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Any computation of metric surface structure from horizontal disparities depends on the viewing geometry, and analysing this dependence allows us to narrow down the choice of viable schemes. For example, all depth-based or slant-based schemes (i.e. nearly all existing models) are found to be unrealistically sensitive to natural errors in vergence. Curvature-based schemes avoid these problems and require only moderate, more robust view-dependent corrections to yield local object shape, without any depth coding. This fits the fact that humans are strikingly insensitive to global depth but accurate in discriminating surface curvature. The latter also excludes coding only affine structure. In view of new adaptation results, our goal becomes to directly extract retinotopic fields of metric surface curvatures (i.e. avoiding intermediate disparity curvature). To find a robust neural realisation, we combine new exact analysis with basic neural and psychophysical constraints. Systematic, step-by-step 'design' leads to neural operators which employ a novel family of 'dynamic' receptive fields (RFs), tuned to specific (bi-)local disparity structure. The required RF family is dictated by the non-Euclidean geometry that we identify as inherent in cyclopean vision. The dynamic RF-subfield patterns are controlled via gain modulation by binocular vergence and version, and parameterised by a cell-specific tuning to slant. Our full characterisation of the neural operators invites a range of new neurophysiological tests. Regarding shape perception, the model inverts widely accepted interpretations: It predicts the various types of errors that have often been mistaken for evidence against metric shape extraction.

Recent investigations have indicated that human perception of the trajectory of objects approaching in the horizontal plane is precise but biased away from straight ahead. This is remarkable because it could mean that subjects perceive objects that approach on a collision course as missing the head. Approach within the horizontal plane through the eyes and the fixation point (the plane of regard) is special, as general motions will also have a component of motion perpendicular to the plane of regard. Thus, we investigated three-dimensional motion perception in the vicinity of the head, including vertical components. Subjects judged whether an object that moved in the mid-sagittal plane was going to hit below or above a well-known reference point on the face like the center of the chin or the forehead (perceptual task). Tactile and proprioceptive information about the reference point significantly improved precision. Precision did not change with distance of the approaching target or with fixation direction. Bias was virtually absent for these vertical motions. When subjects pointed with their index finger to the perceived location of impact on their face (visuo-motor task), they overestimated (1.7 cm) the horizontal eccentricity of the point of impact (pointing task). Vertical bias, however, was again virtually absent. Interestingly, when trajectories intersected the plane of regard, higher precision was observed in the perceptual task regardless of the other conditions. In contrast, neither bias nor precision of the pointing task changed significantly when the trajectories intersected the plane of regard. When asked to point to the location where a trajectory intersected the plane of regard, subjects overestimated the depth component of this intersection location by about 3 cm. The absence of perceptual and pointing bias in the vertical direction in contrast to the clear horizontal bias suggests that different (combinations of) cues are used to judge these components of the trajectory of an approaching object. The results of our perceptual task suggest a role for somatosensory signals in the visual judgment of impending impact.

When we fixate an object in space, the rotation centers of the eyes, together with the object, define a plane of regard. People perceive the elevation of objects relative to this plane accurately, irrespective of eye or head orientation (Poljac et al. (2004) Vision Res, in press). Yet, to create a correct representation of objects in space, the orientation of the plane of regard in space is required. Subjects pointed along an eccentric vertical line on a touch screen to the location where their plane of regard intersected the touch screen positioned on their right. The distance of the vertical line to the subject's eyes varied from 10 to 40 cm. Subjects were sitting upright and fixating one of the nine randomly presented directions ranging from 20 degrees left and down to 20 degrees right and up relative to their straight ahead. The eccentricity of fixations relative to the pointing location varied by up to 40 degrees . Subjects underestimated the elevation of their plane of regard (on average by 3.69 cm, SD=1.44 cm), regardless of the fixation direction or pointing distance. However, when the targets were shown on a display mounted in a table, to provide support of the subject's hand throughout the trial, subjects pointed accurately (average error 0.3 cm, SD=0.8 cm). In addition, head tilt 20 degrees to the left or right did not cause any change in accuracy. The bias observed in the first task could be caused by maintained tonus in arm muscles when the arm is raised, that might interfere with the transformation from visual to motor signals needed to perform the pointing movement. We conclude that the plane of regard is correctly localized in space. This may be a good starting point for representing objects in head-centric coordinates.

Manipulation of objects around the head requires an accurate and stable internal representation of their locations in space, also during movements such as that of the eye or head. For far space, the representation of visual stimuli for goal-directed arm movements relies on retinal updating, if eye movements are involved. Recent neurophysiological studies led us to infer that a transformation of visual space from retinocentric to a head-centric representation may be involved for visual objects in close proximity to the head. The first aim of this study was to investigate if there is indeed such a representation for remembered visual targets of goal-directed arm movements. Participants had to point toward an initially foveated central target after an intervening saccade. Participants made errors that reflect a bias in the visuomotor transformation that depends on eye displacement rather than any head-centred variable. The second issue addressed was if pointing toward the centre of a wide-field expanding motion pattern involves a retinal updating mechanism or a transformation to a head-centric map and if that process is distance dependent. The same pattern of pointing errors in relation to gaze displacement was found independent of depth. We conclude that for goal-directed arm movements, representation of the remembered visual targets is updated in a retinal frame, a mechanism that is actively used regardless of target distance, stimulus characteristics or the requirements of the task.

When we move along we frequently look around. How quickly and accurately can we gaze in the direction of heading? We studied the temporal aspects of heading perception in expanding and contracting patterns simulating self-motion. Center of flow (CF) eccentricity was 15 degrees. Subjects had to indicate the CF by making a saccade to it. A temporal constraint on the response time was introduced, because stimuli were presented briefly (1 s). On average, subjects needed two saccades to find the CF. Initial saccades covered about 50-60% of the distance between the fixation point and the CF. Subjects underestimated the eccentricity of the CF. The systematic radial error ranged from -2.4 degrees to -4.9 degrees. The systematic tangential error was small (about 0.5 degree). The variable radial error ranged from 2.7 degrees to 4.6 degrees. We found a relation between saccade onset time and saccade endpoint error. Saccade endpoint error decreased with increasing saccade onset time, suggesting that saccades were often fired before the heading processing had been completed. From the saccade onset times, saccade endpoint errors and an estimate for the saccadic dead time (interval prior to the saccade during which modification is impossible 70 ms), we estimated the heading processing time (HPT 0.43 s). In three out of four subjects, HPT was longer for trials simulating backward movement than for trials simulating forward movement. For each saccade we determined whether it reduced the distance error. The second saccade reduced the error more effectively per time unit than the initial saccade. On the basis of this finding, we suggest that visual processing that occurs during the saccadic dead time of the first saccade is used in the preparation of the second saccade.

We systematically studied the effect of saccade direction and saccade starting position on the velocity profile of the saccade. Saccades were made between targets placed at optical infinity by dichoptic presentation. This arrangement was chosen to evoke conjugate eye movements. Eye movements were recorded binocularly, including torsion. Horizontal and vertical movements of the eyes are strongly correlated (r > or = 0.95) during the saccade, torsional movements are much less so (r approximately 0.67). Listing's law would predict that the three-dimensional versional velocity of the eye would be located in a plane that is tilted out of Listing's plane by an amount that depends on the saccade's starting position (half angle rule). Taking together all saccades that started from the same initial position a plane could be fitted through the velocity vectors. However, this plane was tilted less relative to Listing's plane than predicted by the half angle rule. The deviation was especially large for the yaw component of the tilt (56% of predicted). For the pitch component the prediction was better (81% of predicted). In addition, we find that the torsional velocity during the fast "intrasaccadic" part of the motion can be unequal in the two eyes. The implications for three-dimensional models of saccadic control are discussed.

Our tendency to constantly shift our gaze and to pursue moving objects with our eyes introduces obvious problems for judging objects' velocities. The present study examines how we deal with these problems. Specifically, we examined when information on rotations (such as eye movements) is obtained from retinal, and when from extra-retinal sources. Subjects were presented with a target moving across a textured background. Moving the background allowed us to manipulate the retinal information on rotation independently of the extra-retinal information. The subjects were instructed to pursue the target with their eyes. At some time during the presentation the target's velocity could change. We determined how various factors influence a subject's perception of such changes in velocity. Under more or less natural conditions, there was no change in perceived target velocity as long as the relative motion between target and background was maintained. However, experiments using conditions that are less likely to occur outside the laboratory reveal how extra-retinal signals are involved in velocity judgements.

Two superimposed gratings, which differ in orientation and move independently, combine into a coherently moving plaid if the component gratings are similar. The effect on the plaid motion percept of the addition of texture to each grating was investigated. The texture disambiguates the motion of each component grating. Under the assumption of recombination of first-stage motion detectors into a second stage, which becomes available to perception, one would expect the perceived motion direction of the plaid to change as a result of texture addition. Subjects perceived the oblique motion direction of textured bars of a single orientation correctly. This occurred for texture details with dimensions down to the resolution limit in the fovea (1 min of arc). Two bar patterns with fine texture (1 min of arc details) which differ in orientation were perceived to cohere into a plaid. The plaid's motion direction, however, was independent of the parallel motion components of the bars. For coarser textures (2 and 4 min of arc details) the bar patterns were perceived to slide past one another. In addition, we found that the plaid motion percept occurred less frequently for longer motion sequences, wider bars and for a combination of the component textures at the intersections which is compatible with partial transparency of the bars. These results do not support the two-stage model of Adelson and Movshon (1982), where only the motion component perpendicular to each grating orientation is encoded and where the perception of the plaid motion results from "recombination" of these perpendicular motion components. The data are more in line with a model where first-stage motion detectors are orientation selective but without the restriction that their preferred direction of motion is perpendicular to their preferred orientation. In the second stage it is proposed that combination occurs across the orientation dimension only. This preserves the direction of motion "labels" at the output of the second stage and allows for representation of transparent as well as coherent plaid motion at this stage of processing.

Humans do not confound the motion of shadows cast upon a surface with the motion of the surface itself, although schemes that propose recombination of orientation-selective motion signals into a rigid motion percept of two-dimensional patterns would predict that they should do so. We propose a simple scheme that avoids recombination and instead attributes perception of two-dimensional pattern motion to the activation of orientation-selective end-stopped units that operate on the logarithm of the luminance. The proposed units respond to the change of contrast along a line, which typically occurs at an intersection. They are not active, however, when a shadow border intersects the edge of an object, because contrast does not change along either of these edges. Thus, end-stopped units signal the motion of transparent intersections weakly or not at all, and the independent motions of the shadow border and the object prevail. We tested two implications of this scheme, using plaids with variable intersection luminance. First, when the intersection luminance was such that it kept the contrast along the intersecting lines nearly constant, the sensitivity for the rigid plaid's direction of motion was minimal, and the sliding motion of the components prevailed. This occurred for light bars on dark backgrounds and for dark bars on light backgrounds. Thus, the effect of the intersection's luminance on the balance between the percepts of rigid-plaid motion and the motion of sliding components was independent of contrast inversion of bar and background. Secondly, when thin lines with the same luminance as the bars covered the borders of the intersection, the intersection's luminance did not affect the rigid-plaid motion percept very much, even when it corresponded to a transparent intersection. This indicates that, when the edges of the intersection and those of the bars were not collinear, the nulling of the end-stopped units did not occur. This result is in line with physiological studies, which showed that the response of an end-stopped cell to a line is only partially inhibited when a similar line is presented non-collinearly with the first in the inhibitory end-zone of its receptive field. Our results are consistent with a scheme in which a second stage of motion detectors combines signals of orientation-selective end-free and orientation-selective end-stopped units for perception of the rigid motion of two-dimensional patterns.

Optokinetic nystagmus in the four principal directions was investigated on the occurrence of directional asymmetries in 7 normal human subjects. Instructions were aimed at obtaining a 'stare' type of OKN. The movement of both eyes was recorded simultaneously with a scleral sensor-coil method. Subjects viewed a full-field random dot pattern rotating at velocities of 9 to 57 deg/s binocularly, as well as monocularly with either eye. Gain was always less than 0.85 and decreased when the pattern velocity increased. Horizontal and vertical nystagmus differed in a number of respects. (1) We found no evidence for an overall asymmetry for rightward or leftward motion. However, human OKN showed a clear preference for upward stimulus motion. Mean gain was ca. 0.15 larger for upward than for downward motion. (2) The decrease of the gain of OKN as a function of increasing stimulus velocity was steeper for vertical than for the horizontal direction. (3) The eyes moved nearly perfectly yoked for vertical pattern movement, irrespective of the viewing conditions. In contrast, during horizontal OKN the gain of the eye tracking in the nasal direction was higher (by about 4%) than the gain of the other eye moving simultaneously in the temporal direction. This difference persisted irrespective of the viewing conditions and appears to be motor, not sensory in origin. In addition, for any direction of the pattern motion a statistically significant increase of the gain occurred when the pattern motion was seen binocularly instead of monocularly with either eye.

We investigated the capacity of 6 humans to make voluntary smooth eye movements with a horizontally stabilized foveal point target. When the target was viewed on a dark field, all subjects were able to make smooth oscillatory eye movements when they attempted to imitate their own normal pursuit of sinusoidal target movement (0.2-0.7 Hz) directly preceding the stabilization on the fovea. The frequency of the imitating eye movement was in general lower than the frequency of normal pursuit by 2-35%. While fixating a foveally stabilized point target superimposed on a large, sinusoidally moving non-stabilized background, all subjects were able to make either no eye movements, eye movements nearly in phase with or eye movements nearly in counterphase with the background movement depending on the instruction to imagine the target as head-stationary, moving in phase, or moving in counterphase with the background. The accuracy of the frequency of the smooth eye movement with the stabilized target on the moving background was higher than during imitation of pursuit on the dark field but the precision of the frequency was lower than during normal pursuit. When the background moved pseudo-randomly all subjects could voluntarily inhibit their smooth eye movements or could make smooth eye movements in phase with the background. Only 2 subjects showed a limited ability to make smooth eye movements opposite to the pseudo-random background movement. The results suggest that with predictable background movement the volition of the subject rather than the movement of the background determines the eye movements when the subject looks at the foveally stabilized target.

The predictive component of human smooth pursuit was studied by perturbing sinusoidal target motion at unpredictable instants. The disturbances consisted of either a brief period of stabilization of the target on the fovea or a replacement of the sine by a ramp displacement for half a period. To minimize the effects of a possible change of the tracking strategy by the subject the transitions were masked and only the initial part of the response to the disturbance was analyzed. After stabilization on the fovea the eye oscillation continued at the frequency of the preceding target movement for about one half-cycle, whereupon the oscillation was rapidly damped. The mean unidirectional smooth eye acceleration was 70% of the mean unidirectional target acceleration prior to the stabilization. This suggests that during pursuit of a sinusoidal target movement about 75% of the oculomotor response is generated by predictive processes. When the sine was replaced by a ramp, starting at the velocity zero-crossing, the eye accelerated away from the target for ca. 180 ms irrespective of the frequency of prior tracking. In contrast, when the ramp started at the peak velocity of the sinusoidal target motion the eye accelerated away from the target for more than a quarter period. After foveal stabilization during pursuit of a pseudorandom stimulus, the eye continued to oscillate for less than one period at approximately the highest frequency present in the stimulus. The frequency characteristics of human smooth pursuit of predictable as well as unpredictable target motion were correctly simulated by a model, which derived its predictive properties from a lead element, tuned to the current frequency of the target motion.