesques is quite narrow (Fach & Sharpe, 1986), the WCE was found to spread over an estimated 45 degrees of visual angle (Pinna et al., 2001). It arises within 100 ms (Reeves, Pinna, & Roxas, 2013) and uniformly bridges the adjacent surface area. Upon repeated viewing, it does not go away even if one examines the physical stimulus with a two-holed aperture, with one hole placed on the ground and the other on the enclosed surface area, recognizing that the filled-in color is illusory. This paper examines what has been learned from studies of the WCE since its inception more than two decades ago. Psychophysical, neurophysiological, and computational approaches have begun to shed light on the processes that may underlie the assimilative coloration and its role in figure–ground segregation. These attempts are briefly reviewed here. 

Phenomenological observations

The WCE occurs on a white surface area enclosed by a wavy double contour such as a dark purple on the outside and a light orange on the inside (Figure 1). As a result, the enclosed surface assumes an orangish tint, spreading uniformly onto the interior, while the surface on the outside appears as a cold white. Other color combinations for the double contour also produce the WCE, albeit not as strongly. Although the WCE is best observed with an undulating contour, suggesting the involvement of curvature detectors, it can also be seen on a stimulus pattern with straight borders (Figure 4). 

Figure 4.

 

Hand drawn. The interspaces between the vertical lines are physically identical, but the wider interspaces look yellowish and are perceptually grouped, overruling the Gestalt factor of proximity. View at low ambient illumination. (Reprinted, by permission, from Pinna et al., 2001.)

When two different inner flanking colors, such as red and green, are juxtaposed, each color spreads about halfway onto the enclosed surface area (Pinna et al., 2001). This is analogous to the color filling-in of the blind spot (Li et al., 2014) and points toward a long-distance filling-in process (Spillmann & Werner, 1996). 

The WCE stands out not just because of its large illusory coloration but also due to its strength in segregating figure and ground. Although the illusory color may seem subtle, in experiments on figure–ground segregation it was found that the WCE is perceptually superior to such Gestalt factors as similarity, proximity, good continuation, closure, parallelism, and symmetry (Pinna, Werner, & Spillmann, 2003; Pinna, 2005; Spillmann et al., 2005). When the WCE is pitted against a given Gestalt factor, it overrules the classical Gestalt factor and wins. This is shown in Figure 4. Figures 5 and 6 show further examples. 

Figure 5.

 

Hand drawn. (A) The WCE versus the Gestalt factor of good continuation. (B) Watercolor versus closure. (C) Watercolor versus parallelism. (D) Watercolor versus convexity. In each case, the area filled by watercolor is seen as a figure, overruling the figure–ground organization predicted by the Gestalt factors. The background in all of the figures is the same throughout. (Reprinted, by permission, from Pinna et al., 2001.)

Figure 6.

 

Hand drawn. When the chromatic double contour is reversed, the yellowish surface area flips. (A) The inner orange fringe induces watercolor spreading over water bodies. (B) The outer orange fringe induces watercolor over land masses. This percept overrules the Gestalt factor of closure. Only in the latter map do subjects spontaneously recognize the Mediterranean and Black Sea. (Reprinted, by permission, from Werner et al., 2007.)

Color spreading in the WCE is present not only in monoptic patterns but also on stimuli presented in dichoptic view. When two differently colored borders are viewed dichoptically, one with each eye, the WCE continues to be perceived (Pinna et al., 2001). Furthermore, color spreading also persists when the inner and outer borders are placed in perceptually different depth planes, thereby producing a colored figure that appears to lie above or behind the white ground. Results show that, for all tested disparities, crossed and uncrossed, watercolor spreads uniformly across the enclosed surface area (Pinna et al., 2001). 

The major results of these studies were reported in Scientific American to a wider audience, together with observations on the Ehrenstein brightness illusion and its variants (Werner et al., 2007). These phenomena demonstrate how neural processing determines illusory color and how illusory color determines form. 

Psychophysical results

Following these qualitative observations, psychophysical measurements were made to quantify the WCE. Using a hue-cancellation task, Devinck, Delahunt, Hardy, Spillmann, and Werner (2005) demonstrated that the WCE becomes stronger with increasing luminance of the inner inducing contour. Similar results were also found using a scaling method (Cao, Yazdanbakhsh, & Mingolla, 2011; Gerardin, Dojat, Knoblauch, & Devinck, 2018). These results suggest that a luminance-dependent mechanism predominately mediates the WCE. The observation by Pinna et al. (2001) that the WCE is still present, although weaker, with equiluminant inducing contours has recently been confirmed (Tyler & Solomon, 2018). 

Devinck, Hardy, Delahunt, Spillmann, and Werner (2006a) also found that the coloration effect increases with increasing chromatic contrast. Approximately complementary colors produce the strongest WCE. On chromatic backgrounds, a faint WCE persists, but it does not perceptually mix with the color of the background (Pinna et al., 2001). Whereas Pinna et al. (2001) estimated that the WCE is strongest for undulating contours having a width of 6 minutes of arc (arcmin) and a spatial frequency of 1.23 cycles per degree (cpd), Devinck, Gerardin, Dojat, and Knoblauch (2014) reported values of 7.5 arcmin and 4 cpd, respectively. Gerardin, Devinck, Dojat, and Knoblauch (2014) additionally found that the strength of the WCE is nearly independent of the amplitude of modulation. Perceived hue shifts were largest when the enclosed surface area was narrow (i.e., a vertical column) and decreased exponentially to 7.4° with increasing surface width (Devinck, Hardy, Delahunt, Spillmann, & Werner, 2006b). This value is much smaller than the one originally reported by Pinna et al. (2001), which may have been obtained at greater eccentricities. 

Contrary to expectation, sharp edges were found to be more effective than ramped edges (Devinck, Spillmann, & Werner, 2006). This is consistent with the observation that optical blurring (by onion skin paper) weakens or even abolishes the WCE (Pinna et al., 2001). Color spreading is also reduced after adaptation to the inducing contours (Coia & Crognale, 2018). This demonstrates the importance of contour salience. 

Spatial contiguity and continuity of the inducing contours are important. When a narrow gap separates the two inducing contours, so that they no longer touch each other, the hue shift rapidly decreases with increasing spacing between them (Devinck & Spillmann, 2009). This is analogous to a decrease of perceived color contrast when a test field is spatially separated from the inducing surround (Brenner & Cornelissen, 1991; Conway, 2012). Similarly, the WCE quickly decreases with increasing distance between the dots (Devinck & Spillmann, 2009), when dotted contours replace the continuous contours. 

Explaining the WCE

Although similar in appearance, the WCE cannot be explained by Bezold- or Helson-type assimilation (Von Bezold, 1874; Helson, 1963; Jameson & Hurvich, 1975), as the assimilated color extends over a much larger area. It is also different from the neon color effect (for a review, see Bressan, Mingolla, Spillmann, & Watanabe, 1997). Neon color is transparent, extends over a relatively short distance (Redies & Spillmann, 1981), and depends on collinear line ends (terminators) opposing each other around a central gap. 

The WCE described here is a striking example of a surface color (Katz, 1911), induced by a thin, colored double contour. In addition, there is a strong figural component segregating the colored surface (the “figure”) from the ground. This property suggests two neural mechanisms for color and form. A wide spectrum of hypotheses has been proposed to understand how the neural representation of edge-induced filling-in of color arises in the brain. These are briefly reviewed here. 

Pinna et al. (2001) originally assumed that color spreading may arise in two steps: first, by weakening of the inner contour through lateral inhibition between differentially activated edge cells (local diffusion), and, second, by the subsequent flow of color or “bleeding” onto the enclosed surface area (global diffusion). More specifically, Devinck et al. (2014) suggested an origin of the WCE in the double-opponent cells in cortical area V1. These cells are known to respond to chromatic edges in a chromatically opponent manner (Daw, 1968; Conway, 2001; Shapley & Hawken, 2011). Yet, because their spatial connectivity may be too small to account for large-scale color assimilation such as in the WCE (Markov et al., 2011), Gerardin et al. (2014) proposed that the WCE is processed hierarchically, requiring a site for contour integration in the orientation-selective cells of cortical area V3. Using functional magnetic resonance imaging (fMRI), Gerardin et al. (2018) recently confirmed that cortical areas V3A and V3B/KO (kinetic occipital area) are active in generating the WCE. They further suggested feedback connections from area V3A to areas V1 and LO (lateral occipital) underlying the WCE (for a review, see Devinck & Knoblauch, 2019). 

Focusing on the Gestalt properties of the WCE, von der Heydt and Pierson (2006) proposed that color spreading arises from neurons, representing surface color in the visual cortex, whereas the figure–ground effect results from neurons sensitive to an asymmetric edge profile. As shown in the monkey, edge polarity neurons in visual areas V2 and V4, responding to a luminance step in one direction but not the other, may be responsible for assigning border ownership (Baumann, van der Zwan, & Peterhans, 1997; Zhou, Friedman, & von der Heydt, 2000) and in this way render the watercolor figure unambiguous. 

From a computational point of view, Pinna and Grossberg (2005) discussed the WCE in terms of the FAÇADE model. Here, the boundary contour system (BCS) is assumed to account for contour grouping, whereas the feature contour system (FCS) accounts for surface color filling-in. 

To explain the illusory coloration, Devinck and Knoblauch (2019) advanced a Bayesian hypothesis, according to which the enclosed area is perceived as a uniformly colorated surface because this is the most likely explanation for the WCE. Finally, Cohen-Duwek and Spitzer (2019) recently presented a computational feedforward model to account for the WCE. Their model is based on a diffusive filling-in process emanating from the double contour due to processing in oriented double-opponent receptive fields. 

The watercolor effect in a Mondrian pattern

An effect like Pinna's WCE has been demonstrated by Broerse, Vladusich, and O'Shea (1999, their figure 1). These authors showed that thin chromatic edges, delineating the thick black grating stripes, spread their color onto the white interspaces between them. For an explanation, the authors distinguished between edge colors (fringes) due to chromatic aberration and spread colors (or surface colors) due to a neural filling-in process, which operates to achieve color uniformity. Yet, the WCE persists even when viewed through an achromatizing lens (Devinck et al., 2006a), thus ruling out chromatic aberration. 

Figure 7, inspired by Broerse et al. (1999), demonstrates watercolor spreading across much larger surfaces in a modified Mondrian pattern. Red and green (Figure 7A) and orange and blue (Figure 7B) surfaces can be generated in this manner, suggesting that a single, colored line flanking a thick black bar suffices to elicit the WCE. All that seems to matter is a dark–light edge profile. 

Figure 7.

 

Watercolor spreading in a Mondrian-type pattern. Compare the color of the rectangles lined with a thin chromatic edge with the white surfaces on the bottom. (Design by Frédéric Devinck. Reproduced by permission.)

The observation that two watercolors may be simultaneously seen, each in its own half, when the juxtaposed inner contours have different chromaticity (Pinna et al., 2001), speaks in favor of propagation from the contour onto the enclosed surface area. The WCE may thus be another example of color filling-in (Friedman, Zhou, & von der Heydt, 1999, Li et al., 2014), which is large scale and seemingly instantaneous and does not require strict fixation for stabilizing the image on the retina. 

Despite its power in determining figure and ground, Tyler and Solomon (2018) suggested that Pinna's WCE plays only a minor role in the perceived color of natural images. This is not surprising, as the inducing stimuli are mere contours, not extended surfaces as in area contrast. Both effects require long-range neural mechanisms (Spillmann & Werner, 1996). 

Conclusions

Since the first presentation of the WCE 25 years ago by Pinna et al. (2001, their table 2), further studies have contributed important additional knowledge of the contour properties, generating long-range filling-in. We now know that (a) watercolor spreading was used not only in cartography but also in op-art before vision science stumbled onto it; (b) it reaches full strength nearly instantaneously; (c) it increases both with increasing luminance contrast and increasing chromatic contrast; (d) it is strongest on surfaces up to about 7° when the contours have a width of 7.5 arcmin and a spatial frequency of 4 cpd; (e) it is weakened by blur as well as by adaptation to the contours; and (f) it requires spatially contiguous and continuous inducing contours. Results obtained with fMRI suggest that double-opponent cells in V1 and cells in visual areas V3A and V3B/KO, if combined with feedback connections from V3A to V1 and LO, are potential neural mechanisms responsible for the WCE. Future investigations should clarify our understanding of the global figure–ground mechanism involved in the WCE, separate from the local coloration effect. A fascinating color illusion inspired by visual art would thus contribute to a better understanding of an intriguing phenomenon in visual science. 

Acknowledgments

The author thanks Patrick Cavanagh for alerting him to the two WCE paintings by Bridget Riley shown in Figures 2A and 2B and an anonymous reviewer for pointing out even more WCE paintings by Riley (shown in Figure 3); Fred Devinck, for help with Figure 6; and Kenneth Knoblauch, John S. Werner, and Michael A. Crognale for reading the manuscript and making extensive comments. Also gratefully appreciated is the help by Saher Semaan in formatting the figures, by Dieter Weber for procuring copyright permission, and the librarians of the Medical Clinic of the University for providing literature. 

Commercial relationships: none. 

Corresponding author: Lothar Spillmann. 

Email: [e-mail]. 

Address: Department of Neurology, University of Freiburg, Freiburg 79085, Germany.