Gerald H. Silverman

Stereoscopic Depth: Its Relation to Image Segmentation, Grouping, and the Recognition of Occluded Objects

Image regions corresponding to partially hidden objects are enclosed by two types of bounding contour: those inherent to the object itself (intrinsic) and those defined by occlusion (extrinsic). Intrinsic contours provide useful information regarding object shape, whereas extrinsic contours vary arbitrarily depending on accidental spatial relationships in scenes. Because extrinsic contours can only degrade the process of surface description and object recognition, it is argued that they must be removed prior to a stage of template matching. This implies that the two types of contour must be distinguished relatively early in visual processing and we hypothesize that the encoding of depth is critical for this task. The common border is attached to and regarded as intrinsic to the closer region, and detached from and regarded as extrinsic to the farther region. We also suggest that intrinsic borders aid in the segmentation of image regions and thus prevent grouping, whereas extrinsic borders provide a linkage to other extrinsic borders and facilitate grouping. Support for these views is found in a series of demonstrations, and also in an experiment where the expected superiority of recognition was found when partially sampled faces were seen in a back rather than a front stereoscopic depth plane.

Precise velocity discrimination despite random variations in temporal frequency and contrast.

Velocity discrimination is not affected by random changes in contrast or temporal frequency. Observers judged the relative velocity of a moving sinusoidal grating when target contrast was varied randomly from trial-to-trial over the range from 5 to 82%. The Weber fraction for the random mixture of interspersed contrast levels was about 0.06, comparable to velocity discrimination for targets presented at a fixed contrast. In a parallel experiment, the spatial frequency of the target was changed randomly from trial-to-trial, a procedure which produced concomitant random changes in the nominal temporal frequency. These variations had little effect on the velocity increment threshold; random changes in temporal frequency ranging from 2.25 to 8.25 Hz increased the Weber fraction from 0.05 to 0.07. Under identical experimental conditions, velocity discrimination was generally more precise than the discrimination of differences in temporal frequency, particularly when temporal frequency thresholds were measured with counterphase gratings. Our results indicate that velocity discrimination depends on velocity.

Detection and discrimination of sinusoidal grating displacements

Vertical sine-wave gratings of varying spatial frequency were stepped instantaneously to the right or to the left at differing phase angles (theta). Separate paradigms measured the contrast threshold for the detection of such a step and for the discrimination of the direction of the same step. By considering the grating before and after its displacement as a rotating phasor, we made the following predictions: (1) Contrast sensitivity for the detection of a displacement should rise as sin(theta). (2) Contrast sensitivity for the discrimination of the direction of the displacement should rise as sin(theta/2). Both predictions were confirmed using a range of spatial frequencies and phase angles. From the results of additional experiments, by measuring the discrimination of the direction thresholds as a function of contrast, we derived a nonlinear contrast response function for the motion system. This function appears to saturate fully at fairly low levels, in the neighborhood of 2 to 3% under the conditions examined. Our results suggest a direct connection among the contrast sensitivity, the contrast response function, and motion-hyperacuity thresholds.

Temporal and spatial characteristics of the upper displacement limit for motion in random dots

The upper displacement limit (Dmax) or Braddick limit was measured in random dots. We then interposed a variable duration pause at half the distance jumped. Of interest was to see the shortest time (delta t) which would yield a value of two times Dmax, thus indicating the time required to process one additional Braddick limit. A surprisingly short interval (as short as 10 msec under some conditions) was required. Furthermore for intermediate durations (20 to over 100 msec), the total limit was often more than doubled, indicating a nonlinear potentiation or sequential recruitment between successive displacements. Increasing field size had the following effects: (1) it increased Dmax, (2) it decreased delta t (the processing time), (3) it increased Vmax (the maximum velocity), (4) it increased the amount of sequential recruitment.

The aperture problem—I. Perception of nonrigidity and motion direction in translating sinusoidal lines

To examine how local velocities from different regions of the visual field combine to form a coherent motion percept, we subjected a sinusoidal line stimulus to translational motion. Horizontal movement of a sinewave line along its axial direction is perceived as nonrigid if the angle at the zero crossing is smaller than a critical angle of about 15 deg. This angle is independent of spatial scale and the number of sinusoidal cycles. To extend the applicability of this concept of angle, we developed a mathematical model to predict an observers sensitivity to small changes in motion direction based on two assumptions: (1) the computed velocity signal is obtained from the intersection of constraint lines defined by local velocity components, (2) local velocity components are contaminated by noise. Measurement of directional discrimination thresholds of moving targets confirmed our expectations. Thresholds varied as a function of the angle of the local contour independent of spatial scale and in quantitative accord with our assumptions.

Sensitivity to shearing and compressive motion in random dots

The sensitivity of the visual system to motion of differentially moving random dots was measured. Two kinds of one-dimensional motion were compared: standing-wave patterns where dot movement amplitude varied as a sinusoidal function of position along the axis of dot movement (longitudinal or compressional waves) and patterns of motion where dot movement amplitude varied as a sinusoidal function orthogonal to the axis of motion (transverse or shearing waves). Spatial frequency, temporal frequency, and orientation of the motion were varied. The major finding was a much larger threshold rise for shear than for compression when motion spatial frequency increased beyond 1 cycle deg−1. Control experiments ruled out the extraneous cues of local luminance or local dot density. No conspicuous low spatial-frequency rise in thresholds for any type of differential motion was seen at the lowest spatial frequencies tested, and no difference was seen between horizontal and vertical motion. The results suggest that at the motion threshold spatial integration is greatest in a direction orthogonal to the direction of motion, a view consistent with elongated receptive fields most sensitive to motion orthogonal to their major axis.

Binocular summation in detection of contrast flashes

We studied monocular and binocular detection of foveal flashes of different contrast. When background contours were binocularly fused, detectability (d’) of binocular test flashes was, on the average, twice the detectability of monocularly presented flashes. The precise amount of binocular advantage varied with test contrast: binocular improvement exceeded full summation for low test contrast, but fell below full summation at higher test contrasts. In the absence of contours in one eye, background luminances are not expected to sum, yet binocular detection is an average of 41.5% better than monocular detection. This indicates a difference in the functional organization of the fused binocular channel and a monocular channel.

Binocular Summation on Fused Annular Backgrounds

A paradigm has been proposed to test the hypothesis that binocular fusion results in simple summation, S, of monocular photopic luminances: S = ΔLBM(L)/ΔLB(2L) = 1, where ΔLBM and ΔLB are threshold luminances for a monocular and a binocular increment, appearing on a fused background of luminance L or 2L, respectively. This prediction was tested psychophysically, with background size as parameter. Thresholds were measured for a brief (20 ms) foveal flash centered on a luminous disk encircled by a massive black annulus serving as a fusion lock. The flash was presented binocularly, or monocularly, at 30 and 60 cd m−2 background luminances. The diameter of the disk was varied from 3 min to 40 min visual angle. The size of the flash was constant (6 min diameter), except for the smallest disk (3 min diameter). All thresholds varied as a function of background size (the known ‘sensitization effect’). The summation index S did not vary with background size. A mean value S = 0.9 was found; this is consistent with the notion that summation of the order of 90% occurs during binocular fusion. We surmise that even a weak monocular test flash makes fusion less than perfect.

Fluctuations of visibility during dichoptic viewing: Preliminary report.

Abstract Detection rates were determined for multiple flashes (20‐msec duration, 7.5 arc min dia) presented foveally to one eye while the other eye had either a uniform target (the “monocular” condition), a congruent grating (fusion), or an orthogonal grating (rivalry). Average detection rates were highest in the monocular condition, and they were about the same in fusion and rivalry. In all conditions, the typical error (some 70% of all errors) was one stimulus missed out of several simultaneously presented. It was concluded that sensitivity fluctuates over the fovea, even in the absence of contours in the other eye. In two observers, the ratio of detection rates for the two eyes was about the same for all conditions; in two other observers, this ratio decreased (eye dominance increased) in fusion, and especially in rivalry, relative to the monocular condition. The question is raised whether a common link exists between spontaneous fluctuations of sensitivity and those induced by dichoptic contours.