Spatio-temporal tuning of motion coherence detection at different luminance levels.

We studied effects of dark adaptation on spatial and temporal tuning for motion coherence detection. We compared tuning for step size and delay for moving random pixel arrays (RPAs) at two adaptation levels, one light adapted (50 cd/m(2)) and the other relatively dark adapted (0.05 cd/m(2)). To study coherence detection rather than contrast detection, RPAs were scaled for equal contrast detection at each luminance level, and a signal-to-noise ratio paradigm was used in which the RPA is always at a fixed, supra-threshold contrast level. The noise consists of a spatio-temporally incoherent RPA added to the moving RPA on a pixel-by-pixel basis. Spatial and temporal limits for coherence detection were measured using a single step pattern lifetime stimulus, in which patterns on alternate frames make a coherent step and are being refreshed. Therefore, the stimulus contains coherent motion at a single combination of step size and delay only. The main effect of dark adaptation is a large shift in step size, slightly less than the adjustment of spatial scale required for maintaining equal contrast sensitivity. A similar change of preferred step size occurs also for scaled stimuli at a light-adapted level, indicating that the spatial effect is not directly linked to dark adaptation, but more generally related to changes in the available low-level spatial information. Dark-adaptation shifts temporal tuning by about a factor of 2. Long delays are more effective at low luminance levels, whereas short delays no longer support motion coherence detection. Luminance-invariant velocity tuning curves, as reported previously [Lankheet, M.J.M., van Doorn, A.J., Bouman, M.A., & van de Grind, W.A. (2000) Motion coherence detection as a function of luminance in human central vision. Vision Research, 40, 3599-3611], result from recruitment of different sets of motion detectors, and an adjustment of their temporal properties.

Ambiguity and the 'mental eye' in pictorial relief.

Photographs of scenes do not determine scenes in the sense that infinitely many different scenes could have given rise to any given photograph. In psychophysical experiments, observers have (at least partially) to resolve these ambiguities. The ambiguities also allow them to vary their response within the space of 'veridical' responses. Such variations may well be called 'the beholder's share' since they do not depend causally on the available depth cues. We determined the pictorial relief for four observers, four stimuli, and four different tasks. In all cases we addressed issues of reliability (scatter on repeated trials) and consistency (how well the data can be explained via a smooth surface, any surface). All data were converted to depth maps which allows us to compare the relief from the different operationalisations. As expected, pictorial relief can differ greatly either between observers (same stimulus, same task) or between operationalisations (same observer, same stimulus). However, when we factor out the essential ambiguity, these differences almost completely vanish and excellent agreement over tasks and observers pertains. Thus, observers often resolve the ambiguity in idiosyncratic ways, but mutually agree--even over tasks--in so far as their responses are causally dependent on the depth cues. A change of task often induces a change in 'mental perspective'. In such cases, the observers switch the 'beholder's share', which resolves the essential ambiguity through a change in viewpoint of their 'mental eye'.

Motion coherence detection as a function of luminance level in human central vision.

We studied the changes and invariances of foveal motion detection upon dark adaptation. It is well-documented that dark adaptation affects both spatial and temporal aspects of visual processing. The question we were interested in is how this alters motion coherence detection for moving random texture. To compare motion sensitivity at different adaptation levels, we adjusted the viewing distance for equal detectability of a stationary pattern. At these viewing distances we then measured velocity tuning curves for moving random pixel arrays (RPAs). Mean luminance levels ranged from 50 down to 0.005 cd m-2. Our main conclusion is that foveal velocity tuning is amazingly close to luminance-invariant, down to a level of 0.05 cd m-2. Because different viewing distances, and hence, retinal image sizes were used, we performed two control experiments to assess variations of these two parameters separately. We examined the effects of retinal inhomogeneities using discs of different size and annuli filled with RPAs. Our conclusion is that the central visual field, including the near periphery is still rather homogeneous for motion detection at 0.05 cd m-2, but the fovea becomes unresponsive at the lowest luminance level. Variations in viewing distance had marked effects on velocity tuning, both at the light adapted level and the 0.05 cd m-2 level. The size and type of these changes indicated the effectiveness of distance scaling, and show that deviations from perfect invariance of motion coherence detection were not due to inaccurate distance scaling.

Direct measurement of the curvature of visual space.

We consider the horizontal plane at eye height, that is all objects seen at the horizon. Although this plane visually degenerates into a line in the visual field, the 'depth' dimension nevertheless gives it a two-dimensional structure. We address the problem of intrinsic curvature of this plane. The classical geometric method is based on Gauss's original definition: The angular excess in a triangle equals the integral curvature over the area of the triangle. Angles were directly measured by a novel method of exocentric pointing. Experiments were performed outside, in the natural environment, under natural viewing conditions. The observers were instructed not to move from a set location and to maintain eye height, but were otherwise free to perform eye, head, and body movements. We measured the angular excess for equilateral triangles with sides of 2-20 m, the vantage position at the barycenter. We found angular excesses and deficits of up to 30 degrees. From these data we constructed the metric. The curvature changes from elliptic in near space to hyperbolic in far space. At very large distances the plane becomes parabolic.

Motion detection from photopic to low scotopic luminance levels.

In this study we quantify the influence of adaptation luminance on the threshold for direction-detection in coherently moving random-pixel arrays (RPAs). Square RPAs of a constant rms-contrast (35%) were used and we determined their 'critical' or threshold-width Wc. Mean retinal illuminances were varied in 13 steps of 0.5 log unit from the low photopic range (screen luminance 0.3 cd/m2) down to 6 log units attenuation, which appeared to be about the absolute threshold of vision under the conditions of our experiment. Moving RPAs were presented at six retinal locations (0, 3, 6, 12, 24 and 48 degrees) from the fovea to the far periphery in the temporal visual field of the right eye of three experienced observers (the authors). In order to ensure an honest comparison between these very disparate conditions, the spatial dimensions (including speed) were scaled according to the acuity, as measured separately for each of the viewing-conditions and observers. Acuity scaling proves to equate the performance for all eccentricities and luminance levels rather well. The fovea is special, but only in the sense that the absolute threshold for light detection is reahed earlier than in peripheral regions. In all other respects foveal results follow the pattern found for peripheral locations. Two different regimes can be discerned in the data, one for high and one for low speeds. In the low speed range Wc is almost constant, regardless of luminance level or eccentricity. The critical 'crossing-time' Tc for any pixel starting at one end of the stimulus and leaving at the opposite end is therefore inversely proportional to velocity in the low-speed range (time-velocity reciprocity). At medium-to-high speeds Wc increases linearly with velocity, so Tc is constant. This constant (minimum) value of Tc differs between subjects, but in all subjects it increases somewhat with decreasing luminance level, even for our acuity-scaled stimuli. The different behaviour for low and high speeds [reported before for photopic viewing conditions by van de Grind, W. A., van Doorn, A. J., & Koenderink, J. J. (1983. Journal of the Optical Society of America, 73, 1674-1683) and van de Grind, W. A., Koenderink, J. J., & van Doorn A. J. (1986. Vision Research, 26, 797-810)] proves to hold from photopic to low scotopic luminance ranges, provided the stimuli are scaled according to acuity. We draw the general conclusion that movement detection is a very robust process that tolerates extremely low retinal illuminance levels. Moreover, the visual system appears to use the same processing principles in combination with an acuity-scaled architecture under all adaptation states and at all eccentricities.

The visual contour in depth.

We asked subjects to match points on the surface of a smooth three-dimensional (3-D) shape with points on the surface of another object that was geometrically identical to the first object but was placed in a different pose, was differently textured, and was differently shaded. In all cases, the fiducial point was on the rim of one of the objects (i.e., the boundary of the visible region of the surface), whereas the matching point was well within the silhouette of the other object. This allowed us to draw (preliminary) conclusions concerning the way monocular human observers are able to handle the neighborhood of the rim, where the local slant assumes arbitrarily high values. All experiments were done in real space with real objects (no computer-simulated scenes), the points being indicated with laser beam illumination. The subject was given control over the direction of the laser beams and was thus able to perform the task by adjustment from the vantage position. We studied both consistency (whether the subject's judgments were invariant against changes of relative pose) and veridicality (whether the depth of the visual contour as calculated from the settings agreed with the true distance as measured by mechanical means). Subjects caught much of the 3-D structure of the contour but did deviate appreciably and apparently idiosyncratically from the true geometry.

Simulating the detection of first-order optical flow components.

Thresholds for the detection of rotation and divergence in the presence of a translational component in sparse random dot patterns are determined for human observers and two computer algorithms. The algorithms only make use of local velocity directions and not of local velocity magnitude (speed). The results show that psychophysical performance in this task can be well described without the need of specialized mechanisms tuned to either rotation or divergence. Possibly, integration of information over more than two frames occurs for low velocities. For high velocities the correspondence problem seems to limit performance.

Effects of changing viewing conditions on the perceived structure of smoothly curved surfaces.

Observers' perceptions of a male and a female torso were investigated using monocular and stereoscopic images under varying conditions of illumination. Observers judged the shapes of these torsos by adjusting a gauge figure to estimate the local slant and tilt at numerous probe points arranged in a lattice over the torso's surface. The results revealed that the judged surfaces in the monocular and stereoscopic conditions were related by an affine stretching transformation in depth that accounted for approximately 95% of the between-condition variance. There was also a strong affine component between the judgments obtained for the different illumination directions, although a further analysis of the residuals indicated that changing the direction of illumination influenced perceived structure in a piecewise manner.

Pictorial surface attitude and local depth comparisons.

We measured local surface attitude for monocular pictorial relief and performed pairwise depth-comparison judgments on the same picture. Both measurements were subject to internal consistency checks. We found that both measurements were consistent with a relief (continuous pictorial surface) interpretation within the session-to-session scatter. We reconstructed the pictorial relief from both measurements separately, and found results that differed in detail but were quite similar in their basic structures. Formally, one expects certain geometrical identities that relate range and attitude data. Because we have independent measurements of both, we can attempt an empirical verification of such geometrical identities. Moreover, we can check whether the statistical scatter in the data indicates that, for example, the surface attitudes are derivable from a depth map or vice versa. We estimate that pairwise depth comparisons are an order of magnitude less precise than might be expected from the attitude data. Thus, the surface attitudes cannot be derived from a depth map as operationally defined by our methods, although the reverse is a possibility.

Perturbation study of shading in pictures.

Pictorial relief was measured for a series of pictures of a smooth solid object. The scene was geometrically identical for all pictures, but the rendering was different. Whereas all pictures were monochrome full-scale photographs, they were taken under different illuminations of the scene, the source being frontal and displaced towards either the upper left, the upper right, the lower right, or the lower left. It was found that different illuminations led to significantly different, systematic alterations of pictorial relief. It is concluded that though shape constancy under changes in illumination might be said to rule in the first rough approximation, the deviations from true constancy are indeed both significant and systematic. Different from either stimulus-reduction or cue-conflict paradigms, this 'perturbation analysis' shows that shading is used as an important source of information even if the particular illumination appears to be ignored at first blush. For all subjects, brighter parts in the stimulus were consistently interpreted as being nearer in pictorial space, both for the global layout and for the subsidiary relief.

Shape constancy in pictorial relief.

Pictorial relief was measured for a series of pictures of a smooth solid object. The scene was geometrically identical (ie the perspective of the three-dimensional scene remained the same) for all pictures, the rendering different. Some of the pictures were monochrome full-scale photographs taken under different illumination of the scene. Also included were a silhouette (uniform black on uniform white) and a 'cartoon'-style rendering (visual contour and key linear features rendered in thin black line on a uniform white ground). Two subjects were naive and started with the silhouette, saw the cartoon next, and finally the full-scale photographs. Another subject had seen the object and did the experiment in the opposite sequence. The silhouette rendering is impoverished, but has considerable relief with much of the basic shape. The cartoon rendering yields well-developed pictorial relief, even for the naive subjects. Shading adds only small local details, but different illumination produces significant alterations of relief. It is concluded that shape constancy under changes in illumination is dominant throughout, but that the (small) deviations from true constancy reveal the effect of cues such as shading in a natural setting. Such a ¿perturbation analysis' appears more promising than either stimulus-reduction or cue-conflict paradigms.

Depth relief.

A study is reported of the depth relief in a simple three-dimensional scene consisting of a white, rough sphere on a planar support, illuminated in a natural manner. Viewing conditions included monocular and binocular as well as 'synoptical' viewing. In the synoptical condition the eyes are optically superimposed. The local surface attitude was probed via a gauge figure that had to appear as a circle painted upon the surface of the object. The measurements allow a reconstruction of the depth relief, which can be compared with the (known) range map. Idiosyncratic differences between three subjects were found that are the exact reverse of what was found for these same subjects for the case of pictorial relief reported in an earlier paper. Apparently the subjects put different weights on sources of sometimes conflicting, sometimes corroborative evidence. The relief is deepest for binocular vision, flatter for monocular vision, and flatter still for synoptical vision. Deviations from veridicality that cannot be explained by mere depth scaling exist and may be due to the nature of the monocular cues.

Detection of vorticity in optical flow fields.

Psychophysical thresholds for the detection of vorticity in the presence of a translational component are determined for human observers. Stimuli consist of sparse random-dot flow patterns. The detection of vorticity depends critically on the translational component. The curvature of the flow lines, however, cannot be the only factor limiting human performance. On the basis of a comparison with an ideal detector, it is found that for small vorticities (< 0.5 rad/s) humans typically use the stimulus information in an optimal manner. For higher vorticities performance gets worse, possibly owing to matching problems. Lifetime and number of dots have hardly any influence on performance. Although this indicates that the human observer can already perform the task by using only local information, it does not imply that global information is disregarded. If the stimulus is disturbed locally, global information is used to full extent.

On so-called paradoxical monocular stereoscopy.

Human observers are apparently well able to judge properties of 'three-dimensional objects' on the basis of flat pictures such as photographs of physical objects. They obtain this 'pictorial relief' without much conscious effort and with little interference from the (flat) picture surface. Methods for 'magnifying' pictorial relief from single pictures include viewing instructions as well as a variety of monocular and binocular 'viewboxes'. Such devices are reputed to yield highly increased pictorial depth, though no methodologies for the objective verification of such claims exist. A binocular viewbox has been reconstructed and pictorial relief under monocular, 'synoptic', and natural binocular viewing is described. The results corroborate and go beyond early introspective reports and turn out to pose intriguing problems for modern research.

Inhomogeneity and anisotropies for motion detection in the monocular visual field of human observers.

Signal-to-noise-ratio (SNR) thresholds were measured for the detection of coherent motion in moving random pixel arrays of constant root-mean-square contrast (35%) and constant average luminance (48 cd/m2) for 8 or 16 directions of motion at 25 positions in the visual field of the right eye. Five observers took part in this perimetric study of motion detection. The 24 eccentric positions were chosen on 8 equally spaced radial lines at the eccentricities 6, 24, and 48 degrees, the 25th position was centred on the fovea. At these positions we analysed the threshold SNR-value as a function of motion direction alpha. A significant modulation of the threshold with alpha is called an anisotropy. Anisotropies were found for low to medium velocities at positions on and near the vertical meridian, where the thresholds proved to be highest for vertical motion directions (up or down). On the horizontal meridian no significant anisotropies were found. Also on the oblique radials anisotropies were found, especially at 225 degrees (lower nasal quadrant of the visual field, upper temporal quadrant of the retina), but these were milder than those on the vertical meridian. The diameter of the stimulus is an important parameter and its influence was explored, albeit incompletely. Also inhomogeneities were found. This is defined as a consistent modulation of the threshold SNR-value with position A, the position along an equi-eccentricity circle (A-inhomogeneity), or with eccentricity E (E-inhomogeneity) or both. A simple acuity-scaling optimized for the nasal retina takes care of most of the E-inhomogeneity, but an A-inhomogeneity stays rather prominent. It too is characterized by higher thresholds near the vertical meridian than near the horizontal meridian. The findings suggest that iso-threshold curves are elliptical or egg-shaped with their long axis on the horizontal meridian and shifted somewhat out of naso-temporal symmetry towards the nasal half of the retinal field. As with the anisotropies the inhomogeneity grows in amplitude for decreasing velocity below medium velocity values of 1-2 pixels/frame, but in contradistinction to the anisotropies it is present and even increases in amplitude for increasing velocities above these medium values of 1-2 pixels/frame as well. The results are discussed in the light of other perimetric studies of motion detection and acuity, in the light of a model postulating the cooperation of groups of velocity-tuned bilocal motion detectors, and in the light of recent ideas on structure and function of primate cortical areas and processing streams.

Surface perception in pictures.

Subjects adjusted a local gauge figure such as to perceptually "fit" the apparent surfaces of objects depicted in photographs. We obtained a few hundred data points per session, covering the picture according to a uniform lattice. Settings were repeated 3 times for each of 3 subjects. Almost all of the variability resided in the slant; the relative spread in the slant was about 25% (Weber fraction). The tilt was reproduced with a typical spread of about 10 degrees. The rank correlation of the slant settings of different observers was high, thus the slant settings of different subjects were monotonically related. The variability could be predicted from the scatter in repeated settings by the individual observers. Although repeated settings by a single observer agreed within 5%, observers did not agree on the value of the slant, even on the average. Scaling factors of a doubling in the depth dimension were encountered between different subjects. The data conformed quite well to some hypothetical fiducial global surface, the orientation of which was "probed" by the subject's local settings. The variability was completely accounted for by single-observer scatter. These conclusions are based upon an analysis of the internal structure of the local settings. We did not address the problem of veridicality, that is, conformity to some "real object."

Viewing-distance invariance of movement detection.

Since visual movement information is often presented in electronic displays or films it is amazing that there is a paucity of research on the influence of viewing distance on motion detection in cinematograms. We report a relatively high degree of detection constancy with changing viewing distance for coherent motion in random-pixel cinematograms. A constant performance irrespective of viewing-distance is called 'distance-invariance' and for motion detection it proves to hold reasonably well for a relatively wide range of viewing distances both for foveal and eccentric vision. The limits of this viewing-distance invariance are explored as a function of screen velocity. Detection performance is quantified by a threshold signal-to-noise-ratio (SNR-) value, S, which is determined as a function of velocity for a range of viewing distances from 53 to 13,476 mm for foveal vision and from 60 to 1925 mm at 24 degrees eccentricity on the nasal horizontal meridian of the right eye's retina. The data can be explained, at least qualitatively, by a model in which a spatial-resolution stack has a stack of velocity-tuned motion detectors at every resolution layer. Such a 'stack-of-stacks' model is in line with proposals for contrast-detection stack-models, but it suggests that the usual hypothesis that motion perception is based on the activity of two separate systems, the short-range and the long-range system, might be superfluous. This two-systems distinction was largely based on the different performance found for moving random dot patterns and moving form-defined stimuli. A moving random pixel array viewed at very close range (e.g. 6 cm) presents the subject with relatively large almost square 'blobs', which are less dissimilar from the phi-stimuli used in classic motion perception studies than random dot stimuli at the usual medium to large viewing distances. It leads to maximum displacement threshold (Dm-) values that are not untypical of the 'long-range' system, but by gradually increasing the viewing-distance and thus decreasing the pixel-size a continuous change is found from typical long-range to typical short-range values of Dm. The two-systems distinction for motion detection appears to refer to the stimulus rather than to the visual system: The motion-detection system might be forced into a local or a global 'mode of operation' by the choice of stimulus.

Affine structure from motion.

A mobile observer samples sequences of narrow-field projections of configurations in ambient space. The so-called structure-from-motion problem is to infer the structure of these spatial configurations from the sequence of projections. For rigid transformations, a unique metrical reconstruction is known to be possible from three orthographic views of four points. However, human observers seem able to obtain much shape information from a mere pair of views, as is evident in the case of binocular stereo. Moreover, human observers seem to find little use for the information provided by additional views, even though some improvement certainly occurs. The rigidity requirement in its strict form is also relaxed. We indicate how solutions of the structure-from-motion problem can be stratified in such a way that one explicitly knows at which stages various a priori assumptions enter and specific geometrical expertise is required. An affine stage is identified at which only smooth deformation is assumed (thus no rigidity constraint is involved) and no metrical concepts are required. This stage allows one to find the spatial configuration (modulo an affinity) from two views. The addition of metrical methods allows one to find shape from two views, modulo a relief transformation (depth scaling and shear). The addition of a third view then merely serves to settle the calibration. Results of a numerical experiment are discussed.

Motion detection in the presence of local orientation changes.

To investigate the orientation selectivity of motion detectors, we measured the perception of horizontal apparent motion of dense patterns of line elements with randomized orientation. Horizontal motion of these displays became invisible when the simultaneous rotation of the line elements exceeded a critical rate (pc). The value of pc increased for higher horizontal velocities, approximately according to a square-root relation. In a direct test of orientation selectivity, the discrimination of horizontal motion direction disappeared when the orientation change per horizontal jump exceeded 30 deg. Thus, for the perception of the global flow the orientation change should not exceed a critical angle during the traverse of a critical distance. The critical distance increases according to a square-root relation as a function of horizontal velocity. These results strongly suggest that bilocal motion detectors are involved in horizontal motion detection and that these detectors are selective for orientation. The properties of these detectors, such as the orientation sensitivity that is reported in this paper, seem highly relevant to the perception of coherent motion.