Object Interpolation in Three Dimensions

Perceptual organization and visual awareness: the case of amodal completion

We investigated the involvement of visual awareness in amodal completion, and specifically, whether visual awareness plays a differential role in local versus global completion, using a primed shape discrimination paradigm and the color-opponent flicker technique to render the prime invisible. In four experiments, participants discriminated the shape of a target preceded by a partly occluded or a neutral prime. All primes were divergent occlusion patterns in which the local completion is based on good continuation of the contours at the point of occlusion and the global completion is based on maximum symmetry. The target corresponded to the shape that could arise as a result of local or global completion of the occluded prime. For each experiment with an invisible prime we conducted a version with a visible prime. Our results suggest that local completion, but not global completion, of a partly occluded shape can take place in the absence of visual awareness, but apparently only when the visible occluded shape generates a single, local completion. No completion, either local or global, appears to take place in the absence of visual awareness when the visible occluded shape generates multiple completions. The implications of these results to the differential role of visual awareness in local and global completions and to the relationship between multiple completions and unconscious amodal completions are discussed.

Visual and haptic cues in processing occlusion

Introduction

Although shape is effective in processing occlusion, ambiguities in segmentation can also be addressed using depth discontinuity given visually and haptically. This study elucidates the contribution of visual and haptic cues to depth discontinuity in processing occlusion.

Methods

A virtual reality experiment was conducted with 15 students as participants. Word stimuli were presented on a head-mounted display for recognition. The central part of the words was masked with a virtual ribbon placed at different depths so that the ribbon appeared as an occlusion. The visual depth cue was either present with binocular stereopsis or absent with monocular presentation. The haptic cue was either missing, provided consecutively, or concurrently, by actively tracing a real off-screen bar edge that was positionally aligned with the ribbon in the virtual space. Recognition performance was compared between depth cue conditions.

Results

We found that word recognition was better with the stereoscopic cue but not with the haptic cue, although both cues contributed to greater confidence in depth estimation. The performance was better when the ribbon was at the farther depth plane to appear as a hollow, rather than when it was at the nearer depth plane to cover the word.

Discussion

The results indicate that occlusion is processed in the human brain by visual input only despite the apparent effectiveness of haptic space perception, reflecting a complex set of natural constraints.

The many facets of shape

Shape is an interesting property of objects because it is used in ordinary discourse in ways that seem to have little connection to how it is typically defined in mathematics. The present article describes how the concept of shape can be grounded within Euclidean and non-Euclidean geometry and also to human perception. It considers the formal methods that have been proposed for measuring the differences among shapes and how the performance of those methods compares with shape difference thresholds of human observers. It discusses how different types of shape change can be perceptually categorized. It also evaluates the specific data structures that have been used to represent shape in models of both human and machine vision, and it reviews the psychophysical evidence about the extent to which those models are consistent with human perception. Based on this review of the literature, we argue that shape is not one thing but rather a collection of many object attributes, some of which are more perceptually salient than others. Because the relative importance of these attributes can be context dependent, there is no obvious single definition of shape that is universally applicable in all situations.

Constant curvature segments as building blocks of 2D shape representation

How the visual system represents shape, and how shape representations might be computed by neural mechanisms, are fundamental and unanswered questions. Here, we investigated the hypothesis that 2-dimensional (2D) contour shapes are encoded structurally, as sets of connected constant curvature segments. We report 3 experiments investigating constant curvature segments as fundamental units of contour shape representations in human perception. Our results showed better performance in a path detection paradigm for constant curvature targets, as compared with locally matched targets that lacked this global regularity (Experiment 1), and that participants can learn to segment contours into constant curvature parts with different curvature values, but not into similarly different parts with linearly increasing curvatures (Experiment 2). We propose a neurally plausible model of contour shape representation based on constant curvature, built from oriented units known to exist in early cortical areas, and we confirmed the model's prediction that changes to the angular extent of a segment will be easier to detect than changes to relative curvature (Experiment 3). Together, these findings suggest the human visual system is specially adapted to detect and encode regions of constant curvature and support the notion that constant curvature segments are the building blocks from which abstract contour shape representations are composed. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Amodal Completion Revisited

Amodal completion (AC) is analyzed, by looking at its historical roots and persisting conceptual difficulties. Looking at the origin of the concept, it becomes clear that it is not equivalent to perception of occluded parts. The role of fragment incompleteness is discussed, to clarify that it cannot be taken as a necessary factor for eliciting AC. The standard view of AC, depicted as a set of processes that extrapolate from veridically represented image fragments, is evaluated and rejected on the basis of evidence that AC modifies also modal parts. The theoretical importance of AC phenomena and their potential to reveal the inner forces of perceptual organization are emphasized, with specific reference to the minimum principle. Instances in which AC might be expected but does not occur are examined, to define the limits of such an integrative process.

Abutting Objects Warp the Three-Dimensional Curvature of Modally Completing Surfaces

Binocular disparity can give rise to the perception of open surfaces or closed curved surfaces (volumes) that appear to vary smoothly across discrete depths. Here I build on my recent papers by providing examples where modally completing surfaces not only fill in from one depth layer's visible contours to another layer's visible contours within virtual contours in an analog manner, but where modally completing surface curvature is altered by the interpolation of an abutting object perceived to be connected to or embedded within that modally completing surface. Seemingly minor changes in such an abutting object can flip the interpretation of distal regions, for example, turning a distant edge (where a surface ends) into rim (where a surface bends to occlude itself) or turning an open surface into a closed one. In general, the interpolated modal surface appears to deform, warp, or bend in three-dimensions to accommodate the abutting object. These demonstrations cannot be easily explained by existing models of visual processing or modal completion and drive home the implausibility of localistic accounts of modal or amodal completion that are based, for example, solely on extending contours in space until they meet behind an occluder or in front of "pacmen." These demonstrations place new constraints on the holistic surface and volume generation processes that construct our experience of a three-dimensional world of surfaces and objects under normal viewing conditions.

The Veiled Virgin illustrates visual segmentation of shape by cause

How the brain reconstructs three-dimensional object shape from two-dimensional retinal light patterns remains a mystery. Most research has investigated how cues—such as shading, texture, or perspective—help us estimate visible surface points on the outside of objects. However, our findings show the brain achieves much more than this. Observers not only infer the visible outer surface but also the hidden internal structure of objects—seeing “beneath the skin.” Our findings suggest the brain parses shapes’ features according to their physical causes, potentially allowing us to separate a single continuous surface into multiple superimposed depth layers. This ability likely aids our interactions with objects, by indicating which surface locations are firmly supported from the inside and thus suitable for grasping.

Three-dimensional (3D) shape perception is one of the most important functions of vision. It is crucial for many tasks, from object recognition to tool use, and yet how the brain represents shape remains poorly understood. Most theories focus on purely geometrical computations (e.g., estimating depths, curvatures, symmetries). Here, however, we find that shape perception also involves sophisticated inferences that parse shapes into features with distinct causal origins. Inspired by marble sculptures such as Strazza’s The Veiled Virgin (1850), which vividly depict figures swathed in cloth, we created composite shapes by wrapping unfamiliar forms in textile, so that the observable surface relief was the result of complex interactions between the underlying object and overlying fabric. Making sense of such structures requires segmenting the shape based on their causes, to distinguish whether lumps and ridges are due to the shrouded object or to the ripples and folds of the overlying cloth. Three-dimensional scans of the objects with and without the textile provided ground-truth measures of the true physical surface reliefs, against which observers’ judgments could be compared. In a virtual painting task, participants indicated which surface ridges appeared to be caused by the hidden object and which were due to the drapery. In another experiment, participants indicated the perceived depth profile of both surface layers. Their responses reveal that they can robustly distinguish features belonging to the textile from those due to the underlying object. Together, these findings reveal the operation of visual shape-segmentation processes that parse shapes based on their causal origin.

From Michotte Until Today: Why the Dichotomous Classification of Modal and Amodal Completions Is Inadequate

The distinction between modal and amodal completion is ubiquitous in the perception literature. It goes back to the seminal publication "Les compléments amodaux des structures perceptives" by A. Michotte, G. Thinès, and G. Crabbé (Publications Universitaires de Louvain: Louvain) in 1964. We review and discuss this work in this article and show commonalities and differences to today's view. We then argue that the dichotomous distinction between modal and amodal completions is problematic in phenomenological, empirical, logical, and theoretical terms. Finally, we propose alternative criteria allowing for a more differentiated classification scheme for completion phenomena. This scheme seems to be consistent with all known empirical findings and can also be generalized to nonvisual domains of perception.

The motion-induced contour revisited: Observations on 3-D structure and illusory contour formation in moving stimuli

The motion-induced contour (MIC) was first described by Victor Klymenko and Naomi Weisstein in a series of papers in the 1980s. The effect is created by rotating the outline of a tilted cube in depth. When one of the vertical edges is removed, an illusory contour can be seen in its place. In four experiments, we explored which stimulus features influence perceived illusory contour strength. Participants provided subjective ratings of illusory contour strength as a function of orientation of the stimulus, separation between inducing edges, and the length of inducing edges. We found that the angle of tilt of the object in depth had the largest impact on perceived illusory contour strength with tilt angles of 20° and 30° producing the strongest percepts. Tilt angle is an unexplored feature of structure-from-motion displays. In addition, we found that once the depth structure of the object was extracted, other features of the display, such as the distance spanned by the illusory contour, could also influence its strength, similar to the notion of support ratio for 2-D illusory contours. Illusory contour strength was better predicted by the length of the contour in 3-D rather than in 2-D, suggesting that MICs are constructed by a 3-D process that takes as input initially recovered contour orientation and position information in depth and only then forms interpolations between them.

Contour interpolation: A case study in Modularity of Mind

In his monograph Modularity of Mind (1983), philosopher Jerry Fodor argued that mental architecture can be partly decomposed into computational organs termed modules, which were characterized as having nine co-occurring features such as automaticity, domain specificity, and informational encapsulation. Do modules exist? Debates thus far have been framed very generally with few, if any, detailed case studies. The topic is important because it has direct implications on current debates in cognitive science and because it potentially provides a viable framework from which to further understand and make hypotheses about the mind's structure and function. Here, the case is made for the modularity of contour interpolation, which is a perceptual process that represents non-visible edges on the basis of how surrounding visible edges are spatiotemporally configured. There is substantial evidence that interpolation is domain specific, mandatory, fast, and developmentally well-sequenced; that it produces representationally impoverished outputs; that it relies upon a relatively fixed neural architecture that can be selectively impaired; that it is encapsulated from belief and expectation; and that its inner workings cannot be fathomed through conscious introspection. Upon differentiating contour interpolation from a higher-order contour representational ability ("contour abstraction") and upon accommodating seemingly inconsistent experimental results, it is argued that interpolation is modular to the extent that the initiating conditions for interpolation are strong. As interpolated contours become more salient, the modularity features emerge. The empirical data, taken as a whole, show that at least certain parts of the mind are modularly organized.

Perceptual mechanisms underlying amodal surface integration of 3-D stereoscopic stimuli

The visual system can represent a partially occluded 3-D surface from images of separated surface segments. The underlying amodal surface integration process accomplishes this by amodally extending each surface segment behind the occluder (amodal surface extension) and integrating the extended surfaces to form a whole surface representation. We conducted five experiments to investigate how depth cues, such as binocular disparity, half-occlusion, and monocular depth cues (T-junctions and L-junctions), contribute to amodal surface extension, and how the geometrical relationship and image similarity among the surface segments affect surface integration. This was achieved by having observers adjust the stereoscopic depth and slant of a comparison stimulus to match those of the tested 3-D stimulus. We found that both binocular disparity and half-occlusion cues are used to determine border-ownership assignment of surface segments and for amodal surface extension. We also found that separated surface segments need to have the same luminance contrast-polarity for them to be integrated as a whole surface. Finally, we found that having the same motion direction, minimum misalignment between boundary contours, and proximity among separated segments facilitate their integration. Overall, our findings reveal a set of "perceptual factors" for amodal surface integration, which arguably reflects our visual system's built-in knowledge of the regularities in natural scenes.

Contour Integration over Time: Psychophysical and fMRI Evidence

The brain integrates discrete but collinear stimuli to perceive global contours. Previous contour integration (CI) studies mainly focus on integration over space, and CI is attributed to either V1 long-range connections or contour processing in high-visual areas that top-down modulate V1 responses. Here, we show that CI also occurs over time in a design that minimizes the roles of V1 long-range interactions. We use tilted contours embedded in random orientation noise and moving horizontally behind a fixed vertical slit. Individual contour elements traveling up/down within the slit would be encoded over time by parallel, rather than aligned, V1 neurons. However, we find robust contour detection even when the slit permits only one viewable contour element. Similar to CI over space, CI over time also obeys the rule of collinearity. fMRI evidence shows that while CI over space engages visual areas as early as V1, CI over time mainly engages higher dorsal and ventral visual areas involved in shape processing, as well as posterior parietal regions involved in visual memory that can represent the orientation of temporally integrated contours. These results suggest at least partially dissociable mechanisms for implementing the Gestalt rule of continuity in CI over space and time.

Visual perception of shape altered by inferred causal history

One of the main functions of vision is to represent object shape. Most theories of shape perception focus exclusively on geometrical computations (e.g., curvatures, symmetries, axis structure). Here, however, we find that shape representations are also profoundly influenced by an object’s causal origins: the processes in its past that formed it. Observers placed dots on objects to report their perceived symmetry axes. When objects appeared ‘complete’—created entirely by a single generative process—responses closely approximated the object’s geometrical axes. However, when objects appeared ‘bitten’—as if parts had been removed by a distinct causal process—the responses deviated significantly from the geometrical axes, as if the bitten regions were suppressed from the computation of symmetry. This suppression of bitten regions was also found when observers were not asked about symmetry axes but about the perceived front and back of objects. The findings suggest that visual shape representations are more sophisticated than previously appreciated. Objects are not only parsed according to what features they have, but also to how or why they have those features.

Learning the 3-D structure of objects from 2-D views depends on shape, not format

Humans can learn to recognize new objects just from observing example views. However, it is unknown what structural information enables this learning. To address this question, we manipulated the amount of structural information given to subjects during unsupervised learning by varying the format of the trained views. We then tested how format affected participants' ability to discriminate similar objects across views that were rotated 90° apart. We found that, after training, participants' performance increased and generalized to new views in the same format. Surprisingly, the improvement was similar across line drawings, shape from shading, and shape from shading + stereo even though the latter two formats provide richer depth information compared to line drawings. In contrast, participants' improvement was significantly lower when training used silhouettes, suggesting that silhouettes do not have enough information to generate a robust 3-D structure. To test whether the learned object representations were format-specific or format-invariant, we examined if learning novel objects from example views transfers across formats. We found that learning objects from example line drawings transferred to shape from shading and vice versa. These results have important implications for theories of object recognition because they suggest that (a) learning the 3-D structure of objects does not require rich structural cues during training as long as shape information of internal and external features is provided and (b) learning generates shape-based object representations independent of the training format.

Created unequal: Temporal dynamics of modal and amodal boundary interpolation

In this study we manipulate the distribution of contrast polarity reversals in inducing configurations to create novel variants of modal and amodal completion. The novel variants, better equated in their geometric and photometric characteristics offer a superior way to probe similarities and differences in the temporal dynamics that underlie different forms of perceptual completion. We use dot localisation to directly compare the spatial characteristics of modally and amodally interpolated contours at presentation durations ranging from 120 to 300ms and find robust differences in the spatiotemporal formation of modally and amodally completed boundaries. Modally completed contours are localised more accurately and with better spatial precision across all presentation durations. Our results challenge the assumption that the boundary interpolation system depends solely on the geometrical relatability of inducing fragments and suggest that boundary interpolation depends on the spatial distribution of local luminance relationships. As an alternative to the strong version of the identity hypothesis, we propose that modal and amodal completion are mediated by different mechanisms, triggered by particular configurations of contrast polarity.

Spatiotemporal Form Integration: sequentially presented inducers can lead to representations of stationary and rigidly rotating objects

Objects in the world often are occluded and in motion. The visible fragments of such objects are revealed at different times and locations in space. To form coherent representations of the surfaces of these objects, the visual system must integrate local form information over space and time. We introduce a new illusion in which a rigidly rotating square is perceived on the basis of sequentially presented Pacman inducers. The illusion highlights two fundamental processes that allow us to perceive objects whose form features are revealed over time: Spatiotemporal Form Integration (STFI) and Position Updating. STFI refers to the spatial integration of persistent representations of local form features across time. Position updating of these persistent form representations allows them to be integrated into a rigid global motion percept. We describe three psychophysical experiments designed to identify spatial and temporal constraints that underlie these two processes and a fourth experiment that extends these findings to more ecologically valid stimuli. Our results indicate that although STFI can occur across relatively long delays between successive inducers (i.e., greater than 500 ms), position updating is limited to a more restricted temporal window (i.e., ~300 ms or less), and to a confined range of spatial (mis)alignment. These findings lend insight into the limits of mechanisms underlying the visual system's capacity to integrate transient, piecemeal form information, and support coherent object representations in the ever-changing environment.

What can fish brains tell us about visual perception?

Fish are a complex taxonomic group, whose diversity and distance from other vertebrates well suits the comparative investigation of brain and behavior: in fish species we observe substantial differences with respect to the telencephalic organization of other vertebrates and an astonishing variety in the development and complexity of pallial structures. We will concentrate on the contribution of research on fish behavioral biology for the understanding of the evolution of the visual system. We shall review evidence concerning perceptual effects that reflect fundamental principles of the visual system functioning, highlighting the similarities and differences between distant fish groups and with other vertebrates. We will focus on perceptual effects reflecting some of the main tasks that the visual system must attain. In particular, we will deal with subjective contours and optical illusions, invariance effects, second order motion and biological motion and, finally, perceptual binding of object properties in a unified higher level representation.

Recovering metric properties of objects through spatiotemporal interpolation

Spatiotemporal interpolation (STI) refers to perception of complete objects from fragmentary information across gaps in both space and time. It differs from static interpolation in that requirements for interpolation are not met in any static frame. It has been found that STI produced objective performance advantages in a shape discrimination paradigm for both illusory and occluded objects when contours met conditions of spatiotemporal relatability. Here we report psychophysical studies testing whether spatiotemporal interpolation allows recovery of metric properties of objects. Observers viewed virtual triangles specified only by sequential partial occlusions of background elements by their vertices (the STI condition) and made forced choice judgments of the object's size relative to a reference standard. We found that length could often be accurately recovered for conditions where fragments were relatable and formed illusory triangles. In the first control condition, three moving dots located at the vertices provided the same spatial and timing information as the virtual object in the STI condition but did not induce perception of interpolated contours or a coherent object. In the second control condition oriented line segments were added to the dots and mid-points between the dots in a way that did not induce perception of interpolated contours. Control stimuli did not lead to accurate size judgments. We conclude that spatiotemporal interpolation can produce representations, from fragmentary information, of metric properties in addition to shape.

The brain creates illusions not just for us: sharks (Chiloscyllium griseum) can "see the magic" as well

Bamboo sharks (Chiloscyllium griseum) were tested for their ability to perceive subjective and illusionary contours as well as line length illusions. Individuals were first trained to differentiate between squares, triangles, and rhomboids in a series of two alternative forced-choice experiments. Transfer tests then elucidated whether Kanizsa squares and triangles, grating gaps and phase shifted abutting gratings were also perceived and distinguished. The visual systems of most vertebrates and even invertebrates perceive illusionary contours despite the absence of physical luminance, color or textural differences. Sharks are no exception to the rule; all tasks were successfully mastered within 3-24 training sessions, with sharks discriminating between various sets of Kanizsa figures and alternative stimuli, as well as between subjective contours in >75% of all tests. However, in contrast to Kanizsa figures and subjective contours, sharks were not deceived by Müller-Lyer (ML) illusions. Here, two center lines of equal length are comparatively set between two arrowheads or -tails, in which case the line featuring the two arrow tails appears to be longer to most humans, primates and birds. In preparation for this experiment, lines of varying length, and lines of unequal length randomly featuring either two arrowheads or -tails on their ends, were presented first. Both sets of lines were successfully distinguished by most sharks. However, during presentation of the ML illusions sharks failed to succeed and succumbed either to side preferences or chose according to chance.

Linking brain to behavior for the visual perception of figures and objects

The dissociation of a figure from its background is an essential feat of visual perception, as it allows us to detect, recognize, and interact with shapes and objects in our environment. In order to understand how the human brain gives rise to the perception of figures, we here review experiments that explore the links between activity in visual cortex and performance of perceptual tasks related to figure perception. We organize our review according to a proposed model that attempts to contextualize figure processing within the more general framework of object processing in the brain. Overall, the current literature provides us with individual linking hypotheses as to cortical regions that are necessary for particular tasks related to figure perception. Attempts to reach a more complete understanding of how the brain instantiates figure and object perception, however, will have to consider the temporal interaction between the many regions involved, the details of which may vary widely across different tasks.

Individual Differences in Mental Rotation

Two experiments tested the hypothesis that imagery ability and figural complexity interact to affect the choice of mental rotation strategies. Participants performed the Shepard and Metzler (1971) mental rotation task. On half of the trials, the 3-D figures were manipulated to create “fragmented” figures, with some cubes missing. Good imagers were less accurate and had longer response times on fragmented figures than on complete figures. Poor imagers performed similarly on fragmented and complete figures. These results suggest that good imagers use holistic mental rotation strategies by default, but switch to alternative strategies depending on task demands, whereas poor imagers are less flexible and use piecemeal strategies regardless of the task demands.

Is interpolation cognitively encapsulated? Measuring the effects of belief on Kanizsa shape discrimination and illusory contour formation

Contour interpolation is a perceptual process that fills-in missing edges on the basis of how surrounding edges (inducers) are spatiotemporally related. Cognitive encapsulation refers to the degree to which perceptual mechanisms act in isolation from beliefs, expectations, and utilities (Pylyshyn, 1999). Is interpolation encapsulated from belief? We addressed this question by having subjects discriminate briefly-presented, partially-visible fat and thin shapes, the edges of which either induced or did not induce illusory contours (relatable and non-relatable conditions, respectively). Half the trials in each condition incorporated task-irrelevant distractor lines, known to disrupt the filling-in of contours. Half of the observers were told that the visible parts of the shape belonged to a single thing (group strategy); the other half were told that the visible parts were disconnected (ungroup strategy). It was found that distractor lines strongly impaired performance in the relatable condition, but minimally in the non-relatable condition; that strategy did not alter the effects of the distractor lines for either the relatable or non-relatable stimuli; and that cognitively grouping relatable fragments improved performance whereas cognitively grouping non-relatable fragments did not. These results suggest that (1) filling-in effects during illusory contour formation cannot be easily removed via strategy; (2) filling-in effects cannot be easily manufactured from stimuli that fail to elicit interpolation; and (3) actively grouping fragments can readily improve discrimination performance, but only when those fragments form interpolated contours. Taken together, these findings indicate that discriminating filled-in shapes depends on strategy but the filling-in process itself may be encapsulated from belief.

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.

Volume completion in 4.5-month-old infants

In this study, we examined 4.5-month-old infants' visual completion of self-occluding three-dimensional objects. A previous study on this topic reported that 6-month-old, but not 4-month-old infants extrapolate a convex, symmetric prism from a limited view of its surfaces (Soska & Johnson, 2008). As of yet, studies on the development of amodal completion of three-dimensional, self-occluding objects are scarce. Given 4-month-old infants' abilities to derive three-dimensional shape from a variety of visual cues, three-dimensional amodal completion may well depend on the perceptual strength of three-dimensionality in the stimulus displays. The first experiments (1A and 1B) tested this hypothesis by means of a habituation paradigm and showed that 4.5-month-old infants are indeed able to amodally complete the back of a self-occluding object when sufficient three-dimensional cues are available. Further support for volume completion in 4.5-month-old infants was found in a second experiment, again using a habituation paradigm, that measured perceived connectedness between two visually separated, self-occluding, three-dimensional objects.

Surface completion affected by luminance contrast polarity and common motion

Our visual system ably integrates the visible parts of a partially occluded surface with the occluded parts (amodal surface completion), mainly by relying on the surface boundary contours of the image. Less known, is whether the visual system also utilizes surface feature information, such as luminance contrast polarity, for surface completion. We conducted three experiments to investigate this issue. Experiment 1 found that when visible segments of a partially occluded rectangle with the same luminance contrast polarity move behind an occluding surface, observers perceive the visible segments as part of the occluded rectangle moving cohesively behind the occluding surface. However, when the visible segments have opposite luminance contrast polarity, the global motion of the segments is barely perceived, suggesting a failure of amodal surface integration. Experiment 2 revealed that this same luminance contrast polarity constraint applies to amodal surface integration of a display without an explicit occluding surface image. Experiment 3 showed that both the shape and luminance contrast polarity of the visible segments of the partially occluded rectangle affect amodal surface completion. Together, these findings demonstrate that luminance contrast polarity, along with surface boundary contour, are important cues for amodal surface integration.

The neural correlates of visuospatial perceptual and oculomotor extrapolation

The human visual system must perform complex visuospatial extrapolations (VSE) across space and time in order to extract shape and form from the retinal projection of a cluttered visual environment characterized by occluded surfaces and moving objects. Even if we exclude the temporal dimension, for instance when judging whether an extended finger is pointing towards one object or another, the mechanisms of VSE remain opaque. Here we investigated the neural correlates of VSE using functional magnetic resonance imaging in sixteen human observers while they judged the relative position of, or saccaded to, a (virtual) target defined by the extrapolated path of a pointer. Using whole brain and region of interest (ROI) analyses, we compared the brain activity evoked by these VSE tasks to similar control judgements or eye movements made to explicit (dot) targets that did not require extrapolation. The data show that activity in an occipitotemporal region that included the lateral occipital cortex (LOC) was significantly greater during VSE than during control tasks. A similar, though less pronounced, pattern was also evident in regions of the fronto-parietal cortex that included the frontal eye fields. However, none of the ROIs examined exhibited a significant interaction between target type (extrapolated/explicit) and response type (oculomotor/perceptual). These findings are consistent with a close association between visuoperceptual and oculomotor responses, and highlight a critical role for the LOC in the process of VSE.

Perception of subjective contours in fish

The ability of fish to perceive subjective (or illusory) contours, ie contours that lack a physical counterpart in terms of luminance contrast gradients, was investigated. In the first experiment, redtail splitfins (Xenotoca eiseni), family Goodeidae, were trained to discriminate between a geometric figure (a triangle or a square) on various backgrounds and a background without any figure. Thereafter, the fish performed test trials in which illusory squares or triangles were obtained by (i) interruptions of a background of diagonal lines, (ii) phase-shifting of a background of diagonal lines, and (iii) pacmen spatially arranged to induce perception of Kanizsa subjective surfaces. In all three conditions, fish seemed to generalise their responses to stimuli perceived as subjective contours by humans. Fish chose, correctly, squares or triangles made of interrupted or phase-shifted diagonal lines from uniform backgrounds of diagonal lines, as well as illusory square or triangle Kanizsa figures from figures in which the inducing pacmen were scrambled. In the second experiment, fish were trained to discriminate between a vertical and a horizontal bar with luminance contrast gradients, and then tested with vertically and horizontally oriented illusory bars, created either through interruption or spatial phase-shift of inducing diagonal lines. Fish appeared to be able to generalise the orientation discrimination to illusory contours. These results demonstrate that redtail splitfins are capable of perceiving illusory contours.

Surface boundary contour strengthens image dominance in binocular competition

We used a binocular rivalry stimulus with one half-image having a vertical grating disk surrounded by horizontal grating, and the other half-image having a horizontal grating disk with a variable spatial phase relative to the surrounding horizontal grating. We found that increasing the phase-shift of the horizontal grating disk, which strengthens the boundary contour, progressively increases its predominance. But the predominance is little affected when a constant gray ring (boundary contour) is added onto the rim of the incrementally phase-shifted horizontal grating. This suggests the influence of boundary contour supersede that of the center-surround-interaction caused by the phase-shift.

Early processing in the human lateral occipital complex is highly responsive to illusory contours but not to salient regions

Human electrophysiological studies support a model whereby sensitivity to so-called illusory contour stimuli is first seen within the lateral occipital complex. A challenge to this model posits that the lateral occipital complex is a general site for crude region-based segmentation, based on findings of equivalent hemodynamic activations in the lateral occipital complex to illusory contour and so-called salient region stimuli, a stimulus class that lacks the classic bounding contours of illusory contours. Using high-density electrical mapping of visual evoked potentials, we show that early lateral occipital cortex activity is substantially stronger to illusory contour than to salient region stimuli, whereas later lateral occipital complex activity is stronger to salient region than to illusory contour stimuli. Our results suggest that equivalent hemodynamic activity to illusory contour and salient region stimuli probably reflects temporally integrated responses, a result of the poor temporal resolution of hemodynamic imaging. The temporal precision of visual evoked potentials is critical for establishing viable models of completion processes and visual scene analysis. We propose that crude spatial segmentation analyses, which are insensitive to illusory contours, occur first within dorsal visual regions, not the lateral occipital complex, and that initial illusory contour sensitivity is a function of the lateral occipital complex.

A unified model of illusory and occluded contour interpolation

Models of contour interpolation have been proposed for illusory contour interpolation but seldom for interpolation of occluded contours. The identity hypothesis (Kellman & Loukides, 1987; Kellman & Shipley, 1991) posits that an early interpolation mechanism is shared by interpolated contours that are ultimately perceived as either illusory or occluded. Here we propose a model of such a unified interpolation mechanism for illusory and occluded contours, building on the framework established in Heitger, von der Heydt, Peterhans, Rosenthaler, and Kubler (1998). We show that a single, neurally plausible mechanism that is consistent with the identity hypothesis also generates contour interpolations in agreement with perception for cases of transparency, self-splitting objects, interpolation with mixed boundary assignment, and "quasimodal" interpolations. Limiting cases for this local, feed-forward approach are presented, demonstrating that both early, local interpolation mechanisms and non-local scene constraints are necessary for describing the perception of interpolated contours.

Development of perceptual completion originates in information acquisition

Adults have little difficulty perceiving objects as complete despite occlusion, but newborn infants perceive moving partly occluded objects solely in terms of visible surfaces. The developmental mechanisms leading to perceptual completion have never been adequately explained. Here, the authors examine the potential contributions of oculomotor behavior and motion sensitivity to perceptual completion performance in individual infants. Young infants were presented with a center-occluded rod, moving back and forth against a textured background, to assess perceptual completion. Infants also participated in tasks to assess oculomotor scanning patterns and motion direction discrimination. Individual differences in perceptual completion performance were strongly correlated with scanning patterns but were unrelated to motion direction discrimination. The authors present a new model of development of perceptual completion that posits a critical role for targeted visual scanning, an early developing oculomotor action system.

Approximation, torsion, and amodally-completed surfaces

Consider a stereoscopic display simulating two rectangular patches, the lower frontoparallel and the upper slanted around the vertical axis. When the two patches are amodally completed and appear as the unoccluded parts of a smooth surface partially hidden by a foreground frontoparallel surface, either real or illusory, their relative slant is underestimated with respect to a baseline condition in which they are perceived as separate rectangles. Slant assimilation was studied in three experiments using with- vs. without-occluder displays and two methods, slant matching and speeded classification of twist direction. In Experiments 1 and 2 we found slant assimilation in with-occluder displays and slant contrast in without-occluder displays. In Experiment 3 we isolated a component of slant assimilation attributable to the mere presence of the occluder. Twist classification performance was impaired even when edge geometry hindered amodal completion, but the performance loss was larger when surface patches were amodally completed. To minimize the required amount of torsion, input fragments are misperceived, indicating that in limiting conditions amodal completion is mediated by approximation rather than interpolation. Slant assimilation decreases as twist angle increases, up to a limit above which the visual system does not support the formation of a smooth amodal surface with torsion.

Recognition of partly occluded objects by fish

The ability to visually complete partly occluded objects (so-called "amodal completion") has been documented in mammals and birds. Here, we report the first evidence of such a perceptual ability in a fish species. Fish (Xenotoca eiseni) were trained to discriminate between a complete and an amputated disk. Thereafter, the fish performed test trials in which hexagonal polygons were either exactly juxtaposed or only placed close to the missing sectors of the disk in order to produce or not produce the impression (to a human observer) of an occlusion of the missing sectors of the disk by the polygon. In another experiment, fish were first trained to discriminate between hexagonal polygons that were either exactly juxtaposed or only placed close to the missing sectors of a disk, and then tested for choice between a complete and an amputated disk. In both experiments, fish behaved as if they were experiencing visual completion of the partly occluded stimuli. These findings suggest that the ability to visually complete partly occluded objects may be widespread among vertebrates, possibly inherited in mammals, birds and fish from early vertebrate ancestors.

Prior experience affects amodal completion in pigeons

In a three-alternative forced-choice task, 4 pigeons were trained to discriminate a target stimulus consisting of two colored shapes, one of which partially occluded the other, from two foil stimuli that portrayed either a complete or an incomplete version of the occluded shape. The dependent measure was the percentage of total errors that the birds committed to the complete foil. At the outset of training, the pigeons committed approximately 50% of total errors to the complete foil, but as training progressed, the percentage of errors to the complete foil rose. When the pigeons were given a second exposure to the initial set of stimuli, they committed 70% of total errors to the complete foil, suggesting that they now saw the complete foil as more similar to the occluded target than the incomplete foil. These results suggest that experience with 2-D images may facilitate amodal completion in pigeons, perhaps via perceptual learning.

Introduction to Michotte's heritage in perception and cognition research

Several decades after Michotte's work was published, it continues to inspire current research in perception, cognition, and beyond. In this special issue we pay tribute to this heritage with a collection of empirical and theoretical papers on amodal completion and the perception of causality, two areas of research within which Michotte's work and ideas have had a lasting influence. As a background to better understand the remaining papers, we briefly sketch Michotte's life and work and the scope (in breadth and in depth) of his impact. We then review Michotte's seminal contributions to the areas covered in this special issue, some of the major research discoveries and themes in the intervening decades, and the major open questions and challenges we are still facing. We also include a sneak preview of the papers in this special issue, noting how they relate to Michotte's work and to each other. This review shows both how much influence Michotte has had on contemporary perception and cognition research, and how much important work remains to be done. We hope that the papers in this special issue will serve both to celebrate Michotte's heritage in this respect, and to inspire other investigators to continue the projects he began.

Visual interpolation is not scale invariant

According to the scale-dependence hypothesis, the visual interpolation of contour fragments depends on the retinal separation of endpoints: as the retinal size of a partially occluded angle increases, the interpolated contour gradually deviates from the shortest connecting path and approaches the shape of the unoccluded angle. In the field model, as the retinal size increases the strength of good continuation increases while the strength of the minimal-path tendency decreases. To test the scale-dependence hypothesis--as well as other hypotheses connected to inclusion, support-ratio dependence, and extended relatability--we ran two experiments using the probe localization technique. Stimuli were regular polygons with rectilinear contours bounding symmetrically occluded angles. Retinal size was manipulated by changing viewing distance. Observers were asked to judge if a probe, briefly superposed on the occlusion region, was inside or outside the amodally completed angle. Retinal size strongly influenced the penetration of interpolated trajectories in the predicted direction. However, support ratio and interpolated angle size interacted with retinal size, consistently with the idea that unification factors are effective within a spatial window. We modified the field model to include the size of such a window as a new parameter and generated model-based trajectories that fitted empirical data closely.