Determinants ofthe perception of sagittal motion

This study examines the change in the perceived distance of an object in three-dimensional space when the object andlor the observer’s head is moved along the line of sight (sagittal motion) as a function of the perceived absolute (egocentric) distance of the object and the perceived motion of the head. To analyze the processes involved, two situations, labeled A and B, were used in four experiments. In Situation A, the observer was stationary and the perceived motion of the object was measured as the object was moved toward and away from the observer. In Situation B, the same visual information regarding the changing perceived egocentric distance between the observer and object was provided as in Situation A, but part or all of the change in visual egocentric distance was produced by the sagittal motion of the observer’s head. A comparison of the perceived motion of the object in the two situations was used to measure the compensation in the perception of the motion of the object as a result of the headmotion. Compensation was often clearly incomplete, and errors were often made in the perception of the motion of the stimulus object. A theory is proposed, which identifies the relation between the changes in the perceived egocentric distance of the object and the tandem motion of the object resulting from the perceived motion of the head to be the significant factor in the perception of the sagittal motion of the stimulus object in Situation B.     

Determinants of the perception of sagittal motion.

This study examines the change in the perceived distance of an object in three-dimensional space when the object and/or the observer's head is moved along the line of sight (sagittal motion) as a function of the perceived absolute (egocentric) distance of the object and the perceived motion of the head. To analyze the processes involved, two situations, labeled A and B, were used in four experiments. In Situation A, the observer was stationary and the perceived motion of the object was measured as the object was moved toward and away from the observer. In Situation B, the same visual information regarding the changing perceived egocentric distance between the observer and object was provided as in Situation A, but part or all of the change in visual egocentric distance was produced by the sagittal motion of the observer's head. A comparison of the perceived motion of the object in the two situations was used to measure the compensation in the perception of the motion of the object as a result of the head motion. Compensation was often clearly incomplete, and errors were often made in the perception of the motion of the stimulus object. A theory is proposed, which identifies the relation between the changes in the perceived egocentric distance of the object and the tandem motion of the object resulting from the perceived motion of the head to be the significant factor in the perception of the sagittal motion of the stimulus object in Situation B.     

Distance discrimination and observer strategy in judgments of relative size

Six paid Ss participated in an experiment designed to assess the effects of observer strategy and the detectability of a distance cue on judgments of relative size. Ss viewed stimulus pairs through a 21-in. tunnel at one end of an 8-ft table. The Standard stimulus, 94 in. from S, was individually paired with three larger and two smaller comparison stimuli 96 in. from S. A slit of light on the table 95 in. from S and 90 deg to his line of sight served as distance cue. Increases in distance detection improved accuracy of relative size judgments when the comparison stimulus was larger than the Standard stimulus, but decreased accuracy when the comparison stimulus was smaller. Magnitude of this effect varied directly with Ss’ post-experimental reports of judgmental strategy. These findings confirm the importance of distance discrimination in judgments of actual size and the necessity to control perceiver characteristics in the study of size-distance relationships.     

Illusory temporal order for stimuli at different depth positions

We used four experiments to examine how the perceived temporal order of two visual stimuli depends on the depth position of the stimuli specified by a binocular disparity cue. When two stimuli were presented simultaneously at different depth positions in front of or around a fixation point, the observer perceived the more distant stimulus before the nearer stimulus (Experiments 1 and 2). This illusory temporal order was found only for sudden stimulus presentation (Experiment 3). These results suggest that a common processing, which is triggered by sudden luminance change, underlies this illusion. The strength of the illusion increased with the disparity gradient and the disparity size (Experiment 4). We propose that this illusion has a basis in the processing of motion in depth, which would alert the observer to a potential collision with an object that suddenly emerges in front of the observer.     

Properties of changing patterns evoking visually perceived oscillation

The aim of this study was to identify some properties of changing proximal stimulus patterns which favor perceived oscillation. By using artificially generated stimulus patterns, it was found that the amount of changes associated with a certain direction of rotation should be small and the rate of these changes low if perceived oscillation was to appear. Great or swift changes were utilized by the visual system to determine perceived direction of rotation, and oscillation was not then reported. It was further found that patterns lacking straight edges perpendicular to the axis of rotation, or with this axis displaced from the middle of the pattern, and patterns with a gradient of texture density were perceived to oscillate more than similar patterns without these properties. Perceived oscillation of ellipses was discussed, and it was concluded that perceived oscillation was a consequence of perceived orientation, which is determined by stimulus properties.     

Depth separation and lateral interference

In four experiments, the perceptual interaction between an annulus and a Landolt C enclosed within it was investigated as a function of their perceived relative depth positions and of the perceived lateral distance between the inner edge of the annulus and the outer edge of the C. To permit facile and unconfounded manipulation of perceived depth, the stimuli were stereoscopic contours formed from dynamic random-lement stereograms. Either one or both stimuli were visible continuously. The effect of the annulus on the Landolt C was assessed by forced-choice recognition thresholds of the C and by judgments of its apparent clarity. The main results were: (1) For both threshold recognition and apparent clarity, perceived depth separation has a strong effect on the strength of perceptual interaction; (2) the effect is asymmetrical in that the stimulus perceived as in front of its partner and closer to the observer has greater perceptual potency; and (3) as spacing between the elements increases, perceptual interaction declines independently of depth position. The implications of these data for general theories of stimulus interaction in three-dimensional space are discussed.     

Spatial compatibility of signal-response position in pointing

Two experiments are reported in which, by means of a pointing task, we studied the stimulus-position effect, i.e. the inverted U-shape form of the reaction-time function in relation to stimulus position in tasks in which stimuli and/or responses are arranged in a horizontal array. The response consisted of aiming the index finger from a central starting point at a target area on a screen. Reaction time was the main dependent variable. The spatial relation between the position of the imperative signal and the position of the response was manipulated by varying the spatial S-R compatibility and physical distance that separated the positions of stimulus and response. The stimulus-position effect was shown to depend on the compatibility of the S-R relation (Exp. 1). In Exp. 2 it was found that the modulation of the stimulus-position effect by spatial compatibility disappeared completely when the distance between the positions of stimulus and response was reduced. None of the experiments revealed that the stimulus position effect depended on signal discriminability, which renders an interpretation of this effect in terms of perceptual processes unlikely. We argue that the attentional model of spatial coding provides the most reasonable explanation of the obtained reaction-time patterns.     

'Perceiving the present' as a framework for ecological explanations of the misperception of projected angle and angular size

An implicit, underlying assumption of most Helmholtzian/Bayesian approaches to perception is the hypothesis that the scene an observer perceives is the probable source of the proximal stimulus. There is, however, a nontrivial latency (on the order of 100 ms) between the time of a proximal stimulus and the time a visual percept is elicited. It seems plausible that it would be advantageous for an observer to have, at any time t, a percept representative of what is out there at that very time t, not a percept of the recent past. If this is so, it implies a modification to the implicit hypothesis underlying most existing probabilistic approaches to perception: the new hypothesis is that, given the proximal stimulus, the scene an observer perceives is the probable scene present at the time of the percept. That is, the hypothesis is that what an observer perceives is not the probable source of the proximal stimulus, but the probable way the probable source will be when the percept actually occurs. A model of an observer's typical movements in the world is developed, and it is shown that projected angles are perceived in a way consistent with the way the probable source will project to the eye after a small time period of forward movement by the observer. The predicted and actual direction of projected-angle misperception is sometimes toward 90 degrees and sometimes away from 90 degrees, depending on whether the probable source angle is lying in a plane parallel or perpendicular to the probable direction of motion, respectively. The perception of angular size for lines in a figure with cues they are lying in a plane perpendicular to the direction of motion is also shown to fit the predictions of the model.     

Depth motion sensitivity functions

Functions reliably describing perception of motion in depth have been established experimentally by using psychophysical methods of size and distance estimations and threshold measurements. The stimuli were generated with a new hybrid technique yielding an image refresh rate of 1667 Hz. In this way it was possible to generate rapid expansions and contractions of the moving checkerboard pattern constituting the stimulus for depth motion perception. The results showed that perceived size constancy as well as depth impression varied with oscillation frequency. Under the conditions of slow motions (oscillation frequencies around 2 Hz), perfect size constancy was obtained. Above that limit, size constancy systematically decreased, and with oscillation frequencies of about 5 Hz the perceived size constancy was close to zero when small-sized patterns were used. Under the conditions of wide field stimulation (when the pattern subtended 66 degrees of visual angle), the cut-off limit increased to 16 Hz. Since the perception of depth motion amplitudes as well as perceived velocities of the visual object are related to perceived size constancy, the findings have certain implications for theoretical explanations of depth motion perception. Received: 15 December 1997 / Accepted: 21 December 1998     

A Differential Geometric Description of the Relationships among Perceptions

We present a differential geometric method for measuring and characterizing the perceptions of an observer of a continuum of stimuli. Because the method is not based on a model of perceptual mechanisms, it can potentially be applied to a wide variety of observers and to many types of visual and auditory stimuli. The observer is asked to identify which small transformation of one stimulus is perceived to be equivalent to a small transformation of a second stimulus, differing from the first stimulus by a third small transformation. The observer's identification of a number of such transformations can be used to calculate an affine connection on the stimulus manifold. This quantity describes how the observer encodes an evolving stimulus as a perceived sequence of "reference" transformations. This type of encoding is a multidimensional generalization of Fechner's method and reduces to his psychophysical scale when the stimulus manifold is one dimensional and the reference transformation is chosen to be a just noticeable difference. The intrinsic aspects of the nature of the observer's perceptions can be characterized by the curvature and torsion tensors derived from the connection. The multidimensional analogues of psychophysical scale functions exist if and only if these quantities vanish. Differences between the affine connections of two observers characterize differences between their perceptions of the same evolving stimuli. The affine connections of two observers can also be used to map a stimulus perceived by one observer onto another stimulus, perceived in the same way by the other observer. Unlike multidimensional scaling techniques, this method does not assume that the observer has a sense of distance (a metric) or that he/she can otherwise compare stimulus pairs that are oriented along perceptually different directions in the manifold. The method was used to measure the affine connections of observers of a dot moving on different background graphics; e.g., a blank screen, a grid, or two converging lines similar to those used to create the Ponzo illusion. The results comprise quantitative measurements of the background graphic's influence on each observer's perceptions of straightness, parallelism, and distance. The measurements demonstrate differences between the perceptions of the two observers. Copyright 2000 Academic Press.     

Effects of pitch distance and likelihood on the perceived duration of deviant auditory events

When a deviant (oddball) stimulus is presented within a series of otherwise identical (standard) stimuli, the duration of the oddball tends to be overestimated. Two experiments investigated factors affecting systematic distortions in the perceived duration of oddball stimuli. Both experiments used an auditory oddball paradigm where oddball tones varied in both their pitch distance from the pitch of a standard tone and their likelihood of occurrence. Experiment 1 revealed that (1) far-pitch oddballs were perceived to be longer than near-pitch oddballs, (2) effects of pitch distance were greater in low-likelihood conditions, and (3) oddballs in later serial positions were perceived to be longer than oddballs in earlier serial positions. The above effects held regardless of whether oddballs were higher or lower in pitch than the standard. Experiment 2 revealed a pattern of response times in an oddball detection task that generally paralleled the pattern of data observed in Experiment 1; across conditions, there was a negative correlation between detection times and perceived duration. Taken together, the results suggest that the observed effects of oddball pitch, likelihood, and position on perceived duration are at least partly driven by how quickly individuals are able to initiate timing the oddball following its onset. Implications for different theoretical accounts of the oddball effect are discussed.     

Visual distance estimation in static compared to moving virtual scenes

Visual motion is used to control direction and speed of self-motion and time-to-contact with an obstacle. In earlier work, we found that human subjects can discriminate between the distances of different visually simulated self-motions in a virtual scene. Distance indication in terms of an exocentric interval adjustment task, however, revealed linear correlation between perceived and indicated distances but with a profound distance underestimation. One possible explanation for this underestimation is the perception of visual space in virtual environments. Humans perceive visual space in natural scenes as curved, and distances are increasingly underestimated with increasing distance from the observer. Such spatial compression may also exist in our virtual environment. We therefore surveyed perceived visual space in a static virtual scene. We asked observers to compare two horizontal depth intervals, similar to experiments performed in natural space. Subjects had to indicate the size of one depth interval relative to a second interval. Our observers perceived visual space in the virtual environment as compressed, similar to the perception found in natural scenes. However, the nonlinear depth function we found can not explain the observed distance underestimation of visual simulated self-motions in the same environment.     

Steering toward a goal by equalizing taus

Steering toward a target can be controlled by equalizing the time-to-closure of the angle between the target and the direction of locomotion and the time-to-passage of the observer by the target. Two experiments required observers to steer through a computer-simulated environment toward a target depicted as either a floating cross that did not optically expand, a floating sphere that optically expanded or a grounded post that optically expanded. Experiment 1 revealed better performance in the post and sphere conditions, suggesting that steering is influenced by local optical expansion but not by perceived spatial target location or distance. Experiment 2 revealed differences in steering behavior between target types that suggested observers attempted to equalize time-to-closure and time-to-passage.     

An analysis of perceptions from changes in optical size

The allocation of perceived size and perceived motion or displacement in depth resulting from retinal size changes (changes in the visual angle of the stimulus) was investigated in situations in which all other cues of perceived changes in distance were absent. The allocation process was represented by the size—distance invariance hypothesis (SDIH), in which, for a given change in visual angle, the perceived depth was determined only by the amount of size constancy available. The changes in perceived size and perceived distance (perceived depth) were measured by kinesthetic observer (open-loop) adjustments in five situations. These situations consisted of optical expansions or contractions presented successively or simultaneously or as a mixture of successive and simultaneous presentations. The amounts of perceived motion or perceived displacement in depth obtained by kinesthetic measures were compared with those obtained from size constancy measures as applied to the SDIH. This latter measure accounted for more of the perceived depth obtained from simultaneous and mixed situations than it did for the perceived depth from the successive situations and more for the perceived depth obtained from the expansion than from the contraction situations, whether these were simultaneous or mixed. Perceived rigidity of the stimulus (perfect size constancy) clearly was not obtained in any of the situations. Significant partial size constancy and some predictive ability of the perceived sagittal motion was found using the SDIH in all the situations except in the successively presented contraction situation, with the predictive ability from the SDIH increasing with increases in the amount of size constancy. The difference between the observer’s measures of the perceived motion or displacement in depth and the amount of perceived motion or displacement predicted from the perceptions of linear size using the SDIH is asserted to be due to a cognitive process associated with the perception of the different stimulus sizes as off-sized objects.     

Oculomotor adjustments and size-distance perception

The relationship between perceived size and distance and oculomotor adjustments were assessed in two experiments. In both experiments, Ss were required to make scalar linear size, angular size, and distance judgments of stimuli subtending a constant retinal image size at different levels of convergence. The results of the first experiment indicate that the perceived linear size, angular size, and distance of the stimulus decreased with increased convergence, the decrease in perceived linear size being greater than that of perceived angular size. While again showing a decrease in perceived linear and angular size, the results of the second experiment also show that there was a smaller decrease in perceived distance with increased convergence when Ss continued to view the stimulus as convergence was changed than when they did not view the stimulus as convergence was changed. The implications these results have for size and distance perception are discussed.     

Perceived angle of oscillatory motion

The general background of these experiments was the fact, known from e.g. trapezoidal window experiments, that rotary motion under certain conditions is perceived as oscillation. The aim was to identify the variables that determine the perceived angle of this oscillatory motion. Different shapes and different methods of generating the stimulation were used. No effect was obtained when varying the degree of trapezoidality of trapezoids, the location of the axis of rotation, the size of the stimulus pattern and the speed of the change. Both the occurrence and the perceived angle of oscillation was effected, however, by the width-height ratio of the stimulation, a decreasing ratio giving increasing occurrence of oscillation and decreasing perceived angle.     

Adaptive processing of visual motion

Three studies relating perception of motion to stimulus uncertainty are reported. Generally, detectability declines when the observer is uncertain about the direction in which a target will move, but the visibility loss associated with direction uncertainty can be attenuated if the observer has adequate practice. This attenuation seems to depend upon the observer's ability to switch among directionally selective visual mechanisms in an adaptive fashion. The implications of these findings for models of motion detection are discussed.     

Speed constancy and the perception of distance

The distance-calibration hypothesis states that retinal velocity is scaled by using distance cues, and judged velocity remains unchanged when distance is changed. The relational hypothesis states that judged velocity depends on retinal velocities, and is proportional to judged distance. These hypotheses were compared in three experiments where the movements of the standard stimulus and the comparison stimulus were manipulated by the ratio of the angular velocity of the comparison stimulus to the angular velocity of the standard stimulus. The presentation conditions of the standard stimulus and the comparison stimulus, and the colour cues of the two stimuli were also manipulated in order to change the strength of the cues available to the observers. The results indicate that judged velocities and the relationship of judged distance and velocity depend on the strength of the cues. When cues are strong, the distance-calibration hypothesis adequately explains speed constancy. When cues are weak, judged velocity and the relationship between judged distance and velocity are consistent with the prediction of the relational hypothesis. The perceived speed of a stimulus depends not only on the physical speed of the stimulus but also on non-motion cues, some of which are distance cues involved in depth perception.     

Are you looking at me? Measuring the cone of gaze

The processing of gaze cues plays an important role in social interactions, and mutual gaze in particular is relevant for natural as well as video-mediated communications. Mutual gaze occurs when an observer looks at or in the direction of the eyes of another person. The authors chose the metaphor of a cone of gaze to characterize this range of gaze directions that constitutes "looking at" another person. In 4 experiments using either a real person or a virtual head, the authors investigated the influences of observer distance, head orientation, visibility of the eyes, and the presence of a 2nd head on the perceived direction and width of the gaze cone. The direction of the gaze cone was largely affected by all experimental manipulations, whereas its angular width remained comparatively stable.     

The angle of visual roll motion determines displacement of subjective visual vertical

The effect of full-field sinusoidal visual roll motion stimuli of various frequencies and peak velocities upon the orientation of subjective visual vertical (SV) was studied. The angle of the optokinetically induced displacement of SV was found to be a linear function of the logarithm of the stimulus oscillation angle. Interindividual slopes of this function varied between 2 and 9. The logarithmic function is independent of stimulus frequency within the range of .02 Hz to .5 Hz and of peak stimulus velocity from 7.5°/sec to 170°/sec. It holds for oscillation angles up to 100°–140°. With larger rotational angles, saturation is reached. With small stimulus angles, a surprisingly high threshold (5°-8°) was observed in our experiments. This may reflect the unphysiological combination of visual roll stimuli without corroborating vestibular and proprioceptive inputs normally present when body sway produces visual stimulation. Under natural conditions, the visual feedback about spontaneous sway stabilizes body posture by integrating rotational velocity over stimulus duration which is equal to rotational angle.