Infants' perception of information along object boundaries: concavities versus convexities

Object parts are signaled by concave discontinuities in shape contours. In seven experiments, we examined whether 5- and 6 1/2-month-olds are sensitive to concavities as special aspects of contours. Infants of both ages detected discrepant concave elements amid convex distractors but failed to discriminate convex elements among concave distractors. This discrimination asymmetry is analogous to the finding that concave targets among convex distractors pop out for adults, whereas convex targets among concave distractors do not. Thus, during infancy, as during adulthood, concavities appear to be salient regions of shape contours. The current study also found that infants' detection of concavity is impaired if the contours that define concavity and convexity are not part of closed shapes. Thus, for infants, as for adults, concavities and convexities are defined more readily in the contours of closed shapes. Taken together, the results suggest that some basic aspects of part perception from shape contours are available by at least 5 months of age.     

Detection of change in shape and its relation to part structure

Using a change detection paradigm (Barenholtz, E., Cohen, E. H., Feldman, J., & Singh, M. (2003). Detection of change in shape: An advantage for concavities. Cognition, 89(1) 1-9), we measured sensitivity to the changes of shapes and in particular the difference between detecting a new convex or concave vertex. We conclude that concave vertices per se are not more salient, but changes in the sequence of convexities and concavities along a contour are salient. We argue that these changes are likely to signal a change in perceived part structure.     

Perceiving parts and shapes from concave surfaces

“A hole is nothing at all, but it can break your neck.” In a similar fashion to the danger illustrated by this folk paradox, concave regions pose difficulties to theories of visual shape perception. We can readily identify their shapes, but according to principles of how observers determine part boundaries, concavities in a planar surface should have very different figural shapes from the ones that we perceive. In three experiments, we tested the hypothesis that observers perceive local image features differently in simulated 3-D concave and convex regions but use them to arrive at similar shape percepts. Stimuli were shape-from-shading images containing regions that appeared either concave or convex in depth, depending on their orientation in the picture plane. The results show that concavities did not benefit from the same global object-based attention or holistic shape encoding as convexities and that the participants relied on separable spatial dimensions to judge figural shape in concavities. Concavities may exploit a secondary process for shape perception that allows regions composed of perceptually independent features to ultimately be perceived as gestalts.     

The role of convexity in perception of symmetry and in visual short-term memory

Visual perception of shape is affected by coding of local convexities and concavities. For instance, a recent study reported that deviations from symmetry carried by convexities were easier to detect than deviations carried by concavities. We removed some confounds and extended this work from a detection of reflection of a contour (i.e., bilateral symmetry), to a detection of repetition of a contour (i.e., translational symmetry). We tested whether any convexity advantage is specific to bilateral symmetry in a two-interval (Experiment 1) and a single-interval (Experiment 2) detection task. In both, we found a convexity advantage only for repetition. When we removed the need to choose which region of the contour to monitor (Experiment 3) the effect disappeared. In a second series of studies, we again used shapes with multiple convex or concave features. Participants performed a change detection task in which only one of the features could change. We did not find any evidence that convexities are special in visual short-term memory, when the to-be-remembered features only changed shape (Experiment 4), when they changed shape and changed from concave to convex and vice versa (Experiment 5), or when these conditions were mixed (Experiment 6). We did find a small advantage for coding convexity as well as concavity over an isolated (and thus ambiguous) contour. The latter is consistent with the known effect of closure on processing of shape. We conclude that convexity plays a role in many perceptual tasks but that it does not have a basic encoding advantage over concavity.     

A search asymmetry reversed by figure-ground assignment

We report evidence demonstrating that a search asymmetry favoring concave over convex targets can be reversed by altering the figure-ground assignment of edges in shapes. Visual search for a concave target among convex distractors is faster than search for a convex target among concave distractors (a search asymmetry). By using shapes with ambiguous local figure-ground relations, we demonstrated that search can be efficient (with search slopes around 10 ms/item) or inefficient (with search slopes around 30–40 ms/item) with the same stimuli, depending on whether edges are assigned to concave or convex "figures." This assignment process can operate in a top-down manner, according to the task set. The results suggest that attention is allocated to spatial regions following the computation of figure-ground relations in parallel across the elements present. This computation can also be modulated by top-down processes.     

Infants' perception of concavity and convexity of shaded objects

The discriminative sensitivities of 30 4‐month‐old and 30 8‐month‐old infants for concave and convex objects were measured using the preferential‐looking method. Five cylinder‐like objects with different magnitudes of concave or convex shaded surfaces and outline contours were presented to the infants in pairs. The results indicated that the 4‐month‐old infants could discriminate better between object convexities than between object concavities. In contrast, the 8‐month‐old infants were able to equally discriminate between object concavities and object convexities, and their sensitivity to both object concavity/convexity was much higher than that of the 4‐month‐old infants. This difference in the sensitivity to object concavity and convexity suggested that younger and older infants might have differential abilities for cue utilization for recovering object structures.     

Concavities count for less in symmetry perception

We investigated the relative importance of convexities (protrusions) and concavities (indentations) for the perception of shape. On the one hand, it has been suggested that convexities determine the shape of an object, whereas concavities merely act as “perceptual glue” between the convexities. On the other hand, it has been argued that concavities are more salient than convexities. We show that participants find it easier to detect asymmetry in a 2-D silhouette when there is a mismatch between the shapes of convexities on either side of the axis of symmetry than when there is a mismatch between the shapes of concavities. This is the case even when the concavities are closest to the axis of symmetry, and despite the usual bias toward this axis in symmetry perception. We suggest that the actual shape of concavities is less important in symmetry perception, because the main role of concavities is to act as part boundaries in the representation of the shape of objects.     

Concavities as basic features in visual search: evidence from search asymmetries

Concave cusps and negative curvature minima play an important role in many theories of visual shape perception. Cusps and minima are taken to be part boundaries, used to segment an object into parts. Because of their important role in determining object structure and because there is some evidence that object structure is processed in parallel, it might be expected that concave cusps and negative curvature minima are processed preferentially. We tested this conjecture in several visual search experiments. Visual search for a target with a concave cusp among totally convex distractors yields nearly flat slopes (< 10 msec/item) for both present and absent trials. Reversing the roles of the target and the distractor results in inefficient search. The same asymmetry is found when the concave cusp is replaced by other types of concavity. We conclude, therefore, the concavities can serve as basic features in visual search experiments. This conclusion implies that the unit of selection in a visual search task is an object, rather than a location.     

Processing convexity and concavity along a 2-D contour: figure–ground, structural shape, and attention

Interest in convexity has a long history in vision science. For smooth contours in an image, it is possible to code regions of positive (convex) and negative (concave) curvature, and this provides useful information about solid shape. We review a large body of evidence on the role of this information in perception of shape and in attention. This includes evidence from behavioral, neurophysiological, imaging, and developmental studies. A review is necessary to analyze the evidence on how convexity affects (1) separation between figure and ground, (2) part structure, and (3) attention allocation. Despite some broad agreement on the importance of convexity in these areas, there is a lack of consensus on the interpretation of specific claims—for example, on the contribution of convexity to metric depth and on the automatic directing of attention to convexities or to concavities. The focus is on convexity and concavity along a 2-D contour, not convexity and concavity in 3-D, but the important link between the two is discussed. We conclude that there is good evidence for the role of convexity information in figure–ground organization and in parsing, but other, more specific claims are not (yet) well supported.     

Display-wide influences on figure–ground perception: The case of symmetry

Past research has demonstrated that convex regions are increasingly likely to be perceived as figures as the number of alternating convex and concave regions in test displays increases. This region-number effect depends on both a small preexisting preference for convex over concave objects and the presence of scene characteristics (i.e., uniform fill) that allow the integration of the concave regions into a background object/surface. These factors work together to enable the percept of convex objects in front of a background. We investigated whether region-number effects generalize to another property, symmetry, whose effectiveness as a figure property has been debated. Observers reported which regions they perceived as figures in black-and-white displays with alternating symmetric/asymmetric regions. In Experiments 1 and 2, the displays had articulated outer borders that preserved the symmetry/asymmetry of the outermost regions. Region-number effects were not observed, although symmetric regions were perceived as figures more often than chance. We hypothesized that the articulated outer borders prevented fitting a background interpretation to the asymmetric regions. In Experiment 3, we used straight-edge framelike outer borders and observed region-number effects for symmetry equivalent to those observed for convexity. These results (1) show that display-wide information affects figure assignment at a border, (2) extend the evidence indicating that the ability to fit background as well as foreground interpretations is critical in figure assignment, (3) reveal that symmetry and convexity are equally effective figure cues and, (4) demonstrate that symmetry serves as a figural property only when it is close to fixation.     

Early computation of contour curvature and part structure: evidence from holes

We used holes to study unilateral border ownership and in particular the information carried by the sign of the curvature along the contour (ie the difference between convex and concave regions). When people perceive a hole, its shape has a reversed curvature polarity (ie a changed sign of curvature) compared to the same region perceived as an object. Bertamini (2001 Perception 30 1295-1310), and Bertamini and Croucher (2003 Cognition 87 33-54) suggested and found evidence to support the hypothesis that, because convex regions are perceived as parts, positional information is more readily available for convex regions. Therefore a change is predicted when a given region is perceived as either a hole or a figure. We confirm that finding in this study, using holes defined by binocular disparity. We conclude that a change from figure to hole always reverses the encoding of curvature polarity. In turn, polarity obligatorily affects perceived part structure and the processing of position.     

On the Relation between Kanizsa's Bias Towards Convexity and the Gestaltists Prägnanz from the Perspective of Current in Shape Recognition

What is the relation between Kanizsa's bias towards convexity and the Gestaltists' demonstrations that perceptual organization obeys a principle of pragnänz, or simplicity? Why should either kind of bias exist? Textbook accounts assign no functional role for these biases. Geon theory (Biederman 1987) proposes that we can understand these biases in terms of fundamental processes by which complex objects are decomposed into convex (or singly concave) regions at points of matched cusps according to the transversality regularity (Hoffman and Richards 1985). Such decomposition yields simple, convex parts segmented between the concavities. A shape that contains concavities is generally regarded as complex insofar as it can be decomposed into the regions, or parts, between the concavities. It is these simple parts that are the stable elements of shape, not the whole object. In fact, geon theory leads to the expectation that shape recognition proceeds most efficiently when the parts are good (in the pragnänz sense) but the object is bad!     

What does the occluding contour tell us about solid shape?

A new theorem is discussed that relates the apparent curvature of the occluding contour of a visual shape to the intrinsic curvature of the surface and the radial curvature. This theorem allows the formulation of general laws for the apparent curvature, independent of viewing distance and regardless of the fact that the rim (the boundary between the visible and invisible parts of the object) is a general, thus twisted, space curve. Consequently convexities, concavities, or inflextions of contours in the retinal image allow the observer to draw inferences about local surface geometry with certainty. These results appear to be counterintuitive, witness to the treatment of the problem by recent authors. It is demonstrated how well-known examples, used to show how concavities and convexities of the contour have no obvious relation to solid shape, are actually good illustrations of the fact that convexities are due to local ovoid shapes, concavities to local saddle shapes.     

The concave cusp as a determiner of figure-ground

The tendency to interpret as figure, relative to background, those regions that are lighter, smaller, and, especially, more convex is well known. Wherever convex opaque objects abut or partially occlude one another in an image, the points of contact between the silhouettes form concave cusps, each indicating the local assignment of figure versus ground across the contour segments. It is proposed that this local geometric feature is a preattentive determiner of figure-ground perception and that it contributes to the previously observed tendency for convexity preference. Evidence is presented that figure-ground assignment can be determined solely on the basis of the concave cusp feature, and that the salience of the cusp derives from local geometry and not from adjacent contour convexity.     

The perceived structural shape of thin (wire-like) objects is different from that of silhouettes

Observers are faster at judging the position of convex vertices compared to concave vertices. This is believed to be due to an explicit representation of position for visual parts. The best evidence comes from comparing the same contours perceived as either figures or holes, because this is a pure figure ground reversal (Bertamini and Croucher, 2003 Cognition 87 33 - 54; Bertamini and Mosca, 2004 Perception 33 35-48). Specifically, an interaction is present between type of object (object or hole) and shape. One assumption is that the contour of a silhouette is perceived as the rim of a solid object. It follows that a different pattern should be found for thin (wire-like) objects compared to silhouettes. We confirm this difference in three experiments. We argue that this is due to the perceived parts when contours can be interpreted as self-occlusion rims.     

Assessment of trypophobia and an analysis of its visual precipitation

We developed and validated a symptom scale that can be used to identify “trypophobia”, in which individuals experience aversion induced by images of clusters of circular objects. The trypophobia questionnaire (TQ) was based on reports of various symptom types, but it nevertheless demonstrated a single construct, with high internal consistency and test–retest reliability. The TQ scores predicted discomfort from trypophobic images, but not neutral or unpleasant images, and did not correlate with anxiety. Using image filtering, we also reduced the excess energy at midrange spatial frequencies associated with both trypophobic and uncomfortable images. Relative to unfiltered trypophobic images, the discomfort from filtered images experienced by observers with high TQ scores was less than that experienced with control images and by observers with low TQ scores. Furthermore, we found that clusters of concave objects (holes) did not induce significantly more discomfort than clusters of convex objects (bumps), suggesting that trypophobia involves images with particular spectral profile rather than clusters of holes per se.     

Rapid figure-ground responses to stereograms reveal an advantage for a convex foreground

Convexity has long been recognised as a factor that affects figure - ground segmentation, even when pitted against other factors such as symmetry [Kanizsa and Gerbino, 1976 Art and Artefacts Ed.M Henle (New York: Springer) pp 25-32]. It is accepted in the literature that the difference between concave and convex contours is important for the visual system, and that there is a prior expectation favouring convexities as figure. We used bipartite stimuli and a simple task in which observers had to report whether the foreground was on the left or the right. We report objective evidence that supports the idea that convexity affects figure-ground assignment, even though our stimuli were not pictorial in that depth order was specified unambiguously by binocular disparity.     

The concavity effect is a compound of local and global effects

Using a change detection paradigm, Barenholtz, Cohen, Feldman, and Singh (2003) found that changes in concave regions of a contour are more easily detected than changes in convex regions. In a series of three experiments, we investigated this concavity effect using the same paradigm. We observed the effect in wire-like stimuli as well as in silhouettes (Experiment 1) and in complex, smoothed images as opposed to angular polygons (Experiment 2). We also observed a systematic effect of the magnitude of the change (Experiment 1). Furthermore, we find that the effect cannot be attributed to either local or global processing effects, but rather to a combination of both "mere" concaveness and an effect due to changes in the perceived part structure of the stimulus object (Experiment 3). For our data analysis, we used a nonparametric bootstrap method, which greatly increases sensitivity (compared to more traditional analyses like ANOVA).     

The shape of holes

The shape of holes can be recognized as accurately as the shape of objects (Palmer, S. E. (1999). Vision science: photons to phenomenology. Cambridge, MA: MIT Press), yet the area enclosed by a hole is a background region, and it can be demonstrated that background regions are not represented as having shape. What is therefore the shape of a hole, if any? To resolve this apparent paradox, we suggest that the shape of a hole is available indirectly from the shape of the surrounding object. We exploited the fact that observers are faster at judging the position of convex vertices than concave ones (Perception 30 (2001) 1295), and using a figural manipulation of figure/ground we found a reversal of the relative speeds when the same contours were presented as holes instead of objects. If contours were perceived as belonging to the hole rather than the surrounding object then there would have been no qualitative difference in responses to the object and hole stimuli. We conclude that the contour bounding a hole is automatically assigned to the surrounding object, and that a change in perception of a region from object to hole always drastically changes the encoded information. We discuss the many interesting aspects of holes as a subject of study in different disciplines and predict that much insight especially about shape will continue to come from holes.     

Haptic curvature comparison of convex and concave shapes

A sculpture and the mould in which it was formed are typical examples of objects with an identical, but opponent, surface shape: each convex (ie outward pointing) surface part of a sculpture has a concave counterpart in the mould. The question arises whether the object features of opponent shapes can be compared by touch. Therefore, we investigated whether human observers were able to discriminate the curvatures of convex and concave shapes, irrespective of whether the shape was convex or concave. Using a 2AFC procedure, subjects had to compare the curvature of a convex shape to the curvature of a concave shape. In addition, results were also obtained for congruent shapes, when the curvature of either only convex shapes or only concave shapes had to be compared. Psychometric curves were fitted to the data to obtain threshold and bias results. When subjects explored the stimuli with a single index finger, significantly higher thresholds were obtained for the opponent shapes than for the congruent shapes. However, when the stimuli were touched by two index fingers, one finger per surface, we found similar thresholds. Systematic biases were found when the curvature of opponent shapes was compared: the curvature of a more curved convex surface was judged equal to the curvature of a less curved concave surface. We conclude that human observers had the ability to compare the curvature of shapes with an opposite direction, but that their performance decreased when they sensed the opponent surfaces with the same finger. Moreover, they systematically underestimated the curvature of convex shapes compared to the curvature of concave shapes.