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Figures and holes Marco Bertamini1, Roberto Casati2

To appear in: Oxford Handbook of Perceptual Organization Oxford University Press Edited by Johan Wagemans 1. Department of Experimental Psychology, University of Liverpool, UK 2. Institut Jean Nicod, Ecole Normale Supérieure, Paris, France Holes have special ontological, topological, and visual properties. Perhaps because of these they have attracted great interest from many scholars. In this chapter we discuss these properties, and highlight their interactions. For instance, holes are not concrete objects, their existence in perception is therefore an exception to the general principle, grounded in evolution, that the visual system parses a scene into regions corresponding to concrete objects. In 1948, Arnheim discussed the role of holes in the sculptures of Henry Moore. Arnheim's analysis was informed by Gestalt principles of figure-ground. In the case of holes within sculptures, given their relative closure and compactness, Arnheim detected a sense of presence. It is worth reporting his words here as this ambiguity is precisely the issue that has been central to much later work: "Psychologically speaking, these statues [..] do not consist entirely of bulging convexities, which would invade space aggressively, but reserve an important role to dells and caves and pocket-shaped holes. Whenever convexity is handed over to space, partial "figure"-character is assumed by the enclosed air-bodies, which consequently appear semi-substantial." (p. 33). This chapter starts with a discussion of the ontology and topology of holes. In the last part of the chapter the focus will be on the role of holes in the study of figure-ground organization and perception of shape. 1. Ontology In philosophy, ontology is the study of the nature of being, and of the basic categories of being and their relations. The ontology of holes moves from the prima facie linguistic evidence that we make statements about holes, thus presupposing their extra-mental existence. At the same time, holes appear to be absences, thus non-existing items. Therefore, if they exist, they are sui generis objects. Within the debate on the nature of holes, materialism maintains that nothing exists in the world but concrete material objects, thus holes should be explained away by reference to properties of objects (Lewis & Lewis 1983). Others, by contrast, maintain that holes exist even though they are not material (Casati & Varzi 1994). If we accept that holes exist, further problems must be addressed. For example whether holes exist independently of the object in which they find themselves, whether they should be equated with the hole linings (and thus be considered as material parts of material objects), and whether one can destroy a hole by filling it up (as opposed to ending up with a filled hole). To consider holes as existing extra-mentally is no trivial assumption. There are some advantages, such as the possibility of describing the shape of a holed object by referring to the shape of the hole in it. For example we

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can describe a star-shaped hole in a square-shaped object. If holes could not be referred to directly, the description of the same configuration would be awkward (Figure 1a). But if holes exist, they are not material objects. Yet they possess geometric properties, and therefore there are some entities with geometric properties that are not objects. This would entail that Gestalt rules can fail in parsing the visual scene into objects. However, if holes have shape like figures, they do not prevent the visual area corresponding to their shape from being seen as ground. Therefore, the same area can behave as figure and ground at the same time, which is, prima facie, problematic for theories of figure-ground segmentation and for the principle of unidirectional contour ownership (Koffka 1935). Border ownership is covered in detail in chapter 13. Various solutions exist. Some may wonder whether ontology is relevant for the study of visual perception. There may exist a property such that anything that is a hole has that property, but this does not entail that to have the impression of seeing a hole one must visually represent that very property: holes can be immaterial bodies, or negative parts of objects (Hoffman and Richards 1984), or portions of object boundaries, and perception may be blind to their real nature, although still delivering the impression of perceiving a hole (Siegel 2009). Alternatively, one may suggest that the process of figure-ground organization misfires in the case of holes, whose Gestalt properties erroneously trigger the "figure" response. That is, holes are (rare) exceptions. Another solution is to say that holes have a special "tag" as the missing part of an object (Nelson, Thierman, & Palmer 2009). The solution that requires less changes to Gestalt principles, however, is to say that the shape properties of the hole are a property of the object-with-hole, just like the large concavity in a letter C. These properties do not make the hole or the concavity of the letter C into a figure in the sense of foreground. What is meant by figure in figure-ground organization is not just something that has shape, but something that is more specific and is closely linked to surface stratification. In all these cases, the visual system makes important decisions about whether holes exist, and about their nature as objects or quasi-object. Some developmental findings comfort this hypothesis. Giralt and Bloom (2000) found that 3 year old children can already classify, track, and count holes. Therefore there is good evidence that the human perceptual system takes holes seriously into account. 2. Topology Holes play an important part in topology, a branch of mathematics dealing with spatial properties. Topological shape-invariance is intuitively understood by imagining that objects are rubber-sheet. In particular, the concept of homotopy classification is used to describe the difference between shapes. Two objects are topologically equivalent if it is possible to transform one of them into the other by just stretching it, without cutting or gluing at any place. Thus a cube is topologically equivalent to a sphere, but neither is equivalent to a doughnut. This classification, in non-technical terms, measures the number of holes in an object. For instance, all letters of the alphabet used in this chapter belong to one of three classes respectively with zero (the capital L), one (capital A) or two holes (capital B). Capital L is topologically equivalent to capital I, Y and V. This explains the joke that says that a topologist can't distinguish a mug from a doughnut (assuming the mug has a handle, they both have just one hole). The joke about topologists hints at a psychologically interesting distinction. Intuitive topological classifications of objects are not well aligned with topological classifications. As there is a naïve physics that departs from standard physics, there appears to be a naïve topology that does not coincide with mathematical topology. For instance, a cube perforated with a Y-shaped hole is topologically equivalent to a cube perforated with two

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parallel I-shaped holes, surprising as this may appear (Figure 1). Moreover, a knot in a hole is invisible to mathematical topology. Naïve topology uses both objects and holes to classify shapes. (a)

(b) Figure 1. (a) The cognitive advantage of holes: the object is easily described as a blue square with a star-shaped hole. A description of the shape of the object that does not mention the shape of the hole would be more difficult. (b) Evidence for naïve topology: Two solids that mathematical topology cannot distinguish but that appear quite different to common-sense classifications. (Redrawn from Casati and Varzi 1994)

Within vision science, Chen has argued that extraction of topological properties is a fundamental function of the visual system, and that topological perception is prior to the perception of other featural properties (for a review see Chen 2005; see Casati 2009 for a criticism). There is some empirical evidence in support of this claim. In particular, Chen has shown that human observers are better at discriminating pairs of shapes that are topologically different than pairs that are topologically the same (Chen 1982) and Todd, Chen and Norman (1998) have found that in a match-to-sample task performance was highest for topological properties, intermediate for affine properties, and lowest for Euclidean properties. More recently, Wang, Zhou, Zhuo and Chen (2007) reported that sensitivity to topological properties is greater in the left hemisphere, and Zhou, Luo, Zhou, Zhuo, and Chen (2010) have found that topological changes disrupt multiple objects tracking. Holes play an important role in studies of topology, and topology is useful in explaining some perceptual phenomena. However, in this context holes are defined as an image property. In other words the letter O is an example of a hole whether or not this is perceived as a black object in front of a white background. The depth order of the white and black regions is irrelevant, and the experiments cited above did not try to establish whether observers perceived the region inside the hole as showing a surface farther in depth than the object itself.

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Hard Context Easy

Figure 2. The configural superiority effect: Target detection improves with the addition of a context. In this example the closed region is easier to find compared to a difference in orientation.

Let us take the phenomenon of configural superiority (Figure 2) studied by Pomerantz (2003; Pomerantz, Sager, & Stoever 1977; see also Chapter 26) and discussed also in Chen (2005). This effect may be taken to demonstrate the salience of perception of a hole over individual sloped lines. But 'closure' may be a better term for this configural property. That is, because depth order is not important, this concept of hole is closer to the concept of closure. This is consistent with the literature because closure is a factor that enhances shape detection (Elder & Zucker 1993) and modulates shape adaptation (Bell, Hancock, Kingdom, & Peirce 2010). Note that closure is on a continuum: even contours that are not closed in a strict image sense can be more or less closed perceptually (Elder & Zucker 1994). This quantitative aspect of closure is important for the concept of hole, because it makes a hole simply the extreme of a continuum of enclosed regions and not something unique. Moreover, if closure is sufficient to define holes then any closed contour creates a hole, which makes holes very common, whereas true holes (i.e. apertures) are relatively rare. 3. Holes as ground regions We have briefly discussed the ontology and topology of holes, holes are especially interesting in the study of perceptual organization, that is, when a hole is defined in terms of figure-ground organization (see chapter 9) and perception of surface layout. A general definition of a visual hole is a region surrounded by a closed contour but perceived as an aperture (a missing piece of surface) through which a further (and farther) surface is visible. This is a definition specific to visual holes, rather than the more general concept of physical holes, as not all physical holes may be visible (Palmer et al. 2006). This usage of the term 'hole' within the literature dealing with perceptual organization critically relies on ordinal depth information. Holes would not exist in a two-dimensional world, but they only require ordinal rather than metric depth. Bertamini (2006) argued that visual holes are ideal stimuli to study the effect of figure-ground reversal on perception of shape: A closed region perceived as object or hole provides a direct comparison between a figure (object) and a ground (hole) that are otherwise identical in shape (congruent). However, Palmer et al. (2008) argued that contour ownership and ordinal depth can be dissociated in figure-ground organization. More specifically, in the case of a visual hole the outside object (the object-with-hole) is foreground, and therefore nearer in depth than the background, but the contour can also describe the ground region inside the hole, contrary to what unidirectional contour ownership would suggest. If holes are special in that they have one property of background (depth order) but also a property of the foreground (contour ownership) then they are not useful in the study of general figure-ground effects, as these would not generalize to other ground regions. We will return to this problem after the discussion of the empirical evidence.

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It is informative to attempt to draw on a piece of paper something that will be perceived immediately as a visual hole. In so doing one discovers that this is a difficult task, and for good reasons. A finite and enclosed region of an image, such as a circle, tends to be perceived as foreground because of factors such as closure and relative size (the closed contour is smaller relative to the page). Therefore, other factors must be present to reverse this interpretation. 4. Factors that make a region appear as a hole In 1954 Arnheim provided a demonstration of the role of convexity in figure ground organisation using a hole (see also Arnheim 1948). As shown in Figure 3a, the shape on top is more likely to be seen as a hole compared to the shape on the bottom. Note that here convexity is used in a piecewise sense as a global property of a complex shape (Bertamini & Wagemans 2012). This role of convexity in figure-ground was later confirmed by Kanizsa and Gerbino (1976). Arnheim's demonstration is elegant because of its simplicity, as the two shapes can be made the same in area or in contour length, and in Figure 3a they are not the shapes of any specific familiar object. The difference between the two regions is thus something about the shape itself. However, neither of the two is unambiguously perceived as a hole, so the key to the demonstration is to ask a relative judgment: which one of the two appears more like a hole. Bertamini (2006) found that when asked this question most observers chose the concave shape, as predicted by Arnheim.

(a) (b) (c) (d)

Figure 3. Figural factors affecting the perception of holes: the hole percept is stronger in the top element of each pair. (a) Arnheim (1954) claimed that globally concave shapes tend to be seen as holes. This figure shows an extreme version of his demonstration in which the set of smooth contour segments are identical in both cases (they are just arranged differently), and have therefore the same curvature and the same total length. For a version with equal area see Bertamini (2006). Most observers, when forced to choose, select the shape on the top as a better candidate for being a hole. (b) Bozzi (1975) used the example of a square within a square to show the role of the relationship between contours, a hole is perceived when edges are parallel. (c) Effect of grouping factors, such as similarity of texture or colour (Nelson & Palmer, 2001). (d) Effect of high entropy (lines with random orientation) (Gillam & Grove, 2011).

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Bozzi (1975) made phenomenological observations on the conditions necessary for the perception of holes. The figure that contains the hole should have a visible outer boundary (unlike the Arnheim examples), there should be evidence that the background visible inside the hole is the same as the background outside, and the boundary of the hole should be related to the outer boundary of the object, for instance when contours are parallel as in the frame of a window (Figure 3b). An early empirical study on the conditions necessary for perception of holes was conducted by Cavedon (1980). She found that observers did not report seeing a hole even when a physical hole was present if there were no detectable depth cues. In a more recent list of factors that affect the perception of a hole, Nelson and Palmer (2001) reported that in addition to depth information grouping factors are also important because they make the region visible inside a hole appear as a continuation of the larger background (for instance because both have the same texture, Figure 3c). Another important contribution to the perception of a hole is information that makes the relationship between the shape of the hole and the shape of the object appear non-accidental. The evidence from Nelson and Palmer (2001) confirmed the observation by Bozzi (1975): if a white region is centered inside a black region it is more likely to be perceived as a hole than if it is slightly crooked. Gillam and Grove (2011) have shown that properties of the ground itself may be important to generate the percept of a hole. Specifically they found that a simple rectangle appears more hole-like when the entropy of the enclosed contours is greater. This can be seen by comparing a region with multiple lines of different orientations (high entropy) and a region with parallel lines (low entropy) (Figure 3d). A final factor that strongly affects figure-ground stratification is shading. For instance Bertamini and Helmy (2012) used shading to create the perception of holes (described later, see also Figure 6). Bertamini and Hulleman (2006) explored the appearance of surfaces seen through holes. In particular they tested whether the surface seen under multiple holes is a single amodally completed surface or whether the background takes on the shape of the complement of the hole (i.e. the contour of the hole itself). Observers found it difficult to judge the extension of these amodal surfaces, and were affected by the context (flanking objects). It is interesting that a hole can show a surface without any information about the bounding contours of that surface. Therefore, the shape of this object is not specified by any form of contour extrapolation (see chapter 11 on perceptual completions). The shape of the hole may still constrain what is hidden in terms of probabilities (Figure 4). For example, given a few basic assumptions, underneath a vertically oriented hole the value of the posterior probability is greater for a vertically oriented rectangle than a horizontal one (Bertamini & Hulleman, 2006).

Figure 4. Assuming that the three grey regions are perceived as holes, what is the shape of the underlying grey surface? Unlike other completion phenomena there is no contour continuation.

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One solution is a single grey object underneath all three holes, a second solution is three shapeless blobs, and finally, as shown by the dashed lines, the contour of the holes, albeit perceived on a different depth plane, can constrain the possible hidden objects.

In another set of observations, Bertamini and Hulleman (2006) used stereograms to test holes that were moving. If a visual hole has an existence independent of the object-with-hole, perhaps it can move independently from that very object. However, a substantial proportion of participants perceived a lens in the aperture of the hole. Also, for objects in which texture changed as they moved (as in would within a hole), the percept was that of detachment of the contour from the texture inside the contour. In all cases where there was accretion/deletion of texture on the figural side, this resulted in detachment of texture, and introduction of a lens-like/spotlight-like appearance. With respect to visual hole the most important finding was that there was strong resistance to perceive holes moving independently from the object-with-hole. 5. Remembering the shape of a hole In his classic book Palmer (1999) discuss the issue of holes in terms of a paradox. An important principle from Gestalt says that ground regions are shapeless (Rubin 1921; Koffka 1935). This follows from the fact that contours are assigned only to the foreground and can only provide information about the shape of the foreground. But we have defined a visual hole as a ground region. Therefore will the hole be shapeless like all other ground regions? If so observers should not be able to describe a hole or remember its shape in a memory task. Although Rubin did not set out to study holes, he did use a set of figures in a study about shape memory, and asked observers to perceived each of them as either figure or ground (1921). When the instructions changed between study phase and test phase, memory performance was very poor. However, in a better controlled set of experiments Palmer et al. (2008) found that memory for the interior shapes of regions initially perceived as holes was as good as the memory for those regions perceived as solid objects. In another set of studies, Nelson, Thierman, and Palmer (2009) noted that memory was good for holes as long as they were located in a single surface. Memory was poor for regions that were enclosed within multiple surfaces, i.e. accidental regions. This is consistent with the definition that says that the hole is a region with a closed contour, and is also consistent with most people’s intuition that a hole has to exist within a single object-with-hole. Because memory for holes is as good as memory for objects, Palmer argued that regions can be represented as having a shape even when they are not figures, and that in the case of holes, although they are not figures and are not material, they are “figures for purposes of describing shape” (p. 287). The idea that hole boundaries are used to describe shape was also in Casati and Varzi (1994, pp. 162-163), who claimed that “in addition to figural boundaries there are topical boundaries, which confer a figural role on some portion of the visual field... without at the same time suggesting that such a role is played by figures in the old sense”. Other authors have subscribed to this position. Feldman and Singh (2005) worked on an analysis of convexity and concavity information along contours. There are important differences in how the visual system treats the two but what is coded as convex or concave depends on figure-ground and therefore for a given closed contour the coding is reversed if the contour is perceived as a figure or a hole. Feldman and Singh suggested that perhaps this does not happen because, as suggested by Palmer, holes may have "a quasi-figural status, as far as shape analysis is concerned" (Feldman & Singh 2005, p. 248).

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6. Visual search and holes Some interesting evidence about perception of holes comes from studies that used the visual search paradigm. In a study focused on preattentive accessibility to stereoscopic depth, O’Toole and Walker (1997) tested visual search for items defined by crossed or uncrossed disparity. Within a random dot stereogram this manipulation created some conditions in which holes were perceived (behind the background at fixation). O’Toole and Walker found some evidence for an advantage for targets in front, relative to targets behind. Interpretation was difficult because of the presence of nonlinear trends in the search slopes, but in general terms O’Toole and Walker suggested that their results are consistent with the emergence of global surface percepts. Bertamini and Lawson (2006) conducted a series of visual search studies using similar random dot stereograms but focusing more directly on the comparison between a search for a simple circular figure and a search for a simple circular hole. Note that for contours such as a circle this type of figure ground reversal means that in one case the target is strictly convex and in the other case the target is strictly concave. A manipulation that was added in Bertamini and Lawson compared to O’Toole and Walker (1997) was the fact that in some cases the background surface was available for preview before the items appeared. Bertamini and Lawson (2006) found that providing a preview benefited search for concavities (holes) more than it did search for convexities (figures) and that for convex figures, nearer targets were responded to more quickly. The effect of background preview is important. The best explanation comes from the observation that when a hole appears on a background that was already present the shape of that surface changes, by contrast adding a figure in front of the background does not cause a change of shape of a pre-existing object. On the key comparison between convexity and concavity, however, there was no evidence that concave targets (holes) were inherently more salient. Hulleman and Humphreys (2005) studied the difference between searching among objects and searching among holes. The target was a “C” and the distractor was a “O”. It was easier to search among objects than to search among holes, although it should be noted that stimuli were always more complex, for instance in terms of additional contours, in the hole conditions. The authors conclude that their results support the idea that the shape of a hole is only available indirectly. Taking the studies about memory and those about visual search one could say that observers must be able to see holes given that they can remember them and find them in a search task. However, it is also possible that observers knew about the properties of the holes only through the shape of the host surface, given that holes are always properties of an object. To know more about how holes are processed we will describe studies in which observers had to respond as fast as possible to specific local or global aspects of the hole.

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7. Attention and visual holes

Figure 5. Colour and shading are powerful ways to affect figure-ground. On the left we perceive surfaces on top of other surfaces but on the right we perceive holes. The convexity (+) and concavity (-) of the vertices is labelled to highlight the complete reversal that takes place with a figure-ground reversal. The hexagon on the top row has only one type of vertices, these are convex (figure) or concave (hole). The hexagon on the bottom row has both types, and they all reverse as we move from figure to hole.

Let us consider the shapes in Figure 5. It is easy to notice that the hexagon is irregular and a pair of vertices is not aligned. In the examples of Figure 5 the vertex on the left in lower than the one on the right, vertically. If observers have to judge which vertex is lower the task difficulty will vary with vertical offset. Using irregular hexagons like those on the left side of Figure 5, Baylis and Driver (1993) have shown that closure of the shape improves performance, i.e. there is a within object advantage. However, as pointed out by Gibson (1994) one has to be careful when comparing vertices that can be perceived as convex or concave. In particular the object on top has convex vertices and the one at the bottom has concave vertices. To manipulate the coding of convexity while retaining the same hexagonal shapes, Bertamini and Croucher (2003) compared figures and holes. This is the manipulation illustrated in Figure 5, although colour and texture were used as figural factors rather than shading. Note that this can be seen as a 2*2 design in which the convexity of the critical vertices varies independently of the overall shape of the hexagon. Results confirmed that figure-ground reversal had an effect on task difficulty: performance was better when the vertices were perceived as convex. In other words the coding of the vertices as convex or concave was more important that the overall shape of the hexagon. The reason it is easier to judge the position of convex vertices is likely to be that there is an explicit representation of position for visual parts, and convexities specify parts (Koenderink 1990; Hoffman & Richards 1984). Therefore the different convexity coding for figures and holes implies a different part structure in the two cases. The advantage for judging the position of convex vertices (as opposed to concave) is supported by evidence that does not rely on holes (Bertamini, 2001), but holes do provide the most direct test of the role of convexity. Holes have been used in subsequent studies by Bertamini and Mosca (2004) and Bertamini and Farrant (2006). Using random dot stereograms Bertamini and Mosca could ensure that there was no ambiguity in figure-ground

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relations. In a random dot stereogram no shape information is available until images have been binocularly fused, and therefore depth order is established at the same time as shape information. In this sense, unlike texture, shading and other factors that can create a hole percept, random dot stereograms create holes that cannot be perceived any other way. Bertamini and Mosca’s experiments confirmed that the critical factor in affecting relative speed on this task was whether the region was seen as foreground or background, thus changing contour ownership. The explanation of the effect relies on the assumption is that the contour of a silhouette is perceived as the rim of an opaque object. To test this Bertamini and Farrant (2006) compared objects and holes to a third case, that of thin (wire-like) objects. As a thin line tends to be perceived as the contour of a surface, these thin objects, which are both objects and holes, can only be created within random dot stereograms. Bertamini and Farrant confirmed that holes created by thin objects are different in terms of performance from both objects and holes. They concluded that thin wire-like objects have a different perceived part structure, which is intermediate between that of objects and that of holes. Albrecht, List and Robertson (2008) studied holes with a cueing paradigm. It is known that responses to uncued locations are faster for probes that are located on the cued surface compared to the uncued surface (Egly, Driver & Rafal 1994). This is taken as evidence of object-based attention. Albrecht et al. compared surfaces to identical rectangular regions perceived as holes. Stereograms were used to ensure that holes were perceived as such. The object-based advantage was not found for holes when the background surface visible through the holes was shared by the two holes, but the effect was present when this background was split, so that different objects were visible through different holes. The findings show clearly that the important factor in deployment of attention is not just the closure of the contours, as this was the same for the rectangles perceived as objects and as holes, but the perceptual organization of the regions as different surfaces in depth. The region cued inside a hole is the background surface, consistently with the idea that a hole is a ground region. That is, what is seen inside the hole belongs to a surface that extends beyond the contour of the aperture. Another paradigm that has been used to study attention is that of multiple objects tracking, in which observers track moving items among identical moving distractors (Pylyshyn, & Storm 1988; Scholl 2009). Horowitz and Kuzmova (2011) compared performance when tracking figures and when tracking holes. Holes were as easy to track as figures. Therefore Horowitz and Kuzmova concluded that holes are proto-objects, that is, bundles that serve as tokens to which attention can be deployed.

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Figure 6. In the top row there is a square contour surrounded by another square contour. This is true for both the object and the hole. In the bottom row there is a square contour surrounded by a circular contour. Therefore these are examples in which the two contours are congruent (same) or incongruent (different). What is different between objects and holes is that in the case of holes the surrounding contour is part of the same surface that also defines the hole.

The results from multiple objects racking are consistent with the results from visual search tasks. Observers can find and attend to locations where a hole is present. But how far can we go in perceiving holes and their shape as if they were the same as objects? To answer that question Bertamini and Helmy (2012) used a shape interference task. Observers were presented with simple shapes and had to discriminate a circle from a square (see Figure 6). However, there was also an irrelevant surrounding contour that could be either a circle or a square. Different (incongruent) inside and outside contours produced interference, but the effect was stronger when they formed an object-with-hole, as compared with a hierarchical set of surfaces or a single hole separating different surfaces (a trench). This result supports the hypothesis that the interference is constrained by which surface owns the contour, and that the shape of a hole cannot be processed independently of the shape of the object-with-hole.

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8. Conclusions This chapter has shown the surprisingly large range and diversity of the studies of holes. Some authors have focused on the nature of holes. We have seen the implications of this characterization for accounts of the perception of holes. Can they act as objects or at least as proto-objects? Other authors have used holes because they are convenient stimuli to manipulate key variables, in particular figure-ground and contour ownership. We can confidently say that holes are not invisible. Observers can remember the shape of holes, they can search among holes and they can perform multiple tracking of holes. For some tasks there is little difference between holes and objects. Therefore, the more difficult question to answer is to what extent holes are treated by vision on a par with objects, and conversely to what extent they are different from other ground regions. In terms of local coding of convexity, it appears that holes are not similar to objects and that convexity is assigned relative to the foreground surface (Bertamini & Mosca 2004). In terms of global shape analysis, here also the shape of a hole cannot be treated independently of the shape of the foreground surface, that is the object-with-hole (Bertamini & Helmy 2012). On the one hand, this makes holes less of a curiosity in the sense that they are not an exception to the principles of figure-ground, and in particular they are not an exception to the principle of unidirectional contour ownership (Bertamini 2006). On the other hand holes as ground regions provide the ideal comparison for their complements. We can compare congruent contours perceived as either objects (foreground) or holes (background) to test the role of a change in figure-ground relations while at the same time factors such as shape, size, and closure are fixed.

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