Perceived structure from optic flow: consistent versus variable mapping of 3-D Euclidean structure

In an earlier study (Börjesson & Lind, 1996), the perception of Euclidean structure from polar projected two‐frame apparent motion sequences was studied. The results showed that Euclidean structure is not perceived. However, at larger visual angles a certain consistency in the mapping between distal and perceived structure exists. The aim of the present study was to more precisely examine how this degree of consistency varies as a function of visual angle. In Experiments 1 and 2, slant judgments of simulated and real planes indicated that the degree of consistency is a positive function of visual angle. No definite sign of a Euclidean mapping could, however, be found even in the full view condition. Experiment 3 examined texture gradients and the response method used. The results showed that texture gradients did not influence the degree of consistency of the mapping between distal and judged depth and that the response method was both reliable and valid. However, texture gradients did influence the absolute values of the slant judgments. The role of Euclidean and affine mappings of distal structure is discussed and it is proposed that the perceptually important distinction is not between affine and Euclidean mapping, but rather between two types of affine mappings—consistent and variable.     

Aging and the perception of slant from optical texture, motion parallax, and binocular disparity

The ability of younger and older observers to perceive surface slant was investigated in four experiments. The surfaces possessed slants of 20°, 35°, 50°, and 65°, relative to the frontoparallel plane. The observers judged the slants using either a palm board (Experiments 1, 3, and 4) or magnitude estimation (Experiment 2). In Experiments 1–3, physically slanted surfaces were used (the surfaces possessed marble, granite, pebble, and circle textures), whereas computer-generated 3-D surfaces (defined by motion parallax and binocular disparity) were utilized in Experiment 4. The results showed that the younger and older observers' performance was essentially identical with regard to accuracy. The younger and older age groups, however, differed in terms of precision in Experiments 1 and 2: The judgments of the older observers were more variable across repeated trials. When taken as a whole, the results demonstrate that older observers (at least through the age of 83 years) can effectively extract information about slant in depth from optical patterns containing texture, motion parallax, or binocular disparity.     

The role of the centre of projection in the estimation of slant from texture of planar surfaces

Displays were presented consisting of a perspective projection of a regular square grid, made up of vertical and horizontal equally spaced white lines, that was slanted in depth. The surface was viewed monocularly, through a circular aperture. A range of slants was shown (0 degree, 10 degrees, 20 degrees, 30 degrees, 40 degrees, 50 degrees, or 60 degrees) and the observers' task was to match the slant by means of a mouse-driven probe. The viewing distance (50, 75, or 100 cm) as well as the focal distance (25, 50, 75, 100, or 125 cm) were varied. We expected the estimation error to be smallest when the viewing distance and the focal distance coincided. This was not the case. Instead, subjects seemed to use the perspective deformation of the texture elements in the stimulus display to make a slant estimation, regardless of the specific combination of viewing distance and focal distance.     

Optical Push by Geographical Slant Affects Postural Sway

This study shows that perceived geographical slant affects postural stability. In 2 experimental conditions participants stood on a force platform that measured center of pressure (COP) during quiet stance while looking at a rigid, flat ramp surface of varying geographical slants. Using an otherwise identical procedure, participants in the second condition also provided verbal estimates of the steepness of the surface in degrees. Several measures of postural stability offered converging evidence that COP sway gradually increased as geographical slant decreased to 0 (horizontal ground). Specifically, COP was sensitive to changes in surface slant. Both the range and the standard deviation of COP showed the same trend of increased variability with decreasing geographical slant angles in both conditions. The area of the ellipse covering COP sway (based on a principal components analysis) showed the same tendency: ellipse area got larger for smaller, more horizontal slants. Nonlinear fractal dynamics of COP sway, as measured by the Hurst exponent of COP, pointed in the same direction: more fractal patterns, known to be correlated with increased muscle activity and decline in postural stability, were measured for shallower surface slants. There were no effects of verbal estimates on any of the measures, suggesting that explicit awareness of slant does not bias postural stability above and beyond the effects of visual environment.     

Haptic perception of texture gradients

To pick up 3-D aspects of pictures is arguably the most difficult problem concerning tactile pictorial perception by the blind. The aim of the experiments reported was to examine the potential utility of texture gradients in this context. Since there is no theoretical basis for predicting absolute values of 3-D properties from 2-D patterns read by the finger pads, the abilities of participants to perceive gradients lying between known maxima and minima were assessed. Experiment 1 involved blindfolded sighted participants making verbal magnitude estimations of texture-gradient magnitudes corresponding to plane surfaces at different slants. In experiment 2 the participants' task was to orient a surface at a slant corresponding to the texture gradients depicted tactually, and experiment 3 required early-blind participants to attempt the same task. The results revealed that participants can scale the magnitudes of texture gradients with high precision and that they can also accurately produce surface slants from depictions, providing the extreme conditions are clearly defined and there are opportunities for learning. Texture gradients appear as informative to the blind as they do to the sighted. To what extent these data can be generalised to other gradients and textures or to other projections of 3-D scenes remains to be investigated.     

Ratings of kinetic depth in multidot displays

Subjects saw kinetic depth displays whose shape (sphere or cylinder) was defined by luminous dots distributed randomly on the surface or in the volume of the object. Subjects rated perceived 3-D depth, rigidity, and coherence. Despite individual differences, all 3 ratings increased with the number of dots. Dots in the volume yielded ratings equal to or greater than surface dots. Each rating varied with 3 of 4 factors (shape, distribution, numerosity, and perspective), but the ratings either between trials or between conditions were often uncorrelated. Object shape affected rigidity but not depth ratings. Veridically perceived polar displays had slightly lower rigidity but higher depth ratings than parallel projection displays. (Reversed polar displays were always grossly nonrigid.) The interaction of ratings and stimulus parameters requires theories and experiments in which different KDE ratings are not treated interchangeably.     

Distortions of depth-order relations and parallelism in structure from motion

Four experiments related human perception of depth-order relations in structure-from-motion dis-plays to current Euclidean and affine theories of depth recovery from motion. Discrimination between parallel and nonparallel lines and relative-depth judgments was observed for orthographic projections of rigidly oscillating random-dot surfaces. We found that (1) depth-order relations were perceived veridically for surfaces with the same slant magnitudes, but were systematically biased for surfaces with different slant magnitudes. (2) Parallel (virtual) lines defined by probe dots on surfaces with different slant magnitudes were judged to be nonparallel. (3) Relative-depth judgments were internally inconsistent for probe dots on surfaces with different slant magnitudes. It is argued that both veridical performance and systematic misperceptions may be accounted for by a heuristic analysis of the first-order optic flow.     

Interpolation across surface discontinuities in structure from motion Asad Satdpour

Interpolation across orientation discontinuities in simulated three-dimensional (3-D). surfaces was studied in three experiments with the use of structure-from-motion (SFM). displays. The displays depicted dots on two slanted planes with a region devoid of dots (a gap). between them. If extended through the gap at constant slope, the planes would meet at a dihedral edge. Subjects were required to place an SFM probe dot, located within the gap, on the perceived surface. Probe dot placements indicated that subjects perceived a smooth surface connecting the planes rather than a surface with a discontinuity. Probe dot placements varied with slope of the planes, density of the dots, and gap size, but not with orientation (horizontal or vertical). of the dihedral edge or of the axis of rotation. Smoothing was consistent with models of 2-D interpolation proposed by Ullman (1976). and Kellman and Shipley (1991). and with a model of 3-D interpolation proposed by Grimson (1981).     

Perception of three-dimensional angular rotation.

In three experiments, difference thresholds (dLs) and points of subjective equality (PSEs) for three-dimensional (3-D) rotation simulations were examined. In the first experiment, observers compared pairs of simulated spheres that rotated in polar projection and that differed in their structure (points plotted in the volume vs. on the surface), axis of rotation (vertical, y, vs. horizontal, x), and magnitude of rotation (20 degrees-70 degrees). DLs were lowest (7%) when points were on the surface and when at least one sphere rotated around the y-axis and varied with changes in the independent variables. PSEs were closest to objective equality when points were on the surface of both spheres and when both spheres rotated about the x-axis. In the second experiment, subjects provided direct estimates of the rotations of the same spheres. Results suggested a reasonable agreement between PSEs for the indirect-scaling and direct-estimate procedures. The third experiment varied sphere diameter (and therefore mean linear velocity of stimulus elements) and showed that although rotation judgments are biased by mean linear velocity, they are not likely to be made solely on the basis of that information. These and past results suggest a model whereby recovery of structure is conducted by low-level motion-detecting mechanisms, whereas rotation (and other) judgments are based on a higher level representation.     

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.     

Slant perception in near space is categorically biased: Evidence for a vertical tendency

The geographical slants of hills are known to appear quite exaggerated. Here, we examine the visual and haptic perception of the geographical slant of surfaces within reach under full-cue conditions and show that the perceived orientation of even these surfaces is biased. An exaggeration with respect to deviations from horizontal is shown to be present cross-modally. Experiment 1 employed numerical estimation to show the effect for visually observed surfaces, while controlling for verbal numerical bias. Experiment 2 demonstrated that the bias is present even when manual measures show good calibration. Experiment 3 controlled for direction of gaze. Experiment 4 measured the same bias for haptic surfaces. Experiment 5 showed that the bias can also be observed using the nonnumeric task of angle bisection. These results constrain theories of geographical slant perception and appear most consistent with functional scale expansion of deviations from horizontal.     

Visual inertia of rotating 3-D objects

Five experiments were designed to determine whether a rotating, transparent 3-D cloud of dots (simulated sphere) could influence the perceived direction of rotation of a subsequent sphere. Experiment 1 established conditions under which the direction of rotation of a virtual sphere was perceived unambiguously. When a near-far luminance difference and perspective depth cues were present, observers consistently saw the sphere rotate in the intended direction. In Experiment 2, a near-far luminance difference was used to create an unambiguous rotation sequence that was followed by a directionally ambiguous rotation sequence that lacked both the near-far luminance cue and the perspective cue. Observers consistently saw the second sequence as rotating in the same direction as the first, indicating the presence of 3-D visual inertia. Experiment 3 showed that 3-D visual inertia was sufficiently powerful to bias the perceived direction of a rotation sequence made unambiguous by a near-far luminance cue. Experiment 5 showed that 3-D visual inertia could be obtained using an occlusion depth cue to create an unambiguous inertia-inducing sequence. Finally, Experiments 2, 4, and 5 all revealed a fast-decay phase of inertia that lasted for approximately 800 msec, followed by an asymptotic phase that lasted for periods as long as 1,600 msec. The implications of these findings are examined with respect to motion mechanisms of 3-D visual inertia.     

Discrimination learning decreases perceived similarity according to an objective measure

Initial identification discriminations between two sizes and between two slants produced better overall performances on subsequent size and slant same-different discriminations, respectively. This size- and slant-specific transfer was due to an improvement on only the different pairs. Time-duration identification discriminations with the identical stimuli and response assignments improved neither overall same-different performances nor performances on different pairs. A good performance on different pairs relative to same pairs should indicate a low perceived similarity. The literature indicates that A-X and B-Y pairings produce a positive transfer on an A-versus-B discrimination when X and Y are relatively low in similarity, and also indicates that a low perceived (not physical) similarity improves discrimination learning. An increase in salience should have also improved performance on the same pairs. The conclusion: the initial discriminations decreased the perceived similarity of parts (size or slant). This decrease resembles perceptual contrast. A discrimination between two parts also seems to increase the extent to which each part is apprehended as a separate group. Therefore, the conclusion accords with the position that two groups are associated with contrast, including for visibility.     

Optic-flow-based perception of two-dimensional trajectories and the effects of a single landmark

Human observers can detect their heading direction on a short time scale on the basis of optic flow. We investigated the visual perception and reconstruction of visually travelled two-dimensional (2-D) trajectories from optic flow, with and without a landmark. As in our previous study, seated, stationary subjects wore a head-mounted display in which optic-flow stimuli were shown that simulated various manoeuvres: linear or curvilinear 2-D trajectories over a horizontal plane, with observer orientation either fixed in space, fixed relative to the path, or changing relative to both. Afterwards, they reproduced the perceived manoeuvre with a model vehicle, whose position and orientation were recorded. Previous results had suggested that our stimuli can induce illusory percepts when translation and yaw are unyoked. We tested that hypothesis and investigated how perception of the travelled trajectory depends on the amount of yaw and the average path-relative orientation. Using a structured visual environment instead of only dots, or making available additional extra-retinal information, can improve perception of ambiguous optic-flow stimuli. We investigated the amount of necessary structuring, specifically the effect of additional visual and/or extra-retinal information provided by a single landmark in conditions where illusory percepts occur. While yaw was perceived correctly, the travelled path was less accurately perceived, but still adequately when the simulated orientation was fixed in space or relative to the trajectory. When the amount of yaw was not equal to the rotation of the path, or in the opposite direction, subjects still perceived orientation as fixed relative to the trajectory. This caused trajectory misperception because yaw was wrongly attributed to a rotation of the path: path perception is governed by the amount of yaw in the manoeuvre. Trajectory misperception also occurs when orientation is fixed relative to a curvilinear path, but not tangential to it. A single landmark could improve perception. Our results confirm and extend previous findings that, for unambiguous perception of ego-motion from optic flow, additional information is required in many cases, which can take the form of fairly minimal, visual information.     

The effect of perceived distance on perceived movement

Equations were developed to predict the apparent motion of a physically stationary object resulting from head movement as a function of errors in the perceived distances of the object or of its parts. These equations, which specify the apparent motion in terms of relative and common components, were applied to the results of two experiments. In the experiments, the perceived slant of an object was varied with respect to its physical slant by means of perspective cues. In Experiment I, O reported the apparent motion and apparent distance of each end of the object independently. The results are consistent with the equations in terms of apparent relative motion, but not in terms of apparent common motion. The latter results are attributed to the tendency for apparent relative motion to dominate apparent common motion when both are present simultaneously. In Experiment II, a direct report of apparent relative motion (in this case, apparent rotation) was obtained for illusory slants of a physically frontoparallel object. It was found that apparent rotations in the predicted direction occurred as a result of head motion, even though under these conditions no rotary motion was present on the retina.     

A test of the gravity lens theory.

Naito and Cole [1994, in Contributions to Mathematical Psychology: Psychometrics and Methodology Eds G H Fischer and D Laming (New York: Springer)] provide a configuration which they describe as the Gravity Lens illusion. In this configuration, four small dots are presented in proximity to four large disks, and one is asked to compare the slope of an imaginary line which connects one pair of dots with the slope of a line which connects the other pair. In fact the slopes are the same, i.e. their axes are parallel, but because of the positioning of the large disks they appear to be at different orientations. Naito and Cole propose that the perceptual bias is analogous to the effects of gravity on the metrics of physical space, such that mental projections in the vicinity of a disk (or an open circle) are distorted just as the path of light is bent as it passes a massive body such as a star. Here we provide a simple test of this concept by having subjects judge alignments of dots which lie near tangents to a circle. Subjects were asked to project straight lines through pairs of stimulus dots, selecting and marking points in open space which were collinear with each pair. As would be predicted by the Gravity Lens theory, the locations selected by subjects were displaced from straight lines. However, the error magnitudes were substantially larger for judgments of dot pairs which had an oblique alignment, as compared with dot pairs which were aligned with a cardinal axis. This differential of effect as a function of stimulus orientation is not predicted by the gravity concept.     

Effects of circular motion on judgment of rotation direction and depth order in visual motion

Abstract:  The rotation direction and depth order of a rotating sphere consisting of random dots often reverses while it is viewed under orthographic projection. However, if a short viewing distance is simulated under perspective projection, the correct rotation direction can be perceived. There are two motion cues for the rotation direction and depth order. One is the speed cue; points with higher velocities are closer to the observer. The other is the vertical motion cue; vertical motion is induced when the dots recede from or approach the observer. It was examined whether circular motion, which does not have any depth information but induces vertical velocities, masks the vertical motion cue. In Experiment 1, the effects of circular motion on the judgment of the rotation direction of a rotating sphere were examined. The magnitude of the two cues (the speed cue and the vertical velocity cue) as well as the angular speed of circular motion was varied. It was found that the performance improved as the vertical velocity increased and that the speed cue had slight effects on the judgment of the rotation direction. It was also found that the performance worsened as the angular speed of the circular motion was increased. In Experiment 2, the effects of circular motion on depth judgment of a rotating half sphere were investigated. The performance worsened as the angular speed of the circular motion increased, as in Experiment 1. These results suggest that the visual system cannot compensate perfectly for circular motion for the judgment of the rotation direction and depth order.     

Intraretinal transfer and the function of the optic lobes in octopus

A method of training octopuses was developed which allowed the part of the retina stimulated to be controlled during training and subsequent transfer tests. Using this method the following results were obtained, (1) There was more stimulus generalization when the edge of the retina was stimulated than there was when the centre of the retina was stimulated, suggesting that discrimination is better with the centre of the retina. (2) Intraretinal transfer is more nearly complete than interocular transfer. (3) Continuity of the optic lobes between the projection areas of different parts of the retina is necessary if receptor transfer is to occur between them. The optic lobes are therefore involved in visual learning in the situation used.     

Measurement and modelling of perceived slant in surfaces represented by freely viewed line drawings

Simple pictures under everyday viewing conditions evoke impressions of surfaces oriented in depth. These impressions have been studied by measuring the slants of perceived surfaces, with probes (rotating arrowheads) designed to respect the distinctive character of depicted scenes. Converging arguments indicated that the perceived orientation of the probes was near theoretical values. A series of experiments showed that subjects formed well-defined impressions of depicted surface orientation. The literature suggests that perceived objects might be 'flattened', but that was not the general rule. Instead, both mean slant and uncertainty fitted models in which slant estimates are derived in a relatively straightforward way from local relations in the picture. Simplifying pictures tended to make orientation estimates less certain, particularly away from the natural anchor points (vertical and horizontal). The shape of the object affected all aspects of the observed-object/percept relationship. Individual differences were large, and suggest that different individuals used different relationships as a basis for their estimates. Overall, data suggest that everyday picture perception is strongly selective and weakly integrative. In particular, depicted slant is estimated by finding a picture feature which will be strongly related to it if the object contains a particular regularity, not by additive integration of evidence from multiple directly and indirectly relevant sources.     

The perception of briefly exposed point-sources of light

Point-sources of light (dots) were exposed for 10 to 50 msec, before five dark-adapted subjects in a dimly illuminated room. During voluntary fixation with one eye, the target was exposed some 10° on the nasal side of the optic axis. The intensity X duration of all targets was 2 X threshold and they consisted of either a single dot, or a pair of dots separated by a distance that was less than that required for two-point discrimination. In two-thirds of trials both the single-dot and the two-dot targets were perceived as short thin lines of various orientation. Although individual percepts were unpredictable, there was a preferred or most likely orientation for responses to the single-dot target; this was near to the horizontal for all five subjects. There was no significant difference between the preferred orientations for single-dot targets tested at sites more than 1° apart in the visual field. When two single-dot targets, separated by about 1°, were exposed simultaneously, the orientations of the perceived lines sometimes differed by as much as 80°; occasionally, one target was reported as a dot while the other was seen as a thin line. If the single-dot was briefly exposed between two continuously visible and parallel straight lines, the target usually appeared as a thin line, parallel to the framing lines. Some of these results appear to be consistent with the hypothesis that the human visual cortex, like that of the cat and monkey, contains neurones that are orientation specific.