Perceiving geographical slant

People judged the inclination of hills viewed either out-of-doors or in a computer-simulated virtual environment. Angle judgments were obtained by having people (1) provide verbal estimates, (2) adjust a representation of the hill’s cross-section, and (3) adjust a tilt board with their unseen hand. Geographical slant was greatly overestimated according to the first two measures, but not the third. Apparent slant judgments conformed to ratio scales, thereby enhancing sensitivity to the small inclines that must actually be traversed in everyday experience. It is proposed that the perceived exaggeration of geographical slant preserves the relationship between distal inclination and people’s behavioral potential. Hills are harder to traverse as people become tired; hence, apparent slant increased with fatigue. Visually guided actions must be accommodated to the actual distal properties of the environment; consequently, the tilt board adjustments did not reflect apparent slant overestimations, nor were they influenced by fatigue. Consistent with the fact that steep hills are more difficult to descend than to ascend, these hills appeared steeper when viewed from the top.     

Mechanisms underlying the slant aftereffect

Transfer of the median plane slant aftereffect was assessed across changes in the type of depth information for the slant of the display. In addition, the effectiveness of monocularpictorial and binocular information in inducing the aftereffect was measured. Binocular information produced a larger aftereffect than did monocular-pictorial information, and adaptation created with one type of depth information induced an aftereffect assessed with presentation of the other type of depth information. The results suggest that the slant aftereffect is not entirely specific to type of depth information presented. The induction of the aftereffect involves a process more general than the sensory mechanisms responsible for adaptation to twodimensional tilt or adaptation to a texture gradient.     

Perceptual slant induced through optical contact

Stimuli simulating a corridor with a pole inside it were presented. The positions of the ends of the pole within the ceiling and ground of the corridor were the optical contacts of concern. The main hypothesis was that a difference between the simulated distances of these optical contacts may influence the apparent slant in depth of the pole. Two experiments were conducted, with 30 and 20 participants (university students). The tasks were a choice between three alternative responses (upward, downward, or no apparent slant) in the first experiment and matching by adjustment in the second. The results supported the hypothesized dependence of apparent slant on differences in optical contacts. The results also revealed a dependence of apparent slant on the interaction between the optical tilt of the pole and its position to the right or left of the vertical median through the stimulus. Comparisons between both effects showed that they combine in a cumulative way and that the former is weightier than the latter. Further findings were a privileged association between null optical tilt of the pole and the no apparent slant response and a bias (for poles with nonnull optical tilt) in favor of the upward apparent slant response.     

Affordances matter in geographical slant perception

We argue that the experimental conditions in the Durgin et al. (2009) study were so different from those in Bhalla and Proffitt (1999) that the results of the former study cannot be generalized to the latter. The participants in the Durgin et al. study viewed a 2-m-long ramp; those in Bhalla and Proffitt viewed expansive hills. When drawing generalizations from one study to another, equating experimental conditions is always important; moreover, from an embodied perspective on perception, equating the opportunities for action also matters.     

An analysis of binocular slant contrast

When a small frontoparallel surface (a test strip) is surrounded by a larger slanted surface (an inducer), the test strip is perceived as slanted in the direction opposite to the inducer. This has been called the depth-contrast effect, but we call it the slant-contrast effect. In nearly all demonstrations of this effect, the inducer's slant is specified by stereoscopic signals; and other signals, such as the texture gradient, specify that it is frontoparallel. We present a theory of slant estimation that determines surface slant via linear combination of various slant estimators; the weight of each estimator is proportional to its reliability. The theory explains slant contrast because the absolute slant of the inducer and the relative slant between test strip and inducer are both estimated with greater reliability than the absolute slant of the test strip. The theory predicts that slant contrast will be eliminated if the signals specifying the inducer's slant are consistent with one another. It also predicts reversed slant contrast if the inducer's slant is specified by nonstereoscopic signals rather than by stereo signals. These predictions were tested and confirmed in three experiments. The first showed that slant contrast is greatly reduced when the stereo-specified and nonstereo-specified slants of the inducer are made consistent with one another. The second showed that slant contrast is eliminated altogether when the stimulus consists of real planes rather than images on a display screen. The third showed that slant contrast is reversed when the nonstereo-specified slant of the inducer varies and the stereo-specified slant is zero. We conclude that slant contrast is a byproduct of the visual system's reconciliation of conflicting information while it attempts to determine surface slant.     

Visual-motor recalibration in geographical slant perception.

In 4 experiments, it was shown that hills appear steeper to people who are encumbered by wearing a heavy backpack (Experiment 1), are fatigued (Experiment 2), are of low physical fitness (Experiment 3), or are elderly and/or in declining health (Experiment 4). Visually guided actions are unaffected by these manipulations of physiological potential. Although dissociable, the awareness and action systems were also shown to be interconnected. Recalibration of the transformation relating awareness and actions was found to occur over long-term changes in physiological potential (fitness level, age, and health) but not with transitory changes (fatigue and load). Findings are discussed in terms of a time-dependent coordination between the separate systems that control explicit visual awareness and visually guided action.     

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.     

Shape constancy and slant perception at birth

Two experiments are described the object of which was to investigate whether perception of shape at birth is determined solely by proximal (retinal) stimulation, or whether newborn babies have the ability to perceive objective, real shape across changes in slant. In experiment 1 looking at (ie preference for) one stimulus, a square, when paired with either of two trapeziums, was found to change in a consistent manner with changes in slant, indicating that these changes in stimulation are detected and can cause considerable changes in looking behaviour. In experiment 2 newborns were desensitized to changes in slant during familiarization trials, and subsequently strongly preferred a different shape to the familiarized shape in a new orientation. This suggests that the real shape had been perceived as invariant across the retinal changes caused by the changes in slant, and further suggests that shape constancy is an organizing feature of perception which is present at birth.     

A perspective metric for visual slant and shape

Summary Linear retinal perspective as a cue for visual slant and shape is analyzed in terms of its geometrical and psychophysical properties. Geometrically, retinal perspective is defined as the visual-angle difference in the projective magnitudes of the near and far edges of slanted rectangles. The psychophysical effectiveness of retinal perspective is then determined in two experiments. In Experiment 1, the sensitivity of the eye to retinal perspective is shown to be inversely related to the visual-angle height of slanted rectangles which are rotated about a horizontal axis. In Experiment 2, the visual shape of monocularly observed slanted rectangles is shown to depend solely on a simple prediction derived from Weber's Law, in which it is assumed that perceived height is a linear function of visual-angle height.

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Zusammenfassung Die geometrischen und psychophysischen Eigenschaften der linearen retinalen Perspektive wurden analysiert, um festzustellen, welchen Einfluß die Perspektive auf gesehene Schräge und Form hat. Geometrisch wird die retinale Perspektive als die Sehwinkeldifferenz in der projektiven Größe der näheren und ferneren Kante schräger Rechtecke definiert. Die psychophysische Wirksamkeit der retinalen Perspektive wurde an Hand zweier Experimente gemessen. Im ersten wurde gezeigt, daß die Sensitivität des Auges für die retinale Perspektive eine negative Funktion der Sehwinkelhöhe schräger Rechtecke ist, wenn diese um eine waagerechte Achse gedreht sind. Im zweiten Experiment wurde festgestellt, daß die Sehform einäugig betrachteter schräger Rechtecke von einer einfachen Ableitung des Weberschen Gesetzes abhängig ist, in der angenommen wird, daß die wahrgenommene Körperhöhe des Rechteckes eine lineare Funktion der Sehwinkelhöhe des Retinabildes ist.

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These investigations were supported by research grants MH-08856 and MH-10,691 from the National Institute of Mental Health, United States Public Health Service. The advice of Robert Seibel in the calculations of the regression lines of Fig. 4, and the assistance of Robert Pasnak in the conduct of Experiment 2 are gratefully acknowledged. Technical assistance was rendered by J. L. Cohen, W. F. Garber, Martha Harsanyi, R. L. Kochman, S. Ludwig, and Judith Ann Muth.     

Perceiving virtual geographical slant: action influences perception

In 4 experiments, the authors varied the extent and nature of participant movement in a virtual environment to examine the influence of action on estimates of geographical slant. Previous studies showed that people consciously overestimate hill slant but can still accurately guide an action toward the hill (D. R. Proffitt, M. Bhalla, R. Gossweiler, & J. Midgett, 1995). Related studies suggest that one's potential to act may influence perception of slant and that distinct representations may independently inform perceptual and motoric responses. The authors found that in all conditions, perceptual judgments were overestimated and motoric adjustments were more accurate. The virtual environment allowed manipulation of the effort required to walk up simulated hills. Walking with the effort appropriate to the visual slant led to increased perceptual overestimation of slant compared with active walking with the effort appropriate to level ground, while visually guided actions remained accurate.     

T-junctions and perceived slant of partially occluded surfaces

H?kkinen and Nyman (1997 Perception 26 29-38) reported that perceived slant is reduced when occlusion is a possible interpretation for the visual system. We present data from three experiments that confirm and expand on their finding. Our stimuli consisted of four types of stereograms depicting white central rectangles flanked on either side by two grey rectangles. The central white rectangles varied in height, thus manipulating the polarity of the T-junction information between the central and flanking rectangles. Perceived slant was smallest or not apparent when T-junction information indicated the central rectangles were nearer than the flanking rectangles and greatest when T-junction information indicated a farther central rectangle. Slant estimates for a stimulus containing a subjective pacmen-induced central rectangle were biased towards a depth step when an occlusion interpretation was possible.     

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.