Strength of visual interpolation depends on the ratio of physically specified to total edge length

We report four experiments in which the strength ofedge-interpoiat-ion in illusory figure displays was tested. In Experiment 1, we investigated the relative contributions of the lengths of luminance-specified edges and the gaps between them to perceived boundary clarity as measured by using a magnitude estimation procedure. The contributionaoLthese variables were found to be best characterized by a ratio of the length of luminance-specified contour to the length of the entire edge (specified plus interpolated edge). Experiment 2 showed that this ratio predicts boundary clarity for a wide range of ratio values and display sizes.There was no evidence that illusory figure boundaries are clearer in displays with small gaps than they are in displays with larger gaps and equivalent ratios. In Experiment 3, using a more sensitive pairwise comparison paradigm, we again found no such effect. Implications for boundary interpolation in general, including perception of partially occluded objects, are discussed. The dependence of interpolation on the ratio of physically specified edges to total edgelength has thedesirable eeological consequence that unit formation will not change with variations in viewing distance.     

Boundary completion in illusory contours: interpolation or extrapolation?

Most computational and neural-style models of contour completion (ie illusory and occluded contours) are based on interpolation: the filling in of an edge between two visible edges. The results of three experiments suggest an alternative conception, that units are formed as a result of extrapolation from visible edges. In three experiments, subjects reported illusory contours between standard illusory-contour inducing elements and forms that do not, by themselves, induce illusory contours. We suggest that these forms are not a special case of inducing elements but that they represent a different class--receiving elements. Receiving elements are forms that can receive an illusory contour but cannot generate one, and they can alter contour formation. In experiment 1, receiving elements increased the judged clarity of illusory contours. In experiment 2, illusory edges were seen to connect to corners, line ends, and even the edges of circles. Boundary formation in motion displays also appears to be based on extrapolation. In experiment 3, subjects reported that small moving dots altered the formation of spatiotemporally defined boundaries. Implications for higher-order operator and network models of boundary formation are discussed.     

The role of discontinuities in the perception of subjective figures

Recently we proposed a theory of visual interpolation (Kellman & Shipley, in press) that addresses a variety of unit formation phenomena, including the perception of partly occluded objects and subjective figures. A basic notion of the theory is that discontinuities in the first derivative of projected edges are the initiating conditions for interpolation of boundaries that are not physically specified. In this paper, we report four experiments in which this claim was tested in the domain of subjective figures. Experiments 1 and 2 demonstrate that discontinuities in the first derivative of the edges of inducing elements have a clear effect on the frequency of report and the perceived clarity of simple subjective figures. Similar effects are found when unfamiliar subjective figures and inducing elements are used (Experiment 3). Experiment 4 rules out the possibility that the discontinuities in the first derivative merely add to the clarity of subjective figures. These experiments suggest that first-order discontinuities play a central role in unit formation.     

The effect of support ratio on infants' perception of illusory contours

We used a preferential looking technique to investigate the effect of support ratio (a ratio of the physically specified contours to the total edge length) on the perception of Kanizsa illusory contours in infants aged 3-8 months. Previous work has shown that for adult observers the illusory-contour strength increases proportionally with the support ratio. When the support ratio was relatively high (66%), infants preferred illusory contours to non-illusory figures by 3-4 months of age (experiment 1). In contrast, only infants 7-8 months old showed this preference for illusory contours when the support ratio was reduced to 37% (experiment 3). Further, infants showed no preference for an outline version of the illusory-contour figure, which produced no illusory contours (experiment 2). This result confirms that the infants' preference reflects their perception of illusory contours. Our results show that (i) illusory-contour perception emerges at around 3-4 months of age, but (ii) that this ability is very limited until around 7-8 months of age.     

Evidence for a boundary effect in roll vection

Large circular displays rotating around the line of sight produce an illusion in which the seen orientation of the true vertical is shifted in a direction opposite to the display’s motion. Two experiments were performed to determine whether the magnitude of this illusory tilt is a function of the area of display elements, of their boundary length, or of their spatial frequency. In Experiment 1, 12 subjects viewed each of nine displays across which the number and area of the circular elements were independently varied. Three of the displays were equated for the area of their elements. The results suggested that tilt magnitude and onset latency could be explained by a boundary length effect. A second experiment tested eight subjects on two displays, equated for element boundary length but differing in the spatial frequency of the elements. The displays produced closely similar illusory trite corroborating the view that, within broad limits, element boundary length—and not spatial frequency or area—determines the size and onset latency of illusory tilt. A third experiment confirmed previous research in finding greater tilt and more rapid onset with more peripherally projected displays.     

The relation between color spreading and illusory contours

In the present study, we examine the relation between neon color spreading (Redies & Spillmann, 1981) and illusory contours. In Experiment 1, the effects of misalignment between the line elements on the illusory contours in the Ehrenstein figure and in the Redies-Spillmann figure were examined. The remarkable overlap of the two curves for the likelihood of perceiving illusory contours in the Ehrenstein figure and in the Redies-Spillmann figure suggests that the illusory contours surrounding brightness enhancement (Ehrenstein, 1941) and those surrounding neon color spreading are caused by the same mechanism. We further examined both the effects of the interposed grids seen either in front of or behind the figures (Experiment 2) and the effects of misalignment (Experiment 3) on the illusory contours and range of color spreading, and found a high correlation between the appearance/disappearance of illusory contours and global/local color spreading. In Experiment 4, we added new lines to induce illusory contours to the line elements inducing local color spreading. We found that global color spreading was seen to cover the area surrounded by the illusory contours. On the basis of these findings, we suggest that there is an interaction between illusory contours and local color spreading.     

3-d interpolation in object perception: evidence from an objective performance paradigm

Object perception requires interpolation processes that connect visible regions despite spatial gaps. Some research has suggested that interpolation may be a 3-D process, but objective performance data and evidence about the conditions leading to interpolation are needed. The authors developed an objective performance paradigm for testing 3-D interpolation and tested a new theory of 3-D contour interpolation, termed 3-D relatability. The theory indicates for a given edge which orientations and positions of other edges in space may be connected to it by interpolation. Results of 5 experiments showed that processing of orientation relations in 3-D relatable displays was superior to processing in 3-D nonrelatable displays and that these effects depended on object formation. 3-D interpolation and 3-D relatabilty are discussed in terms of their implications for computational and neural models of object perception, which have typically been based on 2-D-orientation-sensitive units.     

Amodal completion versus induced inhomogeneities in the organization of illusory figures.

An analysis is presented of a phenomenological model of illusory contours. The model is based on amodal completion as the primary factor giving rise to the illusory figure. In the experiment, conducted by the method of paired comparisons, the same parameter was manipulated in two series of equivalent configurations. The first series yielded examples of amodal completion, the second examples of illusory figures. Three groups of subjects evaluated the magnitude of completion, the brightness contrast of the illusory figure, and the contour clarity of the illusory figure. A control experiment was conducted, which demonstrated that in these configurations amodal completion and amodal continuation behave in the same way. Line displacement did not influence the brightness or the contour clarity of the illusory figures, though it influenced the magnitude of amodal completion. These results are in agreement with the energetic model developed by Sambin.     

Perception of occlusion by young infants: Must the occlusion event be congruent with the occluder?

Four-month-old infants perceive continuity of an object’s trajectory through occlusion, even when the occluder is illusory, and several cues are apparently needed for young infants to perceive a veridical occlusion event. In this paper we investigated the effects of dislocating the spatial relation between the occlusion events and the visible edges of the occluder. In two experiments testing 60 participants, we demonstrated that 4-month-olds do not perceive continuity of an object’s trajectory across an occlusion if the deletion and accretion events are spatially displaced relative to the occluder edges (Experiment 1) or if deletion and accretion occur along a linear boundary that is incorrectly oriented relative to the occluder’s edges (Experiment 2). Thus congruence of these cues is apparently important for perception of veridical occlusion. These results are discussed in relation to an account of the development of perception of occlusion and object persistence.     

Illusory-figure lightness: evidence for a two-component theory

Physical darkness gradients were introduced into an illusory-figure pattern which were sufficient to eliminate the illusory lightness effect otherwise seen there. Next, such a gradient was left in place along one edge of that figure while the other edges were returned to physical homogeneity with the surround. Rather surprisingly, the physical gradient still present along the unaltered edge was now overwhelmed by illusory lightness. It is argued that this anomaly suggests that illusory-figure lightness may be composed of two additive components, one of which is figure-ground contrast enhancement and the other of which is contingent upon that first component.     

Sharp-edged vs. diffuse illusory circles: The effects of varying luminance

As had been found previously, one experiment demonstrated that reducing the luminance of a pattern that induced an abrupt-edged illusory figure increased mean ratings of that illusory effect. More importantly, the same result had not been found for a pattern that induced a diffuse illusory figure; in fact, a second experiment with such patterns produced a reliable tendency in the opposite direction. These results are at variance with the suggestion that an abrupt-edged illusory effect involves merely a minor variation in the boundary definition of a diffuse illusory lightness effect.     

Kinetic subjective contours

Continuous changes in spatially separated figures can evoke perception of subjective contours and figures in physically homogeneous space between them. This occurs when all of the interruptions in the objectively present patterns (inducing elements) can be seen as caused by a unitary figure partly occluding them. Two experiments demonstrated and explored this phenomenon. In both, displays were presented to subjects under three conditions. In one condition, stationary inducing elements were shown as they would be interrupted by a figure rotating in front of them. In another condition, the background and inducing elements rotated, with interruptions occurring as if a stationary figure were in front. In a third condition, observers were shown 10 static views taken from the figure-rotation sequence for each display. Subjects consistently perceived unitary central figures with well-defined forms and clear edges from pattern changes given by figure movement and background movement. As with static subjective figures, kinetic subjective figures appear in front of, partly occluding, the inducing elements. These percepts form rapidly, and they depend upon temporal relations rather than upon information present in momentary views. Subjects occasionally reported subjective edges or a central figure in the stationary displays in Experiment 1, but not at all in Experiment 2, in which guessing tendencies were reduced by more specific instructions. The existence of kinetic subjective contours suggests that the visual system readily utilizes relationships among occlusion events separated in space and time. The minimum conditions for contour perception require neither information all along an edge nor simultaneous specification of the edge at two or more places.     

A theory of visual interpolation in object perception

We describe a new theory explaining the perception of partly occluded objects and illusory figures, from both static and kinematic information, in a unified framework. Three ideas guide our approach. First, perception of partly occluded objects, perception of illusory figures, and some other object perception phenomena derive from a single boundary interpolation process. These phenomena differ only in respects that are not part of the unit formation process, such as the depth placement of units formed. Second, unit formation from static and kinematic information can be treated in the same general framework. Third, spatial and spatiotemporal discontinuities in the boundaries of optically projected areas are fundamental to the unit formation process. Consistent with these ideas, we develop a detailed theory of unit formation that accounts for most cases of boundary perception in the absence of local physical specification. According to this theory, discontinuities in the first derivative of projected edges are initiating conditions for unit formation. A formal notion of relatability is defined, specifying which physically given edges leading into discontinuities can be connected to others by interpolated edges. Intuitively, relatability requires that two edges be connectable by a smooth, monotonic curve. The roots of the discontinuity and relatability notions in ecological constraints on object perception are discussed. Finally, we elaborate our approach by discussing related issues, some new phenomena, connections to other approaches, and issues for future research.     

The monocular-boundary-contour mechanism in binocular surface representation and suppression

Boundary contours are important for representing binocular surfaces, including those in binocular rivalry. Ooi and He (2006, Perception 35 581-603) showed that a half-image with a boundary contour defined by abutting gratings predominates in binocular rivalry. We investigated the monocular-boundary-contour mechanism using Kanizsa square-like rivalry displays. In experiment 1, the left half-image had a vertical illusory contour on the right edge while the right half-image had a vertical illusory contour on the left edge. The Kanizsa elements (discs and pacmen) were filled with a 135 degree grating and placed on a 45 degree-grating background. When fused, observers experienced a strong predominance for perceiving an illusory rectangle in front of four discs. But this percept was replaced by robust rivalry alternations when the stimulus was manipulated by (i) switching the half-images between eyes, (ii)relocating the pacmen in each half-image to form horizontal illusory contours, or (iii) placing the pacmen diagonally (thus eliminating each monocular illusory contour). Such robust rivalry alternations were similar to those experienced when a 135 degree-grating disc was in rivalry with a 135 degree-grating pacman alone on the 45 degree-grating background (experiment 2). Experiment 3 showed that the relatively stable illusory-rectangle percept in experiment 1 is affected by the alignment of the images in the two eyes, in a manner consistent with adherence to the occlusion constraint in binocular surface formation.     

Object interpolation in three dimensions

Perception of objects in ordinary scenes requires interpolation processes connecting visible areas across spatial gaps. Most research has focused on 2-D displays, and models have been based on 2-D, orientation-sensitive units. The authors present a view of interpolation processes as intrinsically 3-D and producing representations of contours and surfaces spanning all 3 spatial dimensions. The authors propose a theory of 3-D relatability that indicates for a given edge which orientations and positions of other edges in 3 dimensions may be connected to it, and they summarize the empirical evidence for 3-D relatability. The theory unifies and illuminates a number of fundamental issues in object formation, including the identity hypothesis in visual completion, the relations of contour and surface processes, and the separation of local and global processing. The authors suggest that 3-D interpolation and 3-D relatability have major implications for computational and neural models of object perception.     

Outlined elements, regular elements and coincidences in illusory-figure patterns

When elements in a pattern which would otherwise produce an illusory figure are modified by outlining or by increasing their regularity (in accordance with a proposed measure of the latter quality), the illusory effect is much reduced. Both results reflect the principle that 'coincidences' in a display play little or no role in the process of segmentation when other circumstances tend to force critical edges to 'belong' to individual elements of the display.     

The relationship between brightness contrast and illusory contours.

One group of subjects rated differences in brightness and another the clarity of illusory contours for eight figure-ground combinations of the Kanizsa and Ehrenstein patterns made from Munsell papers. For four combinations there was a difference in Munsell value (brightness) between figure and ground and for another four no difference. For the latter the pattern was derived from differences in hue or colour quality. For the combinations with a Munsell value difference the ratings of both brightness difference and contour clarity were high and for those of uniform value both were low. The results are interpreted as supporting the argument that illusory contours derive primarily from contrast-induced differences in brightness and possibly in colour between contiguous, physically uniform regions.     

Infants’ perception of curved illusory contour with motion

Recently, Masuda et al. (submitted for publication) showed that adults perceive moving rigid or nonrigid motion from illusory contour with neon color spreading in which the inducer has pendular motion with or without phase difference. In Experiment 1, we used the preferential looking method to investigate whether 3–8-month-old infants can discriminate illusory and non-illusory contour figures, and found that the 7–8-month-old, but not the 3–6-month-old, infants showed significant preference for illusory contour with phase difference. In Experiment 2, we tested the validity of the visual stimuli in the present study, and whether infants could detect illusory contour from the current neon color spreading figures. The results showed that all infants might detect illusory contour figure with neon color spreading figures. The results of Experiments 1 and 2 suggest that 7–8-month-old infants potentially perceive illusory contour from the visual stimulus with phase-different movement of inducers, which elicits the perception of nonrigid dynamic subjective contour in adults.     

Spatial factors of brightness illusion in the Ehrenstein figure

The strength of brightness illusion in an Ehrenstein figure has been examined as a function of two variables--inducing line length and gap size--by a two-alternative forced-choice procedure. The results show an interaction between the two variables; the length of the inducers and gap size are both involved in the formation of the brightness illusion, with gap size as the stronger factor. A spatial limit (corresponding to a gap size of 2.4 deg) was found, below which the illusion is always present regardless of the length of the inducers. An area ratio, defined as the ratio of the area of the ring formed by the four inducing lines of an Ehrenstein figure to the area of the illusory surface, takes into account the different spatial factors studied in the experiment and the global size of the Ehrenstein figure. The strength of the illusion was found to increase linearly with increasing values of the area ratio.     

Attentional signatures of perception: multiple object tracking reveals the automaticity of contour interpolation

Multiple object tracking (MOT) is an attentional task wherein observers attempt to track multiple targets among moving distractors. Contour interpolation is a perceptual process that fills-in nonvisible edges on the basis of how surrounding edges (inducers) are spatiotemporally related. In five experiments, we explored the automaticity of interpolation through its influences on tracking. We found that (1) when the edges of targets and distractors jointly formed dynamic illusory or occluded contours, tracking accuracy worsened; (2) when interpolation bound all four targets together, performance improved; (3) when interpolation strength was weakened (by altering the size or relative orientation of inducing edges), tracking effects disappeared; and (4) real and interpolated contours influenced tracking comparably, except that real contours could more effectively shift attention toward distractors. These results suggest that interpolation's characteristics-and, in particular, its automaticity-can be revealed through its attentional influences or "signatures" within tracking. Our results also imply that relatively detailed object representations are formed in parallel, and that such representations can affect tracking when they become relevant to scene segmentation.