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.     

A theory of dynamic occluded and illusory object perception

Humans see whole objects from input fragmented in space and time, yet spatiotemporal object perception is poorly understood. The authors propose the theory of spatiotemporal relatability (STR), which describes the visual information and processes that allow visible fragments revealed at different times and places, due to motion and occlusion, to be assembled into unitary perceived objects. They present a formalization of STR that specifies spatial and temporal relations for object formation. Predictions from the theory regarding conditions that lead to unit formation were tested and confirmed in experiments with dynamic and static, occluded and illusory objects. Moreover, the results support the identity hypothesis of a common process for amodal and modal contour interpolation and provide new evidence regarding the relative efficiency of static and dynamic object formation. STR postulates a mental representation, the dynamic visual icon, that briefly maintains shapes and updates positions of occluded fragments to connect them with visible regions. The theory offers a unified account of interpolation processes for static, dynamic, occluded, and illusory objects.     

A critical discussion of Kellman and Shipley's (1991) theory of occlusion phenomena

Summary Kellman and Shipley (1991) recently advanced a new theory to explain the perception of partly occluded objects and illusory figures. The theory is a formalization of the Gestalt law of good continuation. In this paper we describe their account of occlusion when the contour of the occluded is completely specified by a display. Next, we outline some critical objections and present a number of counterexamples. Finally, we compare their theory with Wouterlood and Boselie's (in this issue) model of occlusion phenomena, which might also be considered as a formalization of the law of good continuation.     

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.     

Infants' perception of illusory contours in static and moving figures

We investigated 3-8-month-olds' (N=62) perception of illusory contours in a Kanizsa figure by using a preferential looking technique. Previous studies suggest that this ability develops around 8 months of age. However, we hypothesized that even 3-4-month-olds could perceive illusory contours in a moving figure. To check our hypothesis, we created an illusory contour figure in which the illusory square underwent lateral movement. By rotating the elements of this figure, we created non-illusory contour figures. We found that: (1) infants preferred moving illusory contours to non-illusory contours by 3-4 months of age, and (2) only 7-8-month-olds preferred static illusory contours. Our findings demonstrate that motion information promotes infants' perception of illusory contours. Our results parallel those reported in the study of partly occluded objects ().     

Learning to perceive object unity: a connectionist account

To explore questions of how human infants begin to perceive partly occluded objects, we devised two connectionist models of perceptual development. The models were endowed with an existing ability to detect several kinds of visual information that have been found important in infants’ and adults’ perception of object unity (motion, co‐motion, common motion, relatability, parallelism, texture and T‐junctions). They were then presented with stimuli consisting of either one or two objects and an occluding screen. The models’ task was to determine whether the object or objects were joined when such a percept was ambiguous, after specified amounts of training with events in which a subset of possible visual information was provided. The model that was trained in an enriched environment achieved superior levels of performance and was able to generalize veridical percepts to a wide range of novel stimuli. Implications for perceptual development in humans, current theories of development and origins of knowledge are discussed.     

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.     

The demise of the identity hypothesis and the insufficiency and nonnecessity of contour relatability in predicting object interpolation: comment on Kellman, Garrigan, and Shipley (2005)

P. J. Kellman, P. Garrigan, and T. F. Shipley's theory of 3-dimensional object interpolation asserts that existing data, as well as logical considerations, support the view that an identical contour interpolation process underlies the interpolation of partially camouflaged and partially occluded objects (modal completion and amodal completion, respectively). Here, the author argues that recent data show that this theory is incorrect and that the logical arguments offered in support of the identity hypothesis depend on specific unverified models of the phenomena in question. Alternative explanations of these effects are developed to show that such phenomena do not logically implicate an identity hypothesis and, in some cases, provide strong evidence against the identity hypothesis. Finally, the author describes several completion phenomena that reveal that the relatability criteria embodied in Kellman et al.'s model are neither necessary nor sufficient for understanding the interpolation processes the model was designed to explain.     

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.     

Object-based warping: an illusory distortion of space within objects

Visual objects are high-level primitives that are fundamental to numerous perceptual functions, such as guidance of attention. We report that objects warp visual perception of space in such a way that spatial distances within objects appear to be larger than spatial distances in ground regions. When two dots were placed inside a rectangular object, they appeared farther apart from one another than two dots with identical spacing outside of the object. To investigate whether this effect was object based, we measured the distortion while manipulating the structure surrounding the dots. Object displays were constructed with a single object, multiple objects, a partially occluded object, and an illusory object. Nonobject displays were constructed to be comparable to object displays in low-level visual attributes. In all cases, the object displays resulted in a more powerful distortion of spatial perception than comparable non-object-based displays. These results suggest that perception of space within objects is warped.     

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

We report four experiments in which the strength of edge interpolation 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 contributions of these 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 edge length has the desirable ecological consequence that unit formation will not change with variations in viewing distance.     

Synchronous change and perception of object unity: evidence from adults and infants.

Adults and infants display a robust ability to perceive the unity of a center-occluded object when the visible ends of the object undergo common motion (e.g. Kellman, P.J., Spelke, E.S., 1983. Perception of partly occluded objects in infancy. Cognitive Psychology 15, 483-524). Ecologically oriented accounts of this ability focus on the primary of motion in the perception of segregated objects, but Gestalt theory suggests a broader possibility: observers may perceive object unity by detecting patterns of synchronous change, of which common motion is a special case. We investigated this possibility with observations of adults and 4-month-old infants. Participants viewed a center-occluded object whose visible surfaces were either misaligned or aligned, stationary or moving, and unchanging or synchronously changing in color or brightness in various temporal patterns (e.g. flashing). Both alignment and common motion contributed to adults' perception of object unity, but synchronous color changes did not. For infants, motion was an important determinant of object unity, but other synchronous changes and edge alignment were not. When a stationary object with aligned edges underwent synchronous changes in color or brightness, infants showed high levels of attention to the object, but their perception of its unity appeared to be indeterminate. An inherent preference for fast over slow flash rates, and a novelty preference elicited by a change in rate, both indicated that infants detected the synchronous changes, although they failed to use them as information for object unity. These findings favor ecologically oriented accounts of object perception in which surface motion plays a privileged role.     

The role of junctions in surface completion and contour matching

It has been suggested that contour junctions may be used as cues for occlusion. Ecologically, T-junctions and L-junctions are concurrent with situations of occlusion: they arise when the bounding contour of the occluding surface intersects with that of the occluded surface. However, there are other image properties that can be used as cues for occlusion. Here the role of junctions is directly compared with other occlusion cues--specifically, relatability and surface-similarity--in the emergence of amodal completion and illusory contour perception. Stimuli have been constructed that differ only in the junction structure, with the other occlusion cues kept unchanged. L-junctions and T-junctions were eliminated from the image or manipulated so as to be locally inconsistent with the (still valid) global occlusion interpretation. Although the other occlusion cues of relatability and surface similarity still existed in the image, subjects reported not perceiving illusory contours or amodal completion in junction-manipulated images. Junction manipulation also affected the perceived stereoscopic depth and motion of image regions, depending on whether they were perceived to amodally complete with a disjoint region in the image. These results are interpreted in terms of the role of junctions in the processes of surface completion and contour matching. It is proposed that junctions, being a local cue for occlusion, are used to launch completion processes. Other, more global occlusion cues, such as relatability, play a part at a later stage, once completion processes have been launched.     

Perception of partly occluded objects by young chicks

Completion of partly occluded objects is a ubiquitous phenomenon in human visual perception. It is unclear, however, whether it occurs at all in other species: Studies on visual discrimination learning have revealed that animals usually attend to parts and features of the discriminative stimuli rather than to global object properties. We provide here the first demonstration of recognition of partly occluded objects in a bird species, the domestic chickGallus gallus, using the naturalistic setting made available by filial imprinting, a process whereby young birds form attachments to their mothers or some artificial substitute. In Experiment 1, newborn chicks were reared singly with a red cardboard triangle, to which they rapidly imprinted and therefore treated as a social partner. On Day 3 of life, the chicks were presented with pairs of objects composed of either isolated fragments or occluded parts of the imprinting stimulus. Chicks consistently chose to associate with complete or with partly occluded versions of the imprinting object rather than with separate fragments of it. Similarly, in Experiment 2, chicks reared with a partly occluded triangle chose to associate with a complete triangle rather than with a fragmented one, whereas chicks reared with a fragmented triangle chose to associate with a fragmented triangle and not with a complete one. Newborn chicks thus appear to behave as if they could experience amodal completion.     

Perception of partly occluded objects in infancy

Four-month-old infants sometimes can perceive the unity of a partly hidden object. In each of a series of experiments, infants were habituated to one object whose top and bottom were visible but whose center was occluded by a nearer object. They were then tested with a fully visible continuous object and with two fully visible object pieces with a gap where the occluder had been. Patterns of dishabituation suggested that infants perceive the boundaries of a partly hidden object by analyzing the movements of its surfaces: infants perceived a connected object when its ends moved in a common translation behind the occluder. Infants do not appear to perceive a connected object by analyzing the colors and forms of surfaces: they did not perceive a connected object when its visible parts were stationary, its color was homogeneous, its edges were aligned, and its shape was simple and regular. These findings do not support the thesis, from gestalt psychology, that object perception first arises as a consequence of a tendency to perceive the simplest, most regular configuration, or the Piagetian thesis that object perception depends on the prior coordination of action. Perception of objects may depend on an inherent conception of what an object is.     

Complete mergeability and amodal completion.

When image fragments are taken to correspond to the visible portions of a single occluded object, the object is said to 'amodally complete' behind the occluder. Kellman and Shipley (Kellman, P. J., & Shipley, T. F. (1991). A theory of visual interpolation in objective perception. Cognitive Psychology, 23, 144-221) argued that when the virtual contour extensions of such image fragments subtend an obtuse or right angle, the contours are 'relatable' and therefore complete. However, edge and surface relatability are neither necessary nor sufficient for completion to be perceived (Tse, P. U. (1999) Volume completion. Cognitive Psychology). Evidence is offered that completion is not driven directly by image cues such as contour relatability, but is driven, rather, by intermediate representations, such as volumes that are inferred from global image cue relationships. Evidence suggests that several factors, none of which is necessary for amodal completion to occur, contribute to the perceived strength of amodal completion, including similarity of pattern or substance, proximity, and good volume continuation or complete mergeability. Two partially occluded volumes are completely mergeable when they can be extended into occluded space along the trajectory defined by their visible surfaces such that they merge entirely with each other. Mergeability is not measurable in the image because it describes an inferred relationship among volumes that must themselves be inferred from the image.     

Children with spina bifida perceive visual illusions but not multistable figures

We compared 32 children with spina bifida and 32 age-matched controls on two classes of illusory perception, one involving visual illusions and the other, multistable figures. Children with spina bifida were as adept as age peers in the perception of visual illusions concerned with size, length, and area, but were impaired in the perception of multistable figures that involved figure-ground reversals, illusory contours, perspective reversing, and paradoxical figures. That children with spina bifida reliably perceive illusions that rely on inappropriate constancy scaling of size, length, and area suggests that their brain dysmorphologies do not prevent the acquisition of basic perceptual operations that enhance the local coherence of object perception. That they do not perceive multistable figures suggests that their visual perception impairments may involve not object processing so much as poor top-down control from higher association areas to representations in the visual cortex.     

Object and observer motion in the perception of objects by infants

Sixteen-week-old human infants distinguish optical displacements given by their own motion from displacements given by moving objects, and they use only the latter to perceive the unity of partly occluded objects. Optical changes produced by moving the observer around a stationary object produced attentional levels characteristic of stationary observers viewing stationary displays and much lower than those shown by stationary observers viewing moving displays. Real displacements of an object with no subject-relative displacement, produced by moving an object so as to maintain a constant relation to the moving observer, evoked attentional levels that were higher than with stationary displays and more characteristic of attention to moving displays, a finding suggesting detection of the real motion. Previously reported abilities of infants to perceive the unity of partly occluded objects from motion information were found to depend on real object motion rather than on optical displacements in general. The results suggest that object perception depends on registration of the motions of surfaces in the three-dimensional layout.     

Inertia tensor and weight-percept models of length perception by static holding

S. J. Lederman, S. R. Ganeshan, and R. E. Ellis (1996) reported an experiment demonstrating that for occluded rods of equal mass and length but different diameters length perception by static holding was larger for rods of smaller diameter. They concluded that participants inferred length from illusory weight percepts. However, rods of equal mass and length that differ in diameter also differ in the eigenvalues of their respective inertia tensors. In the present experiments, the authors manipulated the diameters (Experiment 1) and the inertial eigenvalues (Experiments 4 and 5) of statically held objects. As has been shown with wielded objects, perceived length was a function of the eigenvalues. Additional experiments failed to confirm the expectation from the weight-percept model that perceived length maps to the estimated weight (Experiments 2 and 3). Physical quantities, not psychological quantities, seem to explain length perception by static holding.     

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.