Influence of surface attitude and curvature scaling on discrimination of binocularly presented curved surfaces

Local Solid Shape

Local solid shape applies to the surface curvature of small surface patches—essentially regions of approximately constant curvatures—of volumetric objects that are smooth volumetric regions in Euclidean 3-space. This should be distinguished from local shape in pictorial space. The difference is categorical. Although local solid shape has naturally been explored in haptics, results in vision are not forthcoming. We describe a simple experiment in which observers judge shape quality and magnitude of cinematographic presentations. Without prior training, observers readily use continuous shape index and Casorati curvature scales with reasonable resolution.

The neuroscience of vision-based grasping: a functional review for computational modeling and bio-inspired robotics

The topic of vision-based grasping is being widely studied in humans and in other primates using various techniques and with different goals. The fundamental related findings are reviewed in this paper, with the aim of providing researchers from different fields, including intelligent robotics and neural computation, a comprehensive but accessible view on the subject. A detailed description of the principal sensorimotor processes and the brain areas involved is provided following a functional perspective, in order to make this survey especially useful for computational modeling and bio-inspired robotic applications.

Toward an understanding of the neural processing for 3D shape perception

In this article we address the major issue of space vision, how the brain represents the 3D shape of objects in the real world, on the basis of psychophysics and neurophysiology. In psychophysics, Gibson found texture gradients and width gradients, as well as the gradient of binocular disparity, as the major cues for surface orientation in depth. Marr proposed that a surface-based representation is the main step towards 3D shape representation. In our neurophysiological studies of the monkey parietal cortex, we have found visual-dominant neurons in area AIP with selectivity in 3D shape of the objects, and also surface-orientation-selective (SOS) neurons in the caudal intraparietal (CIP) area. SOS neurons responded selectively to surface orientation in depth presented in random dot stereograms with a disparity gradient. Many of the SOS neurons responded selectively also to texture gradients and linear perspective, and their responses were enhanced by the combination of these cues. We also found axis-orientation-selective (AOS) neurons in area CIP, responding selectively to the orientation of the longitudinal axis of elongated objects in depth. We present preliminary data here to demonstrate that some of AOS neurons that prefer intermediate thickness are shape-selective, and they are likely to discriminate surface curvature. These data suggest that neurons in and around area CIP may have the capacity to represent 3D shape.

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.

The perception of surface curvature from optical motion

Observers viewed the optical flow field of a rotating quadric surface patch and were required to match its perceived structure by adjusting the shape of a stereoscopically presented surface. In Experiment 1, the flow fields included rigid object rotations and constant flow fields with patterns of image acceleration that had no possible rigid interpretation. In performing their matches, observers had independent control of two parameters that determined the surface shape. One of these, called the shape characteristic, is defined as the ratio of the two principle curvatures and is independent of object size. The other, called curvedness, is defined as the sum of the squared principle curvatures and depends on the size of the object. Adjustments of shape characteristic were almost perfectly accurate for both motion conditions. Adjustments of curvedness, on the other hand, were systematically over-estimated and were not highly correlated with the simulated curvedness of the depicted surface patch. In Experiment 2, the same flow fields were masked with a global pattern of curl, divergence, or shear, which disrupted the first-order spatial derivatives of the image velocity field, while leaving the second-order spatial derivatives invariant. The addition of these masks had only negligible effects on observers' performance. These findings suggest that observers' judgments of three-dimensional surface shape from motion are primarily determined by the second-order spatial derivatives of the instantaneous field of image displacements.

Definition and detection of binocular disparity

Stereoacuity experiments tested definitions of binocularly disparate spatial positions by perturbing the binocular correspondence of the two half-images. Dichoptic translations perturbed zero-order retinal positions; expansions perturbed first-order horizontal separations; rotations perturbed first-order orientations; and anisotropic expansions deformed first-order two-dimensional (2D) structure. Each transformation perturbed relative positions in the two half-images by more than 100 arcsec, but stereoacuity thresholds remained about 10 arcsec. Binocular disparity involves second-order 2D differential structure of the monocular half-images, specifying local surface shape. Stereoacuity is much better than nonstereo acuity, suggesting that monocular spatial signals are binocularly correlated.

Monocular dot-density cues in random-dot stereograms

In the original random-dot stereograms (RDSs) invented by Julesz, binocular disparity could only take on values that were integral multiples of dot width. The other common method for constructing RDSs (the projection method) relaxes this restriction. However, the projection method can introduce dot-density cues into the monocular images. When polar projection is employed, density variation is introduced as an expression of perspective cues; when parallel projection is employed, there are no perspective cues, but density variation is nonetheless introduced whenever disparity varies as a function of horizontal position. de Vries, Kappers, and Koenderink [(1994) Vision Research, 34, 2409-2423] proposed to minimize the density cues by selecting half of the random dots from a uniform random distribution in the right-eye image, projecting them onto the cyclopean surface, and then projecting them back to the left eye image and vice versa. In this paper the precise nature of the density cues introduced by the projection method, and by de Vries et al.'s modification of that method, are derived. It is also shown that the projection method and its modification have very similar density cues near the medial sagittal plane when polar projection is employed, and that they have identical density cues over the entire random-dot field when parallel projection is employed.

Cross-modal slant and curvature matching of stereo- and motion-induced surfaces

In many laboratory setups and in many day-to-day situations, a unique solution of the structure-from-two-views problem is unobtainable. Yet, when the visual system is presented with two projections in a sequence, it nevertheless appears to generate a reasonably stable percept of structure. In the research reported here, we examined whether the same surface would be perceived when subjects were presented with a pair of views that alternated in time monocularly (two-frame motion) or were shown simultaneously to both eyes (stereo). In Experiment 1, we studied slant perception: human observers were asked to match the slant of a motion-induced planar surface with its stereo-induced counterpart. In Experiment 2, the perceived curvature of parabolic surfaces was matched in a similar way. The results show that motion-induced slant is matched with a higher value of the stereo-induced slant. However, the curvature experiment showed that motion-induced curvature is matched with a lower stereo-induced curvature. One possible explanation may be that the slant and curvature are internally inconsistent in at least one of the modalities.