Slope estimation and viewing distance of the observer

The overestimation of geographical slant is one of the most sizable visual illusions. However, in some cases estimates of close-by slopes within the range of the observer’s personal space have been found to be rather accurate. We propose that the seemingly diverse findings can be reconciled when taking the viewing distance of the observer into account. The latter involves the distance of the observer from the slope (personal space, action space, and vista space) and also the eye-point relative to the slope. We separated these factors and compared outdoor judgments to those collected with a three-dimensional (3D) model of natural terrain, which was within arm’s reach of the observer. Slope was overestimated in the outdoors at viewing distances between 2 m and 138 m. The 3D model reproduced the errors in monocular viewing; however, performance was accurate with stereoscopic viewing. We conclude that accurate slant perception breaks down as soon as the situation exits personal space, be it physically or be it by closing one eye.     

Estimator reliability and distance scaling in stereoscopic slant perception

When a horizontal or vertical magnifier is placed before one eye, a frontoparallel surface appears slanted. It appears slanted away from the eye with horizontal magnification (geometric effect) and toward the eye with vertical magnification (induced effect). According to current theory, the apparent slant in the geometric and induced effects should increase with viewing distance. The geometric effect does scale with distance, but there are conflicting reports as to whether the induced effect does. Ogle (1938 Archives of Ophthalmology 20 604-623) reported that settings in slant-nulling tasks increase systematically with viewing distance, but Gillam et al (1988 Perception & Psychophysics 44 473-483) and Rogers et al (1995 Perception 24 Supplement, 33) reported that settings in slant-estimation tasks do not. We re-examined this apparent contradiction. First, we conducted two experiments whose results are consistent with the literature and thus replicate the apparent contradiction. Next, we analyzed the signals available for stereoscopic slant perception and developed a general model of perceived slant. The model is based on the assumption that the visual system knows the reliability of various slant-estimation methods for the viewing situation under consideration. The model's behavior explains the contradiction in the literature. The model also predicts that, by manipulating eye position, apparent slant can be made to increase with distance for vertical, but not for horizontal, magnification. This prediction was confirmed experimentally.     

Journal of experimental psychology: human perception and performance

We examined the nonveridicality of visual direction produced by monocular viewing. In Experiment 1, 19 subjects pointed to a small light and moved a small light to their subjective median plane. The extent of constant error under monocular and binocular viewing conditions differed in both tasks (p less than .001). The monocular-binocular difference was larger when the viewing distance was 25 cm than when it was 50 cm (p less than .01). Also, correlations between phoria and monocular-binocular differences ranged from .58 to .77, depending on viewing distances and tasks. The effects of phoria within the context of Hering's .001). The monocular-binocular difference was larger when the viewing distance was 25 cm than when it was 50 cm (p less than .01). Also, correlations between phoria and monocular-binocular differences ranged from .58 to .77, depending on viewing distances and tasks. The effects of phoria within the context of Hering's .001). The monocular-binocular difference was larger when the viewing distance was 25 cm than when it was 50 cm (p less than .01). Also, correlations between phoria and monocular-binocular differences ranged from .58 to .77, depending on viewing distances and tasks. The effects of phoria within the context of Hering's principle of visual direction can account for these results. In Experiment 2, the same subjects adapted to phoria-induced error by placing a finger over a monocularly viewed target. The difference in their pointing responses before and after the task were reliable (p less than .005), and the correlations between phoria and the pre- to posttest differences were .45 and .77, depending on the number of adaptation trials. We argue that all monocular experiments dealing with visual direction should control for these effects.     

Temporal aspects of slant and inclination perception.

Linear transformations (shear or scale transformations) of either horizontal or vertical disparity give rise to the percept of slant or inclination. It has been proposed that the percept of slant induced by vertical size disparity, known as Ogle's induced-size effect, and the analogous induced-shear effect, compensate for scale and shear distortions arising from aniseikonia, eccentric viewing, and cyclodisparity. We hypothesised that these linear transformations of vertical disparity are processed more slowly than equivalent transformations of horizontal disparity (horizontal shear and size disparity). We studied the temporal properties of the stereoscopic slant and inclination percepts that arose when subjects viewed stereograms with various combinations of horizontal and vertical size or shear disparities. We found no evidence to support our hypothesis. There were no clear differences in the build-up of percepts of slant or inclination induced by step changes in horizontal size or shear disparity and those induced by step changes in vertical size or shear disparity. Perceived slant and inclination decreased in a similar manner with increasing temporal frequency for modulations of transformations of both horizontal and vertical disparity. Considerable individual differences were found and several subjects experienced slant reversal, particularly with oscillating stimuli. An interesting finding was that perceived slant induced by modulations of dilation disparity was in the direction of the vertical component. This suggests the vertical size disparity mechanism has a higher temporal bandwidth than the horizontal size disparity mechanism. However, conflicting perspective information may play a dominant role in determining the temporal properties of perceived slant and inclination.     

Extraction of relief from visual motion

We quantified the ability of human subjects to discriminate the relative distance of two points from a slanted plane when viewing the projected velocities of this scene (orthographic projection). The relative distance from a plane (called relief) is a 3-D property that is invariant under linear (affine) transformations. As such, relief canin principle be extracted from the instantaneous projected velocity field; a metric representation, which requires the extraction of visual acceleration, is not required. The stimulus consisted of a slanted planeP (specified by three points) and two pointsQ ₁ andQ ₂ that are non-coplanar withP. This configuration of points oscillated rigidly around the vertical axis. We have measured thesystematic error andaccuracy with which human subjects estimate the relative distance of pointsQ ₁ andQ ₂ from planeP as a function of the slant of_P. The systematic error varies with slant: it is low for small slant values, reaches a maximum for medium slant values, and drops again for high slant values. The accuracy covaries with the systematic error and is thus high for small and large slant values and low for medium slant values. These results are successfully modeled by a simple relief-from-motion computation based on local estimates of projected velocities. The data are well predicted by assuming (1) a measurement error in velocity estimation that varies proportionally to velocity (Weber’s law) and (2) an eccentricity-dependent underestimation of velocity.     

Perceived direction of rotation of simulated three-dimensional patterns

Direction of rotation judgments were obtained from 72 subjects for computer-generated dot patterns simulating points randomly distributed in a sphere rotating about a vertical axis. The displays were produced either with normal polar projections or with perspective effects limited to the horizontal or to the vertical dimension of the projection. The simulated viewing distance used in the projections and the visual angle subtended by the projected displays were also varied. Accuracy of direction judgments was about the same with perspective effects limited to the vertical dimension as with normal polar projections but did not exceed chance expectations with perspective effects limited to the horizontal dimension. Accuracy was lower at the greater simulated viewing distance and at the greater visual angle.     

Texture size specificity in the slant aftereffect

Transfer of the median plane slant aftereffect was assessed across changes in stimulus texture size (sine-wave grating frequency). Under binocular viewing, reliable decrements in aftereffect magnitude were observed when texture size was changed, compared with no-change control conditions. Under monocular viewing conditions, no significant aftereffects were found. The results indicate a spatial-frequency-specific component of binocular slant aftereffects.     

Perceptual space in the dark affected by the intrinsic bias of the visual system

Correct judgment of egocentric/absolute distance in the intermediate distance range requires both the angular declination below the horizon and ground-surface information being represented accurately. This requirement can be met in the light environment but not in the dark, where the ground surface is invisible and hence cannot be represented accurately. We previously showed that a target in the dark is judged at the intersection of the projection line from the eye to the target that defines the angular declination below the horizon and an implicit surface. The implicit surface can be approximated as a slant surface with its far end slanted toward the frontoparallel plane. We hypothesize that the implicit slant surface reflects the intrinsic bias of the visual system and helps to define the perceptual space. Accordingly, we conducted two experiments in the dark to further elucidate the characteristics of the implicit slant surface. In the first experiment we measured the egocentric location of a dimly lit target on, or above, the ground, using the blind-walking-gesturing paradigm. Our results reveal that the judged target locations could be fitted by a line (surface), which indicates an intrinsic bias with a geographical slant of about 12.4 degrees. In the second experiment, with an exocentric/relative-distance task, we measured the judged ratio of aspect ratio of a fluorescent L-shaped target. Using trigonometric analysis, we found that the judged ratio of aspect ratio can be accounted for by assuming that the L-shaped target was perceived on an implicit slant surface with an average geographical slant of 14.4 degrees. That the data from the two experiments with different tasks can be fitted by implicit slant surfaces suggests that the intrinsic bias has a role in determining perceived space in the dark. The possible contribution of the intrinsic bias to representing the ground surface and its impact on space perception in the light environment are also discussed.     

Do monocular time-to-collision estimates necessarily involve perceived distance?

Motivated by the debate between indirect and direct theories of perception, a large number of researchers have attempted to determine whether judgments of time to collision are based on the ratio of perceived distance to perceived speed or on the ratio theta/(d theta/dt), i.e. tau. Despite the considerable research effort devoted to this question there seems to be no clear resolution. We used a staircase tracking procedure to estimate errors in estimating time to collision for a simulated approaching object. To investigate the role of perceived distance in the judgment of time to collision, we asked observers to alternate between two viewing distances (100 and 500 cm). For the 500 cm viewing distance, we magnified the visual display by a factor of five so that the retinal images [and the values of theta/(d theta/dt) through time] were identical for the two viewing distances. All visual cues to distance were available. There were no significant differences between estimates of time to collision made at the two viewing distances. We conclude that our observers ignored perceived distance when estimating time to collision and based their responses on theta/(d theta/dt). We concur with recent proposals that, in the future, time-to-collision research should move away from the either/or analysis of different information sources that has dominated previous studies towards investigations of how different information sources are integrated.     

Mental imagery and the third dimension

What sort of medium underlies imagery for three-dimensional scenes? In the present investigation, the time subjects took to scan between objects in a mental image was used to infer the sorts of geometric information that images preserve. Subjects studied an open box in which five objects were suspended, and learned to imagine this display with their eyes closed. In the first experiment, subjects scanned by tracking an imaginary point moving in a straight line between the imagined objects. Scanning times increased linearly with increasing distance between objects in three dimensions. Therefore metric 3-D information must be preserved in images, and images cannot simply be 2-D "snapshots." In a second experiment, subjects scanned across the image by "sighting" objects through an imaginary rifle sight. Here scanning times were found to increase linearly with the two-dimensional separations between objects as they appeared from the original viewing angle. Therefore metric 2-D distance information in the original perspective view must be preserved in images, and images cannot simply be 3-D "scale-models" that are assessed from any and all directions at once. In a third experiment, subjects mentally rotated the display 90 degrees and scanned between objects as they appeared in this new perspective view by tracking an imaginary rifle signt, as before. Scanning times increased linearly with the two-dimensional separations between objects as they would appear from the new relative viewing perspective. Therefore images can display metric 2-D distance information in a perspective view never actually experiences, so mental images cannot simply be "snapshot plus scale model" pairs. These results can be explained by a model in which the three-dimensional structure of objects is encoded in long-term memory in 3-D object-centered coordinate systems. When these objects are imagined, this information is then mapped onto a single 2-D "surface display" in which the perspective properties specific to a given viewing angle can be depicted. In a set of perceptual control experiments, subjects scanned a visible display by (a) simply moving their eyes from one object to another, (b) sweeping an imaginary rifle sight over the display, or (c) tracking an imaginary point moving from one object to another. Eye-movement times varied linearly with 2-D interobject distance, as did time to scan with an imaginary rifle sight; time to tract a point varied independently with the 3-D and 2-D interobject distances. These results are compared with the analogous image scanning results to argue that imagery and perception share some representational structures but that mental image scanning is a process distinct from eye movements or eye-movement commands.     

Static and dynamic factors in the perception of rotary motion

Direction of rotation and static slant judgments were collected for a series of outline plane forms in four experiments with 106 subjects. Direction was judged more accurately for forms displaying the same perspective gradients as trapezoids, but with right-angled contours, than for trapezoids. There were no consistent differences among these forms in judged slant. Direction of rotation judgments were affected by a static false interposition cue, with interposition increasing the proportion of veridical judgments when placed in conflict with a relative size gradient and decreasing this proportion when a size gradient was absent. Both a dynamic factor (contour angle change) and a static factor (misperceived relative distance of the vertical sides) were found to affect perceived direction of rotation, with direction judgments based primarily on the dynamic factor.     

Pictorial perspective: perception of size, linear, and texture perspective in children and adults

Perception of size, linear, and texture perspective was investigated in third-grade and sixth-grade children and in college adults in three separate studies. A matching task required the observer to choose from a set of four alternative real scenes the correct match for the test stimulus, which was either a picture or a real scene. Correct performance required that the subject utilize perspective information for both size and distance distance relations. Erroneous choices available to the subject indicated errors in size judgement, in distance judgment, or in both simultaneously. View was either restricted at the correct station point or was free, with head motion. There were no significant effects of grade level. For all three groups, mean percent correct was nearly 100% with the real-scene test stimuli, and significantly below the chance level with the picture test stimuli. Errors in size judgment occurred most frequently, indicating that the geometrically correct rate of perspective convergence was too rapid to be seen by the subjects as perceptually acceptable. With size-perspective information alone, the number of size plus distance errors also increased significantly. There was no significant effect of viewing condition.     

Anisotropic perception of visual angle: implications for the horizontal-vertical illusion, overconstancy of size, and the moon illusion.

Three experiments investigated anisotropic perception of visual angle outdoors. In Experiment 1, scales for vertical and horizontal visual angles ranging from 20 degrees to 80 degrees were constructed with the method of angle production (in which the subject reproduced a visual angle with a protractor) and the method of distance production (in which the subject produced a visual angle by adjusting viewing distance). In Experiment 2, scales for vertical and horizontal visual angles of 5 degrees-30 degrees were constructed with the method of angle production and were compared with scales for orientation in the frontal plane. In Experiment 3, vertical and horizontal visual angles of 3 degrees-80 degrees were judged with the method of verbal estimation. The main results of the experiments were as follows: (1) The obtained angles for visual angle are described by a quadratic equation, theta' = a + b theta + c theta 2 (where theta is the visual angle; theta', the obtained angle; a, b, and c, constants). (2) The linear coefficient b is larger than unity and is steeper for vertical direction than for horizontal direction. (3) The quadratic coefficient c is generally smaller than zero and is negatively larger for vertical direction than for horizontal direction. And (4) the obtained angle for visual angle is larger than that for orientation. From these results, it was possible to predict the horizontal-vertical illusion, over-constancy of size, and the moon illusion.     

Contraction intensity and velocity on vastus lateralis SEMG power spectrum and amplitude

Effect of contraction intensity [100%, 75%, 50%, and 25% maximum voluntary contraction (MVC)] and movement velocity [0 degrees (isometric)], 50 degrees, 100 degrees, 200 degrees, and 400 degrees/sec. [isovelocities]) on root mean square amplitude (SEMG-RMS) and median frequency power spectrum (SEMG-MNF) of vastus lateralis (VL) surface electromyography was investigated with ten healthy female university students. Peak torque (PT), mean torque (MT), SEMG-MNF, and SEMG-RMS, analyzed using separate repeated-measures analyses of variance (p < or = .05), indicated: (1) an inverse relation between PT and MT and movement velocity, (2) greater SEMG-MNF values during all isovelocity conditions compared with isometric conditions, with highest values occurring at 50 degrees /sec. and at 100% and 75% MVC, and (3) at all contraction intensities SEMG-RMS values were higher during dynamic movements than isometric movements and highest at 200 degrees /sec. Isovelocity contractions were inferred to facilitate a greater recruitment of fast-twitch fibers (via increased SEMG-MNF), which was intensified at 50 degrees /sec., whereas greater overall muscle activation was found at 200 degrees /sec.     

The perception of depth and slant from texture in three-dimensional scenes.

The perception of depth and slant in three-dimensional scenes specified by texture was investigated in five experiments. Subjects were presented with computer-generated scenes of a ground and ceiling plane receding in depth. Compression, convergence, and grid textures were examined. The effect of the presence or absence of a gap in the center of the display was also assessed. Under some conditions perceived slant and depth from compression were greater than those found with convergence. The relative effectiveness of compression in specifying surface slant was greater for surfaces closer to ground planes (80 degrees slant) than for surfaces closer to frontal parallel planes (40 degrees slant). The usefulness of compression was also observed with single-plane displays and with displays with surfaces oriented to reduce information regarding the horizon.     

Planar motion permits perception of metric structure in stereopsis.

A fundamental problem in the study of spatial perception concerns whether and how vision might acquire information about the metric structure of surfaces in three-dimensional space from motion and from stereopsis. Theoretical analyses have indicated that stereoscopic perceptions of metric relations in depth require additional information about egocentric viewing distance; and recent experiments by James Todd and his colleagues have indicated that vision acquires only affine but not metric structure from motion--that is, spatial relations ambiguous with regard to scale in depth. The purpose of the present study was to determine whether the metric shape of planar stereoscopic forms might be perceived from congruence under planar rotation. In Experiment 1, observers discriminated between similar planar shapes (ellipses) rotating in a plane with varying slant from the frontal-parallel plane. Experimental conditions varied the presence versus absence of binocular disparities, magnification of the disparity scale, and moving versus stationary patterns. Shape discriminations were accurate in all conditions with moving patterns and were near chance in conditions with stationary patterns; neither the presence nor the magnification of binocular disparities had any reliable effect. In Experiment 2, accuracy decreased as the range of rotation decreased from 80 degrees to 10 degrees. In Experiment 3, small deviations from planarity of the motion produced large decrements in accuracy. In contrast with the critical role of motion in shape discrimination, motion hindered discriminations of the binocular disparity scale in Experiment 4. In general, planar motion provides an intrinsic metric scale that is independent of slant in depth and of the scale of binocular disparities. Vision is sensitive to this intrinsic optical metric.     

Reading performance in middle-aged adults with declines in accommodation

The present study investigated the effects of presbyopia on the reading ability of middle-aged adults in a Japanese reading context, using the rapid serial visual presentation paradigm. Japanese words, each consisting of three characters, were sequentially presented at the same location on a display screen. Participants were instructed to read the words aloud as accurately as possible, irrespective of their order within the sequence. Experiment 1 showed that the reading performance for the presbyopes was far worse for the near-viewing (35?cm) than for the far-viewing (70?cm) conditions when the words were presented at 0.4° in character size. Experiment 2 investigated in detail the effect of luminance contrast on reading at a viewing distance of 35?cm. The minimums of the exposure durations within which the participants could read the words above 89.9?% correct (minimum exposure duration) were 498?ms/word for the presbyopes and 134?ms/word for the nonpresbyopes, both of which values were obtained at 100?% contrast. The critical contrast??that is, the contrast that doubled the minimum exposure duration that had been obtained at 100?% contrast??was considerably higher for the presbyopes (39.2?%) than for the nonpresbyopes (16.4?%). However, the reading performance for the presbyopes was improved more than threefold when the contrast was increased to 100?% in both experiments. Thus, our results provide psychophysical evidence for the dependency of presbyopes?? reading on viewing distance and luminance contrast.     

Assessing effects of viewing distance on normal Chinese reading: Some methodological and theoretical implications

Viewing distance determines a range of factors affecting reading performance. Previous studies of Chinese-character reading have shown considerable disagreement and inconsistency in their choice of viewing distances, however, with obvious implications for research in this area. The present study aimed to resolve this issue by determining the optimal viewing distance for studies of normal Chinese reading. Stimuli were pages of text that were composed of a standard Chinese typeface (Song) that was presented in a standard size (10.5 pt). Forty reading distances were used, ranging from 2.5 to 100.0 cm. Distances within the range of 7.5–55.0 cm produced faster reading rates than did the distances at either end of the continuum, and a regression model showed that 35 cm was the optimal viewing distance. These findings indicate an optimal range of retinal image sizes between 2.0° and 0.3° per character. The implications of these findings for understanding the processes that are involved in Chinese reading and for the appropriate presentation of Chinese stimuli in experiments are discussed.