Rotating columns: relating structure-from-motion, accretion/deletion, and figure/ground

Interaction of contour geometry and optic flow in determining relative depth of surfaces

Dynamic occlusion, such as the accretion and deletion of texture near a boundary, is a major factor in determining relative depth of surfaces. However, the shape of the contour bounding the dynamic texture can significantly influence what kind of 3D shape, and what relative depth, are conveyed by the optic flow. This can lead to percepts that are inconsistent with traditional accounts of shape and depth from motion, where accreting/deleting texture can indicate the figural region, and/or 3D rotation can be perceived despite the constant speed of the optic flow. This suggests that the speed profile of the dynamic texture and the shape of its bounding contours combine to determine relative depth in a way that is not explained by existing models. Here, we investigated how traditional structure-from-motion principles and contour geometry interact to determine the relative-depth interpretation of dynamic textures. We manipulated the consistency of the dynamic texture with rotational or translational motion by varying the speed profile of the texture. In Experiment 1, we used a multi-region figure-ground display consisting of regions with dots moving horizontally in opposite directions in adjacent regions. In Experiment 2, we used stimuli including two regions separated by a common border, with dot textures moving horizontally in opposite directions. Both contour geometry (convexity) and the speed profile of the dynamic dot texture influenced relative-depth judgments, but contour geometry was the stronger factor. The results underscore the importance of contour geometry, which most current models disregard, in determining depth from motion.

The interpretation of dynamic occlusion: Combining contour geometry and accretion/deletion of texture

Conventional accounts of motion perception mostly treat accretion/deletion-the appearance or disappearance of texture at a boundary between regions-as an essentially decisive cue to relative depth: the accreting/deleting surface is interpreted as being behind adjacent surfaces. Under certain circumstances, however, accretion/deletion can be perceived in a radically different way: the accreting or deleting surface is seen as rotating in depth in front of adjacent surfaces. This alternative interpretation suggests a problem in conventional accounts of motion interpretation that cannot account for this phenomenon, in part because they ignore the role of contour geometry. In two experiments, we examined the combined role of contour convexity and accretion/deletion in determining the perception of relative depth by parametrically manipulating the strength of each cue. Our results show that convexity plays a more substantial role, often dominating the 3D percept, even in cases when the saliency of the convexity cue is substantially weakened on a contour where the texture was accreting/deleting at high rates. These results highlight the need for a rethinking of theories of perceptual organization in the critical case of moving stimuli.

When Is Accreting/Deleting Texture Seen as In Front? Interpretation of Depth From Texture Motion

Standard accounts of accretion/deletion of texture treat it as a definite cue to depth ordering: The accreting/deleting surface is interpreted as being behind the adjoining surface. Froyen, Feldman, and Singh showed that accretion/deletion can also, under certain circumstances, be perceived as a 3D column rotating in front, with the accretion/deletion explained by self-occlusion. These displays differ from traditional accretion/deletion displays in a number of factors, including the presence of figure/ground cues, accretion/deletion on both sides of boundaries, and in the number of distinct regions. In a series of experiments, we systematically manipulated each of these factors in order to determine what factors are actually instrumental in creating the rotating column (accretion/deletion in front) interpretation. In Experiment 1, the width of each region was kept fixed while manipulating the number of regions, and in Experiment 2, the width of the overall display was kept fixed. Observers indicated which set of regions they perceived to be in front. In both experiments, accreting/deleting regions were most likely to be seen in front when geometric figural cues favored a figural interpretation and when textural motion was introduced in all regions (rather than on just one side of each boundary). The number of regions had a relatively small effect (although this effect was larger in Experiment 2). These findings indicate that the geometry of the occluding contour is a critical factor in the interpretation of accretion/deleting, and future models of 3D interpretation involving accretion/deletion must include contour geometry as a key component.

Geometric figure-ground cues override standard depth from accretion-deletion

Accretion-deletion is widely considered a decisive cue to surface depth ordering, with the accreting or deleting surface interpreted as behind an adjoining surface. However, Froyen, Feldman, and Singh (2013) have shown that when accretion-deletion occurs on both sides of a contour, accreting-deleting regions can also be perceived as in front and as self-occluding due to rotation in three dimensions. In this study we ask whether geometric figure–ground cues can override the traditional “depth from accretion-deletion” interpretation even when accretion-deletion takes place only on one side of a contour. We used two tasks: a relative-depth task (front/back), and a motion-classification task (translation/rotation). We conducted two experiments, in which texture in only one set of alternating regions was moving; the other set was static. Contrary to the traditional interpretation of accretion-deletion, the moving convex and symmetric regions were perceived as figural and rotating in three dimensions in roughly half of the trials. In the second experiment, giving different motion directions to the moving regions (thereby weakening motion-based grouping) further weakened the traditional accretion-deletion interpretation. Our results show that the standard “depth from accretion-deletion” interpretation is overridden by static geometric cues to figure–ground. Overall, the results demonstrate a rich interaction between accretion-deletion, figure–ground, and structure from motion that is not captured by existing models of depth from motion.

Perceptual representation and effectiveness of local figure-ground cues in natural contours

A contour shape strongly influences the perceptual segregation of a figure from the ground. We investigated the contribution of local contour shape to figure–ground segregation. Although previous studies have reported local contour features that evoke figure–ground perception, they were often image features and not necessarily perceptual features. First, we examined whether contour features, specifically, convexity, closure, and symmetry, underlie the perceptual representation of natural contour shapes. We performed similarity tests between local contours, and examined the contribution of the contour features to the perceptual similarities between the contours. The local contours were sampled from natural contours so that their distribution was uniform in the space composed of the three contour features. This sampling ensured the equal appearance frequency of the factors and a wide variety of contour shapes including those comprised of contradictory factors that induce figure in the opposite directions. This sampling from natural contours is advantageous in order to randomly pickup a variety of contours that satisfy a wide range of cue combinations. Multidimensional scaling analyses showed that the combinations of convexity, closure, and symmetry contribute to perceptual similarity, thus they are perceptual quantities. Second, we examined whether the three features contribute to local figure–ground perception. We performed psychophysical experiments to judge the direction of the figure along the local contours, and examined the contribution of the features to the figure–ground judgment. Multiple linear regression analyses showed that closure was a significant factor, but that convexity and symmetry were not. These results indicate that closure is dominant in the local figure–ground perception with natural contours when the other cues coexist with equal probability including contradictory cases.

A neural model of border-ownership from kinetic occlusion

Camouflaged animals that have very similar textures to their surroundings are difficult to detect when stationary. However, when an animal moves, humans readily see a figure at a different depth than the background. How do humans perceive a figure breaking camouflage, even though the texture of the figure and its background may be statistically identical in luminance? We present a model that demonstrates how the primate visual system performs figure-ground segregation in extreme cases of breaking camouflage based on motion alone. Border-ownership signals develop as an emergent property in model V2 units whose receptive fields are nearby kinetically defined borders that separate the figure and background. Model simulations support border-ownership as a general mechanism by which the visual system performs figure-ground segregation, despite whether figure-ground boundaries are defined by luminance or motion contrast. The gradient of motion- and luminance-related border-ownership signals explains the perceived depth ordering of the foreground and background surfaces. Our model predicts that V2 neurons, which are sensitive to kinetic edges, are selective to border-ownership (magnocellular B cells). A distinct population of model V2 neurons is selective to border-ownership in figures defined by luminance contrast (parvocellular B cells). B cells in model V2 receive feedback from neurons in V4 and MT with larger receptive fields to bias border-ownership signals toward the figure. We predict that neurons in V4 and MT sensitive to kinetically defined figures play a crucial role in determining whether the foreground surface accretes, deletes, or produces a shearing motion with respect to the background.

Rotating Goblet and Talking Profiles: Does a Rotating Goblet Increase the Figural Dominance of Profiles in Rubin's Type of Figure-Ground Reversal Patterns?

We present a novel three-dimensional (3-D) version of Rubin's classical bistable goblet–profiles figure. An actual goblet sculpture was produced and rotated on a turntable in front of a white background. As the goblet rotates about its central axis, small circular asymmetries around the lips and chin region give a clear impression of two white profiles talking to each other. Although the profiles actually correspond to empty space or white background, they are more likely to be perceived as ‘figure’ than the 3-D goblet itself. Four experiments that presented the actual goblet (experiment 1) or two-dimensional (2-D) movies of it (experiments 2–4) were designed to verify these observations. We measured perceptual dominance of profiles as ‘figure’ and rate of reversal as a function of three factors: Motion (static vs rotating), orientation (upright vs inverted), and configuration (face-to-face vs back-to-back). Results for the rotating goblet showed a statistically reliable preference for perceiving the talking profiles as ‘figure’. Deforming the profiles by manipulating the vertex angle of the mouth region produced an inverted U-shaped curve with the peak representing the stimulus condition in which the profiles perception was most remarkable. We discussed a number of 3-D and 2-D figure-ground factors that might apply to this rather complex stimulus situation.