Three-dimensional illusory contours and surfaces

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 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.

Volume Completion Between Contour Fragments at Discrete Depths

Building on the modal and amodal completion work of Kanizsa, Carman and Welch showed that binocular stereo viewing of two disparate images can give rise to a percept of 3D curved, nonclosed illusory contours and surfaces. Here, it is shown that binocular presentation can also give rise to the percept of closed curved surfaces or volumes that appear to vary smoothly across discrete depths in binocularly fused images, although in fact only two binocular disparities are discretely defined between corresponding contour elements of the inducing elements. Surfaces are filled in from one depth layer's visible contours to another layer's visible contours within virtual contours that are interpolated on the basis of good contour continuation between the visible portions of contour. These single depth contour segments are taken not to arise from surface edges, as in Kanizsa's or Carman and Welch's examples, but from segments of "rim" where the line of sight just grazes a surface that continues behind and beyond the rim smoothly. When there are two or more surface-propagating contour segments, the propagated surfaces can continue away from the inferred rim, merge, and then close behind the self-occluding visible surface into an everywhere differentiable closed surface or volume. Illusory surfaces can possess a depth and perceived surface curvature that is consistent with all visible contour segments, despite the absence of local disparity cues at interpolated 3D surface locations far from any visible contour. These demonstrations cannot be easily explained by existing models of visual processing. They place constraints on the surface and volume generation processes that construct our 3D world under normal viewing conditions.

How Does the Cerebral Cortex Work? Development, Learning, Attention, and 3-D Vision by Laminar Circuits of Visual Cortex

A key goal of behavioral and cognitive neuroscience is to link brain mechanisms to behavioral functions. The present article describes recent progress toward explaining how the visual cortex sees. Visual cortex, like many parts of perceptual and cognitive neocortex, is organized into six main layers of cells, as well as characteristic sublamina. Here it is proposed how these layered circuits help to realize processes of development, learning, perceptual grouping, attention, and 3-D vision through a combination of bottom-up, horizontal, and top-down interactions. A main theme is that the mechanisms which enable development and learning to occur in a stable way imply properties of adult behavior. These results thus begin to unify three fields: infant cortical development, adult cortical neurophysiology and anatomy, and adult visual perception. The identified cortical mechanisms promise to generalize to explain how other perceptual and cognitive processes work.

Spatial and temporal properties of stereoscopic surface interpolation

It is well established that under a wide range of conditions when a sparse collection of texture elements varies smoothly in depth, the spaces between the elements are assigned depth values. This disparity interpolation process has been studied in an effort to define some of its fundamental spatial and temporal constraints. To assess disparity interpolation we employed two tasks: a novel task that relies on the bisection of illusory boundaries created when subjective stereoscopic surfaces intersect, and one that relies on a 3-D shape discrimination. The results of both experiments show that there is no improvement in performance when texture density is increased from near 0.20 to 0.85 or when exposure duration is increased from 50-100 to 1000 ms. This lack of dependence on the addition of features that define the interpolated surface, along with the abrupt decline in performance below a critical value, is consistent with the view that surface interpolation is an important function of human stereoscopic vision.

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.

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.

A laminar cortical model for 3D perception of slanted and curved surfaces and of 2D images: development, attention, and bistability

A model of laminar visual cortical dynamics proposes how 3D boundary and surface representations arise from viewing slanted and curved 3D objects and 2D images. The 3D boundary representations emerge from non-classical receptive field interactions within intracortical and intercortical feedback circuits. Such non-classical interactions within cortical areas V1 and V2 contextually disambiguate classical receptive field responses to ambiguous visual cues using cells that are sensitive to colinear contours, angles, and disparity gradients. Remarkably, these cell types can all be explained as variants of a unified perceptual grouping circuit whose most familiar example is a 2D colinear bipole cell. Model simulations show how this circuit can develop cell selectivity to colinear contours and angles, how slanted surfaces can activate 3D boundary representations that are sensitive to angles and disparity gradients, how 3D filling-in occurs across slanted surfaces, how a 2D Necker cube image can be represented in 3D, and how bistable 3D Necker cube percepts occur. The model also explains data about slant aftereffects and 3D neon color spreading. It shows how chemical transmitters that habituate, or depress, in an activity-dependent way can help to control development and also to trigger bistable 3D percepts and slant aftereffects. Attention can influence which of these percepts is perceived by propagating selectively along object boundaries.

Visual completion of three-dimensional, chromatic, moving stimuli in humans

We studied whether visual completion can be produced within three-dimensional (3-D), moving, chromatic objects. Rotating thin and thick discs with red sectors, forming the corners of Kanizsa triangle, were presented on a display. Observers also rotated a hand-held real thin Kanizsa triangle. An illusory, moving contour encompassing an illusory colourful triangle was generally observed. This indicates that the visual system is capable of filling in complex (3-D, moving, chromatic) percepts.

Stereoscopic surface interpolation supports lightness constancy

The human visual system has a remarkable ability to construct surface representations from sparse stereoscopic, as well as texture and motion, information. In impoverished displays where few points are used to define regions in depth, the brain often interpolates depth estimates across intervening blank regions to create a compelling sense of a solid surface. The set of experiments described here examined stereoscopic interpolation using a novel technique based on lightness constancy. The effectiveness of this method is notable because it stands as the only technique to date that unequivocally examines the perception of interpolated surfaces, and not surfaces inferred subjectively from depth information in the stimulus. Further, these data support the growing evidence that a primary function of the stereoscopic system is to define three-dimensional surface structure.

Stereoscopic illusory contours--cortical neuron responses and human perception

In human perception, figure-ground segregation suggests that stereoscopic cues are grouped over wide areas of the visual field. For example, two abutting rectangles of equal luminance and size are seen as a uniform surface when presented at the same depth, but appear as two surfaces separated by an illusory contour and a step in depth when presented with different retinal disparities. Here, we describe neurons in the monkey visual cortex that signal such illusory contours and can be selective for certain figure-ground directions that human observers perceive at these contours. The results suggest that these neurons group stereoscopic cues over distances up to 8 degrees. In addition, we compare these results with human perception and show that the mean stimulus parameters required by these neurons also induce optimal percepts of illusory contours in human observers.

A contour propagation approach to surface filling-in and volume formation

A new approach to surface and volume formation is introduced in response to the question, "Why do some silhouettes look 3 dimensional (3D) and others look 2D?" The central idea is that form information can propagate away from a "propagable segment" (PS) of occluding contour that could have projected onto the image from the visible portion of a cross-section of a surface. A key property of a PS is that it exhibits abrupt curvature changes where it meets the rest of the occluding contour. An algorithm is described for filling in curved surfaces from a PS: When copies of a PS are propagated into the interior, they act as cross-sectional surface contours that also exhibit abrupt curvature changes with the rest of the occluding contour. The result is a nonmetric coding of 3D-shape in terms of local ordinal surface curvature and orientation relationships that is scale, translation, and rotation invariant.

The absence of depth constancy in contour stereograms

Stereoscopic surfaces constructed from Kanizsa-type illusory contours or explicit luminance contours were tested for three-dimensional (3-D) shape constancy. The curvature of the contours and the apparent viewing distance between the surface and the observer were manipulated. Observers judged which of two surfaces appeared more curved. Experiment 1 allowed eye movements and revealed a bias in 3-D shape judgment with changes in apparent viewing distance, such that surfaces presented far from the observer appeared less curved than surfaces presented close to the observer. The lack of depth constancy was approximately the same for illusory-contour surfaces and for explicit-contour surfaces. Experiment 2 showed that depth constancy for explicit-contour surfaces improved slightly when fixation was required and eye movements were restricted. These experiments suggest that curvature in depth is misperceived, and that illusory-contour surfaces are particularly sensitive to this distortion.

Illusory contour strength does not depend on the dynamics or relative phase of the inducers

We use a new objective measure of illusory contour strength, threshold reduction for aspect ratio discrimination, to examine the effect of dynamics and relative phase on the Kanizsa illusion. We found no dependence of illusory contour strength on the relative phase of flickering inducers (in phase, antiphase, or in quadrature phase) either for the standard Kanizsa square, or for modifications that facilitated or interfered with amodal completion. Comparison with a vernier acuity task indicates that the distance between the inducers, rather than the nature of the task, accounts for the insensitivity to relative phase.

Inter-attribute tilt effects and orientation analysis in the visual brain

A test grating appears to be tilted away from an inducing grating for small angular separations (repulsion), but towards the inducing grating for larger angular separations (attraction). Previous research on luminance gratings suggests that repulsion is caused by local inhibition in cortical areas V1 and/or V2, and that the attraction involves global interactions beyond V1, in extrastriate areas. Experiments reported here demonstrate attribute invariant attraction and repulsion effects for gratings specified by luminance, motion, and disparity contrasts. A frame surrounding the inducing grating abolishes only the attraction effect, but a spatial frequency difference, or a small gap between the inducer and test gratings, abolishes only the repulsion effect, irrespective of the attributes that specify the gratings. It is proposed that detectors selectively sensitive to attribute invariant orientation and size exist in early cortical sites such as V1 and/or V2.

Neon colour spreading in three-dimensional illusory objects in humans

We studied whether neon spreading can be induced within three-dimensional illusory triangles. Kanizsa triangles were induced by black pacman disks consisting of red sectors with curved sides. Viewing our stimuli monocularly produced two-dimensional illusory contours and surfaces as well as neon spreading in each figure. Triangles appeared concave or convex under stereoscopical viewing. Neon colour spreading was induced within illusory figures bending in three-dimensional space, suggesting that neural contour completion and surface filling-in interact across depth. Surprisingly, neon spreading was induced above the intervening surface even when the inducers were below the surface. Neon colour and illusory configuration were preserved behind the intervening surface only when it appeared transparent.

Using motor tasks to quantitatively judge 3-D surface curvatures

The primary objective of this study was to quantitatively investigate the human perception of surface curvature by using virtual surfaces and motor tasks along with data analysis methods to estimate surface curvature from drawing movements. Three psychophysical experiments were conducted. In Experiment 1, we looked at subjects' sensitivity to the curvature of a curve lying on a surface and changes in the curvature as defined by Euler's formula, which relates maximum and minimum principal curvatures and their directions. Regardless of direction and surface shape (elliptic and hyperbolic), subjects could report the curvature of a curve lying on a surface through a drawing task. In addition, multiple curves drawn by subjects were used to reconstruct the surface. These reconstructed surfaces could be better accounted for by analysis that treated the drawing data as a set of curvatures rather than as a set of depths. A pointing task was utilized in Experiment 2, and subjects could report principal curvature directions of a surface rather precisely and consistently when the difference between principal curvatures was sufficiently large, but performance was poor for the direction of zero curvature (asymptotic direction) on a hyperbolic surface. In Experiment 3, it was discovered that sensitivity to the sign of curvature was different for perceptual judgments and motor responses, and there was also a difference for that of a curve itself and the same curve embedded in a surface. These findings suggest that humans are sensitive to relative changes in curvature and are able to comprehend quantitative surface curvature for some motor tasks.

Illusory volumes from conformation

The purpose of this paper is to offer demonstrations of 'illusory volumes' in the spirit of the illusory flat surfaces described by Kanizsa. These demonstrations of illusory volumes exploit a new cue to the recovery of surface curvature from ambiguous images: conformation. In assuming conformation, the visual system assumes that the surface of a volume conforms to the curvature of its neighboring, underlying, or supporting surface, in the absence of image cues to the contrary. Demonstrations that exploit the assumption of conformation provide several insights into the nature of the inferential processing that underlies contour, surface, and volume formation. In particular, these demonstrations imply that the visual system does not calculate local surface curvature, illusory contours, or occlusion relationships before it analyzes global surface relationships.

Illusory motion capture and release in rotating 3-D figure in humans

An illusory bar emerges in a cleft between two opposing gratings. When the gratings rotated around the vertical axis in three-dimensional (3-D) space, the illusory bar was seen either (i) rotating with the inducing gratings or (ii) as a stationary and opaque tape located in front of gratings. This illusion seems to be caused by the different temporal dynamics of the illusion and its inducers, especially by the slower extinction rate for the illusory bar than its inducers. The illusion is a psychophysical demonstration of an illusory figure becoming spatially and temporally loose from its inducers, suggesting that they are processed separately in the brain. This indicates that illusory figures are not only by-products of normal vision but have their own important function.

Orientation discrimination and tilt aftereffects with luminance and illusory contours

Orientation discrimination and tilt aftereffects (TAEs) were measured to determine if the orientation of luminance and illusory contours are processed by separate mechanisms. The assumption was made that if a single mechanism supports the perception of both types of contours, then illusory and luminance contours that support the same level of orientation discrimination will be equally effective adapting patterns. Experiment I found that orientation discrimination psychometric functions for illusory and luminance contours are similar, confirming that performance could be matched. Experiment II measured orientation discrimination for a range of intensities for both contours. Experiment III measured TAEs following adaptation to illusory and luminance contours that supported a similar range of orientation discrimination. Similar TAEs were not observed, thus rejecting the single mechanism hypothesis. Experiments IV and V sought to validate the assumption that equivalent orientation discrimination predicts equivalent TAEs by using stimuli that seemed likely to be represented by the same visual mechanism. Luminance contours masked by randomly placed dots and unmasked luminance contours were used with the same procedures as experiments II and III. Equal TAEs were not observed for masked and unmasked contours matched on orientation discrimination, suggesting the assumption relating discriminability to adaptation was incorrect.

Three-dimensionally slanted illusory contours capture stereopsis

In stereo capture a stereogram of a crossed illusory figure pulls a texture bounded by the illusory contours to the same depth plane with the illusory figure. We investigated whether three-dimensionally curved and slanted illusory figures could capture a repeating background texture. According to results, stereoscopic capture was perceived when a disparate illusory contour was slanted provided that the period of the background texture was consistent with the three-dimensional geometry of the illusory surface. We suggest that stereo capture is actually induced by disparate rows of points defined by vertical cut-out sectors and the induced disparity spread is constrained by illusory contours and possible discrete matches of the background texture.

Colour in a larger perspective: the rebirth of Gestalt psychology

This overview takes the reader from the classical contrast and assimilation studies of the past to today's colour research, in a broad sense, with its renewed emphasis on the phenomenological qualities of visual perception. It shows how the shift in paradigm from local to global effects in single-unit recordings prompted a reappraisal of appearance in visual experiments, not just in colour, but in the perception of motion, texture, and depth as well. Gestalt ideas placed in the context of modern concepts are shown to inspire psychophysicists, neurophysiologists, and computational vision scientists alike. Feedforward, horizontal interactions, and feedback are discussed as potential neuronal mechanisms to account for phenomena such as uniform surfaces, filling-in, and grouping arising from processes beyond the classical receptive field. A look forward towards future developments in the field of figure-ground segregation (Gestalt formation) concludes the article.

Stochastic completion fields; a neural model of illusory contour shape and salience

We describe an algorithm- and representation-level theory of illusory contour shape and salience. Unlike previous theories, our model is derived from a single assumption: that the prior probability distribution of boundary completion shape can be modeled by a random walk in a lattice whose points are positions and orientations in the image plane (i.e., the space that one can reasonably assume is represented by neurons of the mammalian visual cortex). Our model does not employ numerical relaxation or other explicit minimization, but instead relies on the fact that the probability that a particle following a random walk will pass through a given position and orientation on a path joining two boundary fragments can be computed directly as the product of two vector-field convolutions. We show that for the random walk we define, the maximum likelihood paths are curves of least energy, that is, on average, random walks follow paths commonly assumed to model the shape of illusory contours. A computer model is demonstrated on numerous illusory contour stimuli from the literature.

Phenomena of illusory form: can we bridge the gap between levels of explanation?

The study of illusory brightness and contour phenomena has become an important tool in modern brain research. Gestalt, cognitive, neural, and computational approaches are reviewed and their explanatory powers are discussed in the light of empirical data. Two well-known phenomena of illusory form are dealt with, the Ehrenstein illusion and the Kanizsa triangle. It is argued that the gap between the different levels of explanation, bottom-up versus top-down, creates scientific barriers which have all too often engendered unnecessary debate about who is right and who is wrong. In this review of the literature we favour an integrative approach to the question of how illusory form is derived from stimulus configuration which provide the visual system with seemingly incomplete information. The processes that can explain the emergence of these phenomena range from local feature detection to global strategies of perceptual organisation. These processes may be similar to those that help us restore partially occluded objects in everyday vision. To understand better the Ehrenstein and Kanizsa illusions, it is proposed that different levels of analysis and explanation are not mutually exclusive, but complementary. Theories of illusory contour and form perception must, therefore, take into account the underlying neurophysiological mechanisms and their possible interactions with cognitive and attentional processes.

Depth release of illusory contour shape in the Ehrenstein grid

In the Ehrenstein grid, bright illusory patches delineated by illusory contours are seen. In order to assess whether the illusory patches possess shape constancy, the Ehrenstein grid was viewed straight on and at various angles of slant with respect to the observer. Observers matched the apparent shape of the illusory patches with a circle or an ellipse defined by real lines in a reference stimulus. Results show that, when viewed at a slanted angle, the shape of the bright patches was deformed and became oval. Such deformation was much less when the illusory contours were replaced by real contours. We label this dissociation of shape perception from depth cues depth release to contrast it with the previously described phenomenon of depth capture in which depth cues displace the illusory patches in depth. As a common explanation for both effects, it is proposed that the illusory contours induced by line ends or line ends themselves provide only weak or ineffective depth signals.

Human stereovision without localized image features

Many theories of human stereovision are based on feature matching and the related correspondence problem. In this paper, we present psychophysical experiments indicating that localized image features such as Laplacian zerocrossings, intensity extrema, or centroids are not necessary for binocular depth perception. Smooth one-dimensional intensity profiles were combined into stereograms with mirror-symmetric half-images such that these localized image features were either absent or did not carry stereo information. In a discrimination task, subjects were asked to distinguish between stereograms differing only by an exchange of these half-images (ortho- vs. pseudoscopic stereograms). In a depth ordering task, subjects had to judge which of the two versions appeared in front. Subjects are able to solve both tasks even in the absence of the mentioned image features. The performance is compared to various possible stereo mechanisms. We conclude that localized image features and the correspondences between them are not necessary to perceive stereoscopic depth. One mechanism accounting for our data is correlation or mean square difference.

Occlusion, transparency, and stereopsis: a new explanation for stereo capture

Stereo capture occurs when a regular pattern of repeating elements with zero disparity is superimposed on a disparate subjective figure. The elements enclosed within the subjective contours, but not those outside them, are perceptually captured and pulled on the same depth plane of the disparate figure. The phenomenon has been interpreted as the result either of a spreading of disparity signals from the subjective figure or of the attribution of the depth of certain salient image features to the finer texture elements enclosed in them. We suggest here that, instead, the fact that stereo capture is limited to the texture elements lying within the boundaries of the subjective figure is simply due to ambiguous occlusion information at the monocular level. When the texture elements occlude the inducers of the subjective figure as well, the elements lying outside the boundaries of the subjective figure are also captured. We propose that stereo capture arises as the solution to a conflict between information provided by retinal disparity and occlusion, and show how this effect is related to other previously observed phenomena of conflicting cues to depth.

Independent encoding of surface orientation and surface curvature

Marr [(1982) Vision, San Francisco, Calif.: Freeman] proposed that we represent surface geometry in terms of a viewer-centred description of surface orientation and distance. This description is computed by a range of independent processing systems which take as input particular kinds of information present in images, like surface texture, shading, retinal disparity and motion parallax. The outputs of these modules are integrated in order to provide a unitary representation of the layout of visible surfaces. Higher order properties of surface geometry, like surface curvature, might be computed from this symbolic representation or might be encoded independently from the visual information available at the retinae. We measured surface slant and surface curvature discrimination thresholds for surface patches defined by shading, texture and retinal disparity as a function of the elevation of the illumination. We found that observers judgements about the curvature of local surface patches were too precise to be based on a symbolic representation of surface orientation and we conclude that surface curvature is computed directly from depth cues present in the retinal images.

Three-dimensional illusory objects produced by rotation in depth

Rotation of a Kanizsa triangle in depth around its vertical axis causes a perception of a three-dimensional object with a flat, rigid illusory triangle between the inducing discs. When the inducing discs of a Kanizsa triangle were made thicker, the illusory triangle between the discs also became thicker. In the experiments both computer animation and real inducers made of plastic were used. The method promoted border perception in a three-dimensional illusory figure. We suggest that the perception of three-dimensional illusory objects is due to a process which is also used in the perception of real three-dimensional objects.

Shape from shading. I: Surface curvature and orientation

The human visual system makes effective use of shading alone in recovering the shape of objects. Pictures of sculptures are readily interpreted--a situation where shading provides virtually the sole cue to shape. However, shading has been considered a poor cue to depth in comparison with retinal disparity and kinetic cues. Curvature discrimination thresholds were measured with the use of a surface-alignment task for a range of surface curvatures from 0.16 cm-1 to 1.06 cm-1. Weber fractions were around 0.1, demonstrating considerable precision in this task. Weber fractions did not vary substantially as a function of surface curvature. Rotation of the light source around the line of sight had no effect on curvature discrimination but rotation towards the viewer increased discrimination thresholds. In contrast, slant discrimination declined with rotation of the light-source vector towards the viewpoint. When a band-limited random grey-level texture was mapped onto the sphere, curvature discrimination thresholds increased gradually as a function of texture contrast, even though texture and shading provided consistent cues to depth. Adding texture also increased slant discrimination thresholds, demonstrating that texture can act as a source of noise in shape-from-shading tasks. The psychophysical findings have been used to evaluate whether current algorithms for shape from shading in computer vision could serve as models of human three-dimensional shape analysis and to highlight low-level intramodular interactions between depth cues. It is demonstrated that, in the case of surfaces defined by shading, curvature descriptions are primary and do not depend upon the prior encoding of surface orientation, and Koenderink's local-shape index is suggested as an alternative intermediate representation of surface shape in the human visual system.

The neural representation of stereoscopic depth contrast

Stereoscopic vision provides examples of contrast phenomena broadly analogous to those seen with brightness. Several authors have suggested that lateral inhibition between disparity-tuned neurons might underlie these phenomena. This type of lateral inhibition would differ from the more familiar kind which occurs with retinal ganglion cells, where an inhibitory surround has essentially a linear subtractive effect. Lateral inhibition by disparity-tuned units would introduce the nonlinearity of the tuning curve. I argue here that the evidence nonetheless suggests that a linear subtractive mechanism operates in the stereo realm--in fact, that there is a stereo equivalent of the classical centre-surround. This seems at first sight implausible, partly because of the occurrence of the nonlinearity mentioned above, but also because disparity is only provided at certain locations in the retinal field, namely those where appropriate features are matched. I show that both objections can be easily overcome, the first because Laplacian-like centre-surrounds can be constructed from disparity-tuned cells, the second because interpolation can fill in between features, and can provide precisely the quantitative dependence upon disparities of neighbouring features which matches the experimental data.