The contributions of slant and tilt to the detection of local surface orientation in structure from motion

The contribution of slant and tilt to the detection of differences in local surface orientation was examined for structure-from-motion (SFM) displays of a complex sinusoidal surface. Observers judged whether an elliptical SFM gauge figure appeared to be lying on the surface or intersecting it. The gauge figure orientation either matched the local surface orientation or differed from it in slant, tilt, or both. Similar sensitivity was found for deviations in slant and tilt, but greater biases and variability were found when the gauge figure deviated from the local surface orientation in slant, depending on the sign of the difference between the gauge figure and local surface orientation and the position of the gauge figure. The results are consistent with Stevens' (Biological Cybernetics, 46 (1983) 183-195) discussion of the computational advantages of slant and tilt contributing independently to the detection of differences in local surface orientation. The effects of changes in perceived surface slant and tilt during rotation and of the misperception of surface depth on the detection of local orientation in dynamic images are discussed.     

Modeling V1 neuronal responses to orientation disparity

The contribution of interocular orientation differences to depth perception, at either the neuronal or the psychophysical level, is unclear. To understand the responses of binocular neurons to orientation disparity, we extended the energy model of Ohzawa et al. (1990) to incorporate binocular differences in receptive-field orientation. The responses of the model to grating stimuli with interocular orientation differences were examined, along with the responses to random dot stereograms (RDS) depicting slanted surfaces. The responses to combinations of stimulus orientations in the two eyes were left-right separable, which means there was no consistent response to the binocular orientation difference. All existing neuronal data concerning orientation disparity can be well described by this type of model (even a version with no disparity selectivity). The disparity sensitive model is nonetheless sensitive to changes in RDS slant, although it requires narrow orientation bandwidth to produce substantial modulation. The disparity-insensitive model shows no selectivity to slant in this stimulus. Several modifications to the model were attempted to improve its selectivity for orientation disparity and/or slant. A model built by summing several disparity-sensitive models showed left-right inseparable responses, responding maximally to a consistent orientation difference. Despite this property, the selectivity for slant in RDS stimuli was no better than the simple disparity-selective model. The range of models evaluated here demonstrate that interocular orientation differences are neither necessary nor sufficient for signaling slant. In contrast, within the framework of the energy model, positional disparity sensitivity appears to be both necessary and sufficient.     

Common mechanisms for 2D tilt and 3D slant after-effects

By presenting oriented Gabor patches either monocularly or binocularly, we dissociated retinal orientation from perceived tilt and perceived slant. After adapting to binocular patches, with zero apparent tilt and non-zero slant, small tilt after-effects (TAEs) and large slant after-effects (SAE) were measured. Adapting to monocular patches with non-zero tilt and zero slant produced large TAEs and smaller SAEs. This pattern of results suggests that a common, low-level adaptation to monocular orientation is involved in slant and tilt after-effects. However, the incomplete transfer between slant and tilt makes it clear that higher-level adaptation is also involved, perhaps at the level of surface representation.     

Visual discrimination of local surface structure: slant, tilt, and curvedness

In four experiments, observers were required to discriminate interval or ordinal differences in slant, tilt, or curvedness between designated probe points on randomly shaped curved surfaces defined by shading, texture, and binocular disparity. The results reveal that discrimination thresholds for judgments of slant or tilt typically range between 4 degrees and 10 degrees; that judgments of one component are unaffected by simultaneous variations in the other; and that the individual thresholds for either the slant or tilt components of orientation are approximately equal to those obtained for judgments of the total orientation difference between two probed regions. Performance was much worse, however, for judgments of curvedness, and these judgments were significantly impaired when there were simultaneous variations in the shape index parameter of curvature.     

Tilt dependency of slant aftereffect

Slant aftereffect (SAE), the negative aftereffect of slant induced after prolonged observation of a surface, is considered as evidence that slant is encoded in the visual system. Because slant and tilt are mathematically independent dimensions, Stevens (Stevens, K. A. (1983a). Biological Cybernetics, 46, 183-195) assumed that slant and tilt are processed independently in the visual system. To confirm this assumption, we investigated whether SAE is induced independently of the difference in tilt between the adapting and test stimuli. The stimuli were displayed by simulating the motion disparity of rotating disks. After adaptation to a surface of 60 degrees slant, the subjective 0 degree slants of the test stimulus were measured with the tilt differences of 0, 45, 90, 135 and 180 degrees. The magnitude of SAE was greatest when the tilt difference was zero, and decreased with increasing tilt difference. The results suggest that slant and tilt are not processed independently in the visual system and that the slant detector in the visual system is sensitive not only to slant but also to tilt.     

Perception of 3D surface orientation from skew symmetry.

In this paper, we investigate how symmetry can be used to perceive 3D surface orientation. When a symmetric planar object is viewed from an angle, the projected contour has skew symmetry, which provides partial information about the 3D orientation of the object. For a given skew symmetry, this information can be characterized by a constraint curve of possible slant/tilt combinations that are consistent with a mirror-symmetric interpretation. These constraint curves move around when an object is rotated within a plane, and depend on what we will term the spin of the object: the angle between its axis of symmetry and the direction of tilt. To test the influence of symmetry constraint curves, we presented subjects with stereo images of symmetric objects that varied in spin, and had them perform an orientation-matching task. We found that the judgments showed biases that depended on the spin of the objects. Since other sources of information depend only on slant and tilt, not on spin, the biases imply that skew symmetry contributed to subjects' judgments. In a second experiment, we introduced conflicts between stereo and symmetry cues, and found that the spin-dependent biases can be modulated by selectively changing stereo slant. We propose an explanation of these results involving the optimal integration of stereo and skew symmetry, and present a Bayesian model that can account for the pattern of biases.     

Perception of surface slant from oriented textures

When a surface covered with a regular texture is viewed in perspective, the projected texture provides a number of cues to 3D surface orientation. For oriented textures, one cue is perspective convergence: symmetry lines that are parallel along the surface project to lines that vary systematically in orientation. We investigated the contribution of perspective convergence to perception of 3D slant and tested whether slant from convergence depends on oriented spectral components. Subjects judged the sign of slant about a vertical axis of rotation. Textures were composed of filled circles in three spatial arrangements: a hex grid with symmetry lines at 0 and +/-60 deg relative to the tilt direction (aligned condition), a hex grid with symmetry lines at 90 and +/-30 deg (perpendicular condition), and random arrangements with similar average spacing (isotropic condition). The two hex grid textures differed in the amount of spectral energy present in the tilt direction (horizontal) but were otherwise closely matched. Slant discrimination thresholds for monocular stimuli were higher for isotropic textures than for either of the two hex grid textures and were higher for the perpendicular texture than for the aligned texture. In a second experiment, we measured the weight given to texture relative to binocular slant information for cue conflict stimuli (+/-5 deg). Weights were found to agree with individual subjects' monocular thresholds, in accordance with optimal estimation theory. We conclude that the visual system uses perspective convergence to perceive slant and that effective use of convergence requires the presence of spectral components aligned with the tilt direction.     

The effect of perceived surface orientation on perceived surface albedo in binocularly viewed scenes

We examined how observers discount perceived surface orientation in estimating perceived albedo (lightness). Observers viewed complex rendered scenes binocularly. The orientation of a test patch was defined by depth cues of binocular disparity and linear perspective. On each trial, observers first estimated the orientation of the test patch in the scene by means of a gradient probe and then matched its perceived albedo to a reference scale. We found that observers' perception of orientation was nearly veridical and that they substantially discounted perceived orientation in estimating perceived albedo.     

Simultaneous orientation contrast for lines in the human fovea

When it is surrounded by lines of a differing orientation, a test line changes its apparent orientation in a direction away from that of the surround lines. Using a nulling technique to arrive at numerical values, the properties of this simultaneous orientation contrast have been analyzed: it diminishes with distance of the surround lines; rises and then falls off as a function of surround line orientation; decreases with exposure duration; is sharply tuned (+/- 100 msec) for synchrony of test and surround line presentation; is robust to differences between test and surround line disparity but not intensity; and is reduced with dichoptic presentation of test and surround lines. Orientation contrast can be induced in a variety of oriented features, including illusory contours, an ellipse, a moving dot and a row of dots or lines, but two dots alone don't suffice. The results are taken as evidence that orientation is a domain sui generis, in which simultaneous contrast is exhibited in the same manner as in the domains of color, brightness and disparity.     

Plasticity of orientation specific chromatic aftereffects

Changes in the orientation of McCollough effects were explored with and without prolonged exposure to prismatic tilt and subsequent viewing of chromatic inducing stimuli. Prolonged exposure to prism adaptation generates a reduction in the optically induced tilt and thus a disparity between the perceived and the retinal orientation of the chromatic inducing stimuli. Saturated chromatic aftereffects, following prism adaptation and subsequent induction of the McCollough effect, were obtained when the orientation of the achromatic test gratings matched the perceived, rather than the retinal, orientation of the inducing chromatic gratings.