Underestimation of curvature and task dependence in visual perception of form

Perceived curvatures of circular arcs were compared with those of circles. The length and orientation of the arcs varied. In all cases the curvatures of the arcs were underestimated, and the error was a decreasing exponential function of arc length. The results are consistent with the notion that tendency (efferent readiness) to perform rectilinear eye movements produces underestimation of curvature. The results discredited the explanation of the “Gibson normalization effect” as an instance of increase in perceptual accuracy. The overestimation of curvature found in earlier studies was interpreted as resulting from an inappropriate perceptual task and uncontrolled effects of illusions of extent.     

Masking,aftereffect, and illusion in visual perception of curvature

Masking, aftereffect, and illusion paradigms were used to establish the spatial selectivity of curvature detectors in human vision. Arcs with the same chord orientation mask each other maximally when they are identical in radius and direction of curvature. There is gradual reduction in masking over an extensive spatial range as arcs diverge in curvature. The transition from convexity to concavity does not produce discontinuity in the masking function. The extent to which a straight line appears curved also depends on the curvature of arcs shown previously (aftereffect) or at the same time (illusion). It is suggested that these effects could occur through selective adaptation of detectors responsive to either global curvature or the orientation of local straight-line approximations within an arc. Evidence is reviewed in support of the latter interpretation.     

Motion in depth: adequate and inadequate simulation

We measured errors in estimating the absolute time to collision with a simulated approaching textured object. The texture elements were circular bright dots. When we matched the rate of angular expansion of the simulated object, the rate of expansion of the texture dots, and the rate of increase of dot separation, so as to accurately simulate an approaching object, errors were small underestimations that were independent of dot size (mean of 3.2%). When dot angular size was held constant during the simulated approach, errors were the same as when the simulation was accurate, provided that dot size was less than 2.2-4.4 min of arc. As dot size was progressively increased, errors changed to overestimations. For the largest dot size used (10.5 min of arc at time t = 0), time to collision was overestimated by up to 21%. A sufficiently large overestimation would mean that measures taken to avoid collision would be too late. We suggest that the relevance to everyday life of data on the perception of motion in depth and self-motion collected using constant-sized dot displays might be questionable if dot size exceeds 2.2-4.4 min of arc.     

Curvature biases in stereoscopic vision: a nasotemporal asymmetry

The reliability of curvature judgments for linear elements was studied, with stereograms that contained a binocular arc with curvature in depth, and either a binocular frontoparallel arc or a monocular one, on a background representing a hemiellipsoid. The subjects made about 15% errors on binocular arcs with curvature in depth, and 60%-80% of these occurred when both the hemiellipsoid and the arc were convex, the arc being perceived as concave, by transparency through the hemiellipsoid. There were also about 15%-30% errors on frontoparallel arcs, but spread among all situations, with a small prevalence of concave judgments. Curvature in depth was assigned to the monocular stimuli in more than 60% of the cases. There was a curvature bias when the monocular arcs were on the nasal side, and were viewed against a concave background. Assuming parallel viewing, nasal ingoing arcs were usually perceived as concave, and nasal outgoing arcs usually perceived as convex, in agreement with geometrical likelihood. Nasal-side elements captured by one eye are, in general, those with the highest likelihood of having matching elements in the other eye. Then the observed nasal bias effect suggests that the matching process in stereopsis could be driven from the nasal sides of the projections in the two cerebral hemispheres.     

The bisection of a spatial interval by the pigeon

Pigeons pecked two response keys to move a white dot until it was equidistant from two other dots on a screen. Continuous records of dot position showed the effects of reinforcement and stimulus parameters upon the accuracy with which the dot was positioned. The method may prove useful for studying the perception of distance in non-human organisms.     

Memory for locations within regions: Spatial biases and visual hemifield differences

Memory for location of a dot inside a circle was investigated with the circle in the center of a computer screen (Experiment 1) or with the circle presented in either the left or the right visual field (Experiment 2). In both experiments, as in Huttenlocher, Hedges, and Duncan’s (1991) study, the task was to relocate the dot by marking the remembered location. When errors in angular and radial estimates were considered separately, it was found that, in both experiments, the angular locations of estimates of the dots’ positions regressed toward different locations inside each quadrant of the circle; the radial locations of the estimates of dots’ positions tended to regress toward locations near the circumference. These variations in the direction of bias appeared to reflect a general shift of estimates toward the upper left arc of the circle. The second experiment replicated the preceding effects but also revealed that the regressions within quadrants of angular values were stronger after right visual field than after left visual field presentations. We interpret the dissociation between visual fields as evidence that memory for categorical spatial relations (Kosslyn, 1987) is more dependent on left-hemisphere than on right-hemisphere processing.     

Interpolation in structure from motion.

We investigated surface interpolation in displays of structure from motion (SFM). To do so, we introduced a new method for measuring surface perception in dynamic displays--the SFM probe. An SFM probe is a dot that moves rigidly with the dots on a simulated surface, and whose distance from that surface can be adjusted with a joystick or similar control. The displays we studied were random-dot cylinders containing a vertical strip devoid of feature points (the gap). Subjects adjusted an SFM probe, presented in the gap, until the probe dot appeared to be on the surface. Variability in probe-dot placement decreased with increasing texture density on the cylinder and increased with increasing gap width. Subjects showed a consistent bias to place the probe dot outside the cylinder. This bias increased with increasing texture density for the SFM displays. (The opposite bias was found in a static two-dimensional interpolation task with an arc whose curvature matched that of the cylinder: Subjects placed the probe dot inside the arc.) This outside bias is inconsistent with several theoretical approaches to surface interpolation.     

Interpolation in structure from motion

We investigated surface interpolation in displays of structure from motion (SFM). To do so, we introduced a new method for measuring surface perception in dynamic displays—theSFM probe. An SFM probe is a dot that moves rigidly with the dots on a simulated surface, and whose distance from that surface can be adjusted with a joystick or similar control. The displays we studied were random-dot cylinders containing a vertical strip devoid of feature points (thegap). Subjects adjusted an SFM probe, presented in the gap, until the probe dot appeared to be on the surface. Variability in probe-dot placement decreased with increasing texture density on the cylinder and increased with increasing gap width. Subjects showed a consistent bias to place the probe dot outside the cylinder. This bias increased with increasing texture density for the SFM displays. (The opposite bias was found in a static two-dimensional interpolation task with an arc whose curvature matched that of the cylinder: Subjects placed the probe dot inside the arc.) This outside bias is inconsistent with several theoretical approaches to surface interpolation.     

Figural goodness and the predictability of figural elements

All 126 patterns composed of five dots distributed over the cells of a 3 by 3 matrix were examined for the predictability of their elements. The predictability of a given dot in a given pattern was measured as the percentage of Ss who indicated that dot as one “implied or suggested” by the subpattern composed of the remaining four dots of the pattern. The dots comprising a figurally good five-dot pattern were generally more predictable, one from the others, than the dots comprising a poor pattern. This finding accords with the Gestaltist conception of a good figure as one whose elements are well organized, and it is the state of affairs required by Garner’s hypothesis that better figures are perceived to have fewer alternatives than poorer figures. A mechanism mediating the prediction of an element of a pattern from the other elements was suggested.     

Effects of laterality and visual angle on time judgments: a phenomenological investigation of time durations

20 students from an undergraduate class participated in an experiment designed to study the effects of laterality and visual angle on time judgments. Using a standard two-field tachistoscope , subjects were exposed to two experimental conditions, (1) stimulus cards with a single red or blue dot in the center and several dots clustered on both sides near the center and equidistant from it (visual angle of .6 degrees) and (2) stimulus cards with a single red or blue dot in the center and several dots clustered on both sides away from the center on the edge of the card (visual angle of 2.6 degrees). Five cards containing a single red or blue dot were used to control for response bias. The subjects were asked to indicate whether they saw dots in the left, right, or both fields, and whether they perceived a time duration between fields. No difference in time duration existed, however, as all cards were exposed to both fields for equal durations. The predictions that the judged duration of dot patterns would be more accurate favoring the left visual-field and more accurate where the distance between the point of fixation and stimulus was larger were supported.     

Enumeration of dots: An eye movement analysis

The present study reports the measurement of response latencies and the recording of eye movements in a task in which adults had to enumerate dots in figures that differed in number of dots (n^d = 19–23) and grouping of dots. The functional relationship between latencies per dot and mean group size was in agreement with earlier findings (van Oeffelen & Vos, 1982). Temporal information from eye movement data indicated that the relative contribution of fixation durations to overall latency was far larger than the contribution of saccades, which superseded the contribution from eyeblinks. Spatial information in the form of eye movement trajectories indicated that, in general, there occurred one or two fixations at the starting position. From this position onward, eye movements were directed toward areas of dots rather than to each dot in particular. Scanning behavior was sometimes reiterative, in the sense that groups of dots were visited more than once. The results are discussed with respect to the nature of strategies employed during a dot-enumeration task.     

Static visual noise and the ansbacher effect

In Experiment I subjects made estimates of the apparent length of a 12 cm. long light arc-line rotating around a central fixation point at arc speeds of 66, 99, 132 and 165 cm./sec. Apparent contraction of the arc occurred as a function of speed, there being greater contraction in the presence of a superimposed random pattern of I cm. light squares (visual noise) than in its absence. The results of Experiment II indicated that there was no significant difference in length due to visual noise when the arcs were stationary. In Experiment III subjects made estimates of the speed of rotation of the arc and it was found that visual noise did not significantly affect the apparent arc-speed.     

Visual misalignment in arc and chevron figures

Five experiments investigated an apparent misalignment effect in 90 degrees arc figures. Preliminary observations showed that the effect occurs also in chevron figures, in an afterimage of the arc figure, and haptically in arc- and chevron-shaped objects. The experiments showed that the effect is greater with 3 radial lines than with 2, absent without them, and present in a figure consisting of only 3 radial lines. The effect with arc figures was consistently greater than that with chevron figures, a difference found not to be due to an apex marking the midpoint of the latter, and it was of intermediate size in figures with 1 arc boundary and 1 chevron boundary. The misalignment was also greater in narrow, elongated figures. The issues singled out for discussion are the effect of context on the misalignment effect with 3 radial lines, a possible explanation in terms of perceptual compromise, the difference in the effect between arcs and chevrons, and the relationship between this illusion and the Morinaga illusion.     

Vernier acuity as affected by target length and separation

Vernier acuity was measured for vertical lines of different lengths; the threshold (about 4 sec of arc) was almost as good for the shortest stimuli (1 min 20 sec squares) as for the longest (21 min 20 sec × 1 min 20 sec rectangles) and did not change when two round dots were shown in positions corresponding to the squares. The threshold for the two dots measured in terms of minimum detectable lateral offset increased when the vertical separation between the dots increased, but, when replotted in terms of the angle of tilt between them with respect to vertical, the threshold improved with dot separation; moreover, at asymptote, the threshold was comparable to that obtained for detecting that an actual line was tilted out of vertical. Our data suggest that, in performing the vernier task, Ss do not extrapolate the edges of the vernier elements; instead, they judge the deviation of the inner ends of the stimuli from verticality. This hypothesis explains the effect of increasing separation between vernier elements and also accounts for other types of acuity, such as the detection of curvature.     

Perceptual grouping between successively presented stimuli and its relation to visual simultaneity and masking

Summary A 4×4 matrix of dots was presented by a tachistoscope. The first and the third columns of the stimulus pattern were presented first for 20 ms and then the second and the fourth columns were presented for 20 ms with SOAs of 0 to 170 ms. Luminous dots on a dark background, black dots on a white background, and black dots and small outline circles on a white background were used in Experiments I, II, and III, respectively. In each experiment, 5 Ss were asked to report whether the stimulus dots were seen as 4 horizontal rows or 4 vertical columns, and whether they were seen simultaneously or successively. The experimental results showed that the time range of successive grouping was nearly the same as that of perceptual simultaneity in Experiments I and II, but was much greater than the latter in Experiment III where the similarity factor favored successive grouping. Successive grouping generally occurred in the same time range with visual masking of dot patterns by random dots, temporal organization of patterns from successive stimulus elements. But the time range was generally wider than those of contrast reduction caused by temporal luminance summation, metacontrast, and apparent movement.A part of this study was conducted during the junior author's stay at Chiba University and presented by him at the 20th International Congress of Psychology at Tokyo, August 13–19, 1972 (Yamada and Oyama, 1972)     

Visual discrimination of shape by octopus circles and squares, and circles and triangles

An investigation of the relative discriminability of circles and squares, and circles and triangles for octopus is described. The main findings were: (1) The three pairs of figures, circle and square with base horizontal, circle and square with base at 45° to the horizontal, circle and equilateral triangle were equally discriminable for the octopus. (2) Complete transfer occurred to larger and smaller figures. (3) No transfer occurred from a square in one orientation to a square rotated through 45°, nor did training with the square in one orientation lead to any saving when the discrimination was relearned with the square in the other orientation. (4) No transfer occurred from a square to a pentagon. (5) The method of training with reward on every positive trial leads to quicker initial learning of a discrimination than training with reward only where the positive figure is attacked, but discriminatory performance with the two methods approached the same asymptote. The results are in agreement with findings with other animals where these are available for comparison.     

Perceptual processes that may create stick figures and balance

A series of experiments looked at the pattern of dot placements created when people individually placed a single dot inside empty outline figures. The superimposed results were found to compare better with the predictions of Blum's grassfire model than with a size-constancy process. The pattern of superimposed dots conformed to the stick figure of the outlined contours. A perceptual model based on spatial harmonic analysis of complex visual scenes is offered as an explanation for the pattern of results.     

Size,convexity, and curvature magnitude estimations of curvilinear forms

Groups of Os made magnitude estimates of size, convexity, and curvature of patterns along a shape continuum. College Os repeated the procedure for a given physical measure in three successive sessions, but high school Os made only one set of estimates. The apparent size for the patterns was found to grow with an exponent between .700 and .755 for high school and college Os. The magnitude estimates for convexity and curvature were less reliable than the size estimates both between college and high school Os and within college Os over successive sessions. The magnitude estimates from the high school and college Os showed a faster apparent growth of curvature than of convexity.     

Hierarchical number estimation

We investigated number estimation using dot patterns grouped by proximity into larger clusters. Participants estimated the number of dots and clusters in separate trials. Estimation was most accurate when the numbers of elements on both scales were the same. When the number of elements on the unattended scale was higher, overestimation occurred. Conversely, when the number of elements on the unattended scale was lower, underestimation occurred. In Experiment 2, response cues were blocked to reduce any tendency toward attending the irrelevant level. The results were essentially unchanged, indicating response confusion alone cannot account for the effect. The data support the existence of an opposite scale effect in which the number of elements at the unattended level influence the processing of number.The preliminary results of the two experiments were presented at the Annual Meeting of The Association for Research in Vision and Ophthalmology, April 29–May 4, 2001, in Fort Lauderdale, Florida, USA     

Span of attention,backward masking,and reaction time

A test pattern consisting of 0 to 15 dots and a following random dot masking pattern were presented for 5 msec each with SOAs varying between 30 and 200 msec. The subject was asked to report the perceived number of dots in the test pattern as soon as possible and to assign a confidence rating to each report. The span of attention (upper limit for 50% correct numerosity judgments) increased from 2.4 to 9.5 as the SOA increased. Backward masking reduced the reported number of dots from the actual number in the test pattern, especially with small SOAs. Reaction time increased linearly at a low rate (approximately 40 msec/dot) up to 4 dots in the test pattern and then increased linearly at a high rate (approximately 370 msec/dot) as thereported, orperceived, number of dots increased. The two different branches of the reaction time curve were considered to represent two separate processes,subitizing andcounting, as suggested by Klahr (1973), who found similar dual increase rates as a function of the actual number of dots. These findings, as well as causal inference based on partial correlations and path analysis, indicated that the reported (perceived) number of dots and confidence rating were both determined by the number of stimulus dots and the SOA and that the reaction time was determined by the so-determined perceived number of dots and level of confidence. A multistage model is proposed.