The watercolor illusion (see Figs. 1-3) is a long-range assimilative spread of color emanating from a thin colored contour juxtaposed to a darker chromatic contour and imparting figure-ground and object-hole effects across a large area (Broerse & O'Shea, 1995; Broerse, Vladusich & O'Shea, 1999; Pinna, 1987; Pinna, 2005; Pinna, Brelstaff & Spillmann, 2001; Pinna & Grossberg, 2005; Pinna, Werner & Spillmann, 2003; Werner, Pinna & Spillmann, 2007).
The watercolor illusion and its phenomenal effects
The coloration effect
The coloration effect shows the following main properties.
(i) It is approximately uniform.
(ii) The coloration extends up to about 45 deg.
(iii) It fills in about 100 ms.
(iv) All the colors can generate the coloration effect.
(v) The illusory coloration occurs on colored and black backgrounds.
(vi) The optimal contour thickness is approx. 6 arc min.
(vii) Even if the coloration effect is stronger with wiggly contours, it also occurs with straight contours and with chains of dots.
(viii) High luminance contrast between inducing contours shows the strongest coloration effect, however, it is clearly visible at near equiluminance.
(ix) The contour with a less luminance contrast relative to the background spreads proportionally more than the contour with a higher luminance contrast.
(x) The color spreads in directions orthogonal to the contour orientation.
(xi) By reversing the colors of the two juxtaposed contours, the coloration reverses accordingly.
(xii) Phenomenally, the coloration appears solid, impenetrable and epiphanous as a surface color.
(xiii) Similarly to neon color spreading, the watercolor illusion induces a complementary color when one of the two juxtaposed contours is achromatic and the other chromatic (Pinna & Grossberg, 2005).
The figure-ground effect
The figure-ground effect shows the following properties.
(i) The watercolor illusion strongly enhances the ‘unilateral belongingness of the boundaries’, that is a phenomenal property stating that the boundaries belong only to the figure and not to the background, which appears as an empty space without a shape (Rubin, 1921).
(ii) It follows that the figure-ground segregation is not reversible and unequivocal.
(iii) Under watercolor conditions both the figure and the background assume new properties becoming respectively bulging object and empty space both with a 3-D volumetric appearance.
(iv) By reversing the colors of the two adjacent contours, the figure-ground segregation reverses accordingly.
(v) The watercolor illusion determines grouping and figure-ground segregation more strongly than the classical Gestalt principles. The principles of grouping by Wertheimer (1923) determine how elements group in parts that in their turn group in overall objects. The question they answer is how individual elements create larger wholes separated from others. The principles of figure-ground segregation by Rubin (1921) represent the rules of belongingness of the boundaries to the figure and not to the ground. The question they answer is what appears as a figure and what as a background. The figure-ground effect of the watercolor illusion wins against the following gestalt principles: proximity, good continuation, Prägnanz, relative orientation, closure, symmetry, convexity, past experience, similarity, surroundedness and parallelism.
(vi) By reversing the luminance contrast of the background, e.g. from white to black, while the luminance contrast of the contours is kept constant, the figure-ground segregation reverses.
Dissociation between coloration and figure-ground effects
The study of the relationship between the coloration and the figure-ground effects is a basic problem of Vision Science, with at least two main questions: Are color and figure-ground processes independent? How and where does the integration between the two processes occur?
Coloration without figure-ground effect
Pinna & Reeves (2006) showed that coloration without a figure-ground effect is induced through a dichoptic composite stimulus, where the orange contour is presented to one eye while the purple one to the other eye. Under these conditions, the coloration is clearly perceived within the inner edges, but the figure-ground effect is totally absent. The binding between the coloration and the figure-ground effects is weakened by reversing the figure-ground organization where the coloration occurs.
Coloration without any figure-ground effect can be obtained by using equiluminant adjacent contours that, even if they spread their colors, they show a flat and reversible figure-ground organization. This condition is related to Figure 12 , where in the gray range (central region), in which neither the stars nor the crosses prevail as a figure against the other, the coloration effect occurs. Another case of coloration without figure-ground effect is illustrated in Figure 14.
Figure-ground without coloration effect
In Figure 15, an example of figure-ground effect without coloration is illustrated: the crosses clearly emerge as rounded convex figures while the coloration is absent.
The watercolor surface capture
A demonstration of the figure-ground effect of Figure 15 is illustrated in Figure 16. This is called: “watercolor surface capture” (Pinna & Reeves, 2006). The white within the stars of Figure 15 is also captured in a more elevated depth plane by the figural effect of the crosses.
The lighting illusion
By adding new adjacent contours, another case of the figure-ground effect without coloration is obtained (see Figure 17). This is the lighting illusion (Pinna, 2006; Pinna & Reeves, 2006).
The object-hole effect and the principle underlying the watercolor illusion
The object-hole effect
The object-hole effect of the watercolor illusion goes beyond the figure-ground segregation. It can be considered as the emergence of the figure as a volumetric object and of the empty space as a solid 3-D hole. The perception of the hole is an important problem useful to understand the more general problem of object perception and shape formation. Palmer (1999) demonstrated that holes imply quasi-figural properties. Other findings suggest that holes behave like other background regions (see Bertamini, 2006). The hole induced by the watercolor illusion is more than something in between figure and background and can solve the problem of perception of holes. In fact, the boundaries appear to belong to it and at the same time to the complementary watercolored region in a clear 3-D appearance (see Figure 18). The object-hole effects related to the watercolor illusion contain a paradox: if the hole appears as an empty space with a shape, where the boundaries belong to the hole and, at the same time, to the complementary region, then the hole can be perceived as a background that is a “figure” emerging from a surrounding figure behaving as a “background”. If this is true, then several related paradoxical phenomena could be created where the holes behave both like figures and backgrounds (see Figure 19). By imparting motion to the outer or inner squares of Figure 18a, the figure-ground segregation, eliciting the static hole, is expected to be broken (see Figure 20). The question is now: If the watercolor illusion induces a strong figural property to the holes, are they still perceived when motion is imparted to them? The answer is illustrated in the movie of Figure 21. Under the watercolor conditions, moving holes appear paradoxically more as figures than the watercolor objects.
The asymmetric luminance contrast principle
The figurality paradox of the holes, induced by the watercolor illusion, suggest that the watercolor illusion can be considered as the result of a new principle of grouping and figure-ground segregation much stronger than the gestalt ones. This principle, called “asymmetric luminance contrast principle” (Pinna, 2005), states that, all else being equal, given an asymmetric luminance contrast on both sides of a boundary, the region, whose luminance gradient is less abrupt, is perceived as a figure relative to the complementary more abrupt region perceived as a background. This figure-ground principle can also be expressed in terms of grouping. This principle can be considered as part of the more general problem of “figurality” (Pinna & Reeves, 2006) – i.e. the phenomenal appearance of what is perceived as a figure with a whole color, within the three-dimensional space and under a perceived illumination – and its underlying principles, that are the topic of the next Section.
From the watercolor illusion to the principles of figurality
From the watercolor illusion to the discoloration illusion
Under our conditions, the key point to understand the watercolor illusion and its figurality properties are the juxtaposed contours. The lighting illusion (see Section 2.2.2) demonstrates that by increasing the number of juxtaposed contours (i) the coloration effect decreases or is annulled, (ii) the object-hole and volumetric effects increase and (iii) the lighting effect increases. If the inner region of a blue undulated shape, similar to Figure 17, is physically filled with a light chromatic tint (e.g. pink), the perceived result is a blue undulated shape with a three-dimensional (volumetric) appearance illuminated by a bright light. Under these conditions, the inner region appears white: the pink discolors (Figure 22a). This is called “discoloration Illusion” (Pinna, 2006; Pinna & Reeves, 2006).
The switch from the watercolor illusion to the discoloration illusion depends on the bunch of contours, on their number and on the role of each contour with respect to the others. The different roles derive from the specific and relative position of each contour within the bunch of contours. On the basis of the previous illusions it can be stated that most of the information about figurality resides on the boundary contours. The principles of figurality, similar in spirit to the well-known gestalt principles of organization, extracted from different luminance gradient profiles across boundary contours, define the phenomenal roles played by the juxtaposed contours in defining the phenomenal appearance of the figure – its color and spatial volume, seen under an apparent illumination.
The principles of figurality
The principles of figurality complement the grouping and figure-ground principles. The main question these principles intend to answer is: how variations in boundaries and luminance gradient profiles define the figurality properties (Pinna & Reeves, 2006). Thus figurality proceeds beyond the properties of the figure as defined by Rubin’s and Wertheimer’s principles. Rubin’s unilateral belongingness of the boundaries, also called “border ownership” can be considered as the first law of figurality.
Principle 1: The boundary contours belong unilaterally to the figure, but not to the background.
This principle operates also with the limiting case of one contour only. Given more than two or three juxtaposed contours.
Principle 2: The juxtaposed contour with the highest luminance contrast in relation to the homogenous surrounding regions tends to appear as the outermost boundary of the figure. This is called “boundary contour".
This principle clearly applies to the watercolor illusion and to all the other conditions previously illustrated, including the quasi-equiluminant conditions where the figure-ground segregation is reversible.
Principle 3: The bunch of contours with lower and decreasing luminance contrast in relation to the homogenous surrounding regions, adjacent to the boundary contour, model the volume depicting lights and shades. They are the “shading contours”.
The role of the shading contours appears clearly in the watercolor, the lighting and the discoloration illusions.
Principle 4: The contour, placed next to the shading contours where the luminance contrast decreases, determines the whole color of the object. This is called “object color contour”.
In the watercolor illusion, induced by only two juxtaposed contours, there is no differentiation between shading and color lines, because only one contour plays both roles.
Principle 5: The innermost contour at the extreme of the gradient with the lowest luminance contrast in relation to the homogenous surrounding region defines the properties of the lighting (its color and intensity). This is called “lighting contour”.
The extreme of the gradient is placed in the borderland between different regions, namely the juxtaposed contours and a large white homogeneous area, thus delimiting the boundaries of these two regions and separating the object from “something else”: the most lighted area. This is similar to the contour with the highest luminance contrast that separates the object from the background. Therefore, while the boundary contour defines and delimits the object, the lighting contour delimits and defines the property of the light (see Figure 23).
The backlighting illusion
Principle 6: The outermost contour at the opposite extreme of the gradient with a luminance contrast lower than the boundary line is the “backlighting line”. This contour does not define object properties, but only the properties (color and intensity) of the illumination coming from behind.
In Figure 24, the backlighting illusion is illustrated.
These differentiated and specialized figural roles of the juxtaposed contours complete the figurality of the object in which the color plays several important roles: it defines the color of the whole object and its parts (when there are more colors located in different regions within the object) and determines the chromatic properties of the incident light and of the backlighting. These roles demonstrate that (i) colors phenomenally organize themselves within the more general problem of figurality and that (ii) the amodal completion of color is the basic phenomenon of the organization of color.
The amodal completion of color
Color can complete amodally like shape. The amodal completion of color can be considered as the most common form of visual completion occurring when the color of an object is hidden, due to its occlusion behind illumination or behind another color. The term “amodal” refers to the fact that, despite not perceiving a color within the entire object, observers have a vivid perception of color completeness and unity. The simple questions, useful to understand the amodal completion of color and referred to the lighting illusion (Figure 17), are: What color is the undulated object? Is it blue with a white center (the whole color of the object is blue and the white appears as a bright light reflected from the object), white with a blue periphery (the whole color is white and the blue is some kind of undefined coloration) or two-tone (without any whole color)? If the object is blue, what is the exact blue among the six juxtaposed ones behind the bright light? Which of the six adjacent contours fits the best in terms of color of the perceived amodal color of the object? If the object is blue, what is the white inner region? Is it color or something else? If, conversely, the object is white what is the blue periphery? Similar questions can be asked with respect to the watercolor illusion and to all the other illusions presented here. The amodal completion of color obeys several rules:
Rule 1: Given more than one chromatic color within an object, the color perceived as the whole color (amodal coloration) of the object is only one among many (principle of uniqueness of the whole object color).
Rule 2: If only one color becomes the whole color of the object, the other colors assume other roles: they become the colors of parts or specific regions of the object and complete the figurality properties by defining the reflected or the backlighting light (principle of multiplicity and of specialization of roles).
Rule 3: Different colors within an object are perceived as organized and included one within or “behind” the others. This is mostly the case of the whole color of the object (principle of the amodal completion of color).
Rule 4: The whole color (amodal coloration) and the roles of the other colors are determined by different specific spatial locations within the object (principle of correspondence between roles and spatial locations).
Neural mechanisms underlying the watercolor illusion
The relative separation between the coloration and figural effects suggests the existence of parallel but strongly related mechanisms. The FACADE model (Grossberg, 1997) posits that boundary grouping and surface filling-in processes can explain the two effects in the watercolor illusion. They are substantiated by the cortical interblob and blob streams, respectively, within cortical areas V1 through V4. These boundary and surface processes show complementary properties and their interaction generates a consistent perceptual representation that overcomes the complementary deficiencies of each stream, acting on its own. Boundary and surface processes are modeled by the Boundary Contour System (BCS) and by the Feature Contour System (FCS). Several findings (Zhou et al., 2000; von der Heydt et al., 2003; Friedman et al., 2003) showed that neurons in V2 respond with different strength to the same contrast border, depending on the side of the figure to which the border belongs, implying a neural correlate process related to the unilateral belongingness of the boundaries. Figure-ground segregation may be processed in areas V1 and V2, in inferotemporal cortex and the human lateral occipital complex. Not only the figure-ground segregation, but also the color tint of the watercolor illusion might have its explanation in the cortical representation of borders (von der Heydt & Pierson, 2006). The differentiated and specialized figural roles of the juxtaposed contours and of their colors suggest a possible neural scenario where multiple juxtaposed lines may stimulate neurons selective for different asymmetric luminance profiles and signaling not only the unilateral belongingness of the boundaries but also the coloration, the volumetric and the illumination effects. Due to the gradient variations at different scales, it can be suggested that these neurons, at the beginning undifferentiated, become more and more specialized by assuming different roles but at the same time becoming part of the more global integrated process of figurality.
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