Contribution of disparity to the perception of 3D shape as revealed by bistability of stereoscopic Necker cubes.

The Necker cube is a famous demonstration of ambiguity in visual perception of 3D shape. Its bistability is attributed to indecisiveness because monocular cues do not allow the observer to infer one particular 3D shape from the 2D image. A remarkable but not appreciated observation is that Necker cubes are bistable during binocular viewing. One would expect disparity information to veto bistability. To investigate the effect of zero and non-zero disparity on perceptual bistability in detail, perceptual dominance durations were measured for luminance- and disparity-defined Necker cubes. Luminance-defined Necker cubes were bistable for all tested disparities between the front and back faces of the cubes. Absence of an effect of disparity on dominance durations suggested the suppression of disparity information. Judgments of depth between the front and back sides of the Necker cubes, however, showed that disparity affected perceived depth. Disparity-defined Necker cubes were also bistable but dominance durations showed different distributions. I propose a framework for 3D shape perception in which 3D shape is inferred from pictorial cues acting on luminance- and disparity-defined 2D shapes.

Depth cue combination in spontaneous eye movements.

Where we look when we scan visual scenes is an old question that continues to inspire both fundamental and applied research. Recently, it has been reported that depth is an important variable in driving eye movements: the directions of spontaneous saccades tend to follow depth gradients, or, equivalently, surface tilts (L. Jansen, S. Onat, & P. König, 2009; M. Wexler & N. Ouarti, 2008). This has been found to hold for both simple and complex scenes and for a variety of depth cues. However, it is not known whether saccades are aligned with individual depth cues, or with a combination of depth cues. If saccades do follow a combination of depth cues, then it is interesting to ask whether this combination follows the same rules as the well-studied case of depth cue combination in conscious perception. We showed subjects surfaces inclined in depth, in which perspective and binocular disparity cues specified different plane orientations, with different degrees of both small and large conflict between the two sets of cues. We recorded subjects' spontaneous saccades while they scanned the scene, as well as their reports of perceived plane orientation. We found that distributions of spontaneous saccade directions followed the same pattern of depth cue combination as perceived surface orientation: a weighted linear combination of cues for small conflicts, and cue dominance for large conflicts. The weights assigned to the cues varied considerably from one subject to the next but were strongly correlated for saccades and perception; moreover, for both perception and saccades, cue weights could be modified by manipulating cue reliability in a way compatible with Bayesian theories of optimal cue combination. We also measured vergence, which allowed us to calculate the orientation of the plane fitted to points scanned in depth. Contrary to perception and saccades, vergence was dominated by a single cue, binocular disparity.

Depth cues, rather than perceived depth, govern vergence.

We studied the influence of perceived surface orientation on vergence accompanying a saccade while viewing an ambiguous stimulus. We used the slant rivalry stimulus, in which perspective foreshortening and disparity specified opposite surface orientations. This rivalrous configuration induces alternations of perceived surface orientation, while the slant cues remain constant. Subjects were able to voluntarily control their perceptual state while viewing the ambiguous stimulus. They were asked to make a saccade across the perceived slanted surface. Our data show that vergence responses closely approximated the vergence response predicted by the disparity cue, irrespective of voluntarily controlled perceived orientation. However, comparing the data obtained while viewing the ambiguous stimulus with data from an unambiguous stimulus condition (when disparity and perspective specified similar surface orientations) revealed an effect of perspective cues on vergence. Collectively our results show that depth cues rather than perceived depth govern vergence.

Coarse-to-fine eye movement strategy in visual search.

Oculomotor behavior contributes importantly to visual search. Saccadic eye movements can direct the fovea to potentially interesting parts of the visual field. Ensuing stable fixations enables the visual system to analyze those parts. The visual system may use fixation duration and saccadic amplitude as optimizers for visual search performance. Here we investigate whether the time courses of fixation duration and saccade amplitude depend on the subject's knowledge of the search stimulus, in particular target conspicuity. We analyzed 65,000 saccades and fixations in a search experiment for (possibly camouflaged) military vehicles of unknown type and size. Mean saccade amplitude decreased and mean fixation duration increased gradually as a function of the ordinal saccade and fixation number. In addition we analyzed 162,000 saccades and fixations recorded during a search experiment in which the location of the target was the only unknown. Whether target conspicuity was constant or varied appeared to have minor influence on the time courses of fixation duration and saccade amplitude. We hypothesize an intrinsic coarse-to-fine strategy for visual search that is even used when such a strategy is not optimal.

Organisation of signals involved in binocular perception and vergence control.

A novel type of dynamic random-dot stereogram (DRS) was used to study vergence movements and depth detection in response to temporal modulations of interocular correlation. Each DRS consisted of the repeated presentation of a pair of correlated images alternated by the presentation of a pair of uncorrelated images. The intervals of high (T(c)) and low (T(u)) correlation varied from 14 to 224 ms in steps of 14 ms. Depth detection and vergence responses behaved very different from each other as functions of T(c) and T(u). The different behaviours suggest that depth and vergence most likely result from independent streams of disparity processing. It is speculated that magnocellular layers process disparities that drive vergence and that a parvocellular stream of disparity processing is involved in depth perception. This suggestion is discussed in relation to recent findings on binocularly perceived direction and depth. The discussion leads to suggesting a headcentric organisation of signals involved in binocular perception and a retinal organisation of signals involved in vergence control.

Adaptation to disparity but not to perceived depth.

The purpose of the present study was to investigate whether adaptation can occur to disparity per se. The adapting stimuli were large random-dot patterns of which the two half-images were transformed such that the depth effects induced by the vertical transformations were nulled by horizontal transformations. Thus, the adapting stimuli were perceptually the same, whereas the disparity fields differed from each other. The adapting stimuli were presented for five minutes. During that period, the percept of a fronto-parallel surface did not change. After the adapting period, subjects perceived a thin untransformed strip as either slanted or curved depending on the adapting transformation. The thin strips provided negligible information about the vertical disparity field. In a forced-choice task we measured the amount of horizontal transformation that was required to null the acquired adaptation. We found that the amounts of horizontal transformation required to perceive the test strip fronto-parallel were significantly different from zero. We conclude that the visual system can adapt to disparity signals in the absence of a perceptual drive.

Strength of depth effects induced by three types of vertical disparity.

The goal of the present study is to compare the strengths of depth effects induced by different types of vertical disparity. We use a nulling task, in which the depth effects induced by vertical disparity are nulled by horizontal disparity. The advantage of this method is that it prevents cue conflicts from arising between disparity and other depth cues. The ratios between horizontal and vertical disparity that evoke the percept of a fronto-parallel stimulus vary per type of vertical disparity. The ratios determined for vertical scale and vertical quadratic mix (vertical scale with a horizontal gradient) vary strongly across subjects. The ratios for vertical shear are constant, since all subjects needed the same amount of horizontal and vertical shear to perceive a fronto-parallel plane. In these experiments, one conflict cannot be avoided, namely the conflict between vertical disparity and oculomotor signals. This conflict may cause differential weighting of vertical disparity and oculomotor signals, which could explain the individual differences. The different ratios for different types of vertical disparity suggest that weighting is specific for each type of vertical disparity and the associated oculomotor signal.

Is there an interaction between perceived direction and perceived aspect ratio in stereoscopic vision?

In monocular vision, the horizontal/vertical aspect ratio (shape) of a frontoparallel rectangle can be based on the comparison of the perceived directions of the rectangle's edges. In binocular vision of a typical three-dimensional scene (when occlusions are present), this is not the case: Frontoparallel rectangles would be perceived in a distorted fashion if an observer were to base perceived aspect ratio on the perceived directions of the rectangle's edges. We psychophysically investigated stereoscopically perceived aspect ratios of frontoparallel occluding and occluded rectangles for various distances and fixation depths. We found that observers did not perceive the distortions that would be predicted on the basis of the above-mentioned comparison of the perceived visual directions of the edges of the rectangle. Our results strongly suggest that the mechanism that determines perceived aspect ratio is dissociated from the mechanism that determines perceived direction. The consequences of the findings for the Kanizsa, Poggendorff, and horizontal/vertical illusions are discussed.

Perceived direction during monocular viewing is based on signals of the viewing eye only.

Perceived visual directions are derived from combining retinal signals and oculomotor signals. Up to now the general belief is that the oculomotor signals of the two eyes are first pooled before they become available for perception of depth and direction. In this sense the eyes are believed to act together as one unit known as the cyclopean eye. This study, however, shows that during monocular viewing in daylight conditions, the perceived directions of objects are indicated by their retinal locus in combination with the angular position of the viewing eye only, the angular position of the closed eye being irrelevant. This result indicates that in binocular vision the integration of left and right eye signals first occurs after retinal and oculomotor signals have been integrated of each eye separately. This conclusion challenges the prevailing concept of cyclopean vision and current views about stereoscopic depth perception.

Comparison of external load compensation during rhythmic arm movements and rhythmic jaw movements in humans.

Experiments were performed on human elbow flexor and extensor muscles and jaw-opening and -closing muscles to observe the effect on rhythmic movements of sudden loading. The load was provided by an electromagnetic device, which simulated the appearance of a smoothly increasing spring-like load. The responses to this loading were compared in jaw and elbow movements and between expected and unexpected disturbances. All muscles showed electromyographic responses to unexpected perturbations, with latencies of approximately 65 ms in the arm muscles and 25 ms in the jaw. When loading was predictable, anticipatory responses started in arm muscles approximately 200 ms before and in jaw muscles 100 ms before the onset of loading. The reflex responses relative to the anticipatory responses were smaller for the arm muscles than for the jaw muscles. The reflex responses in the arm muscles were the same with unexpected and expected perturbations, whereas anticipation increased the reflex responses in the jaw muscles. Biceps brachii and triceps brachii showed similar sensory-induced responses and similar anticipatory responses. Jaw muscles differed, however, in that the reflex response was stronger in masseter than in digastric. It was concluded that reflex responses in the arm muscles cannot overcome the loading of the arm adequately, which is compensated by a large centrally programmed response when loading is predictable. The jaw muscles, particularly the jaw-closing muscles, tend to respond mainly through reflex loops, even when loading of the jaw is anticipated. The differences between the responses of the arm and the jaw muscles may be related to physical differences. For example, the jaw was decelerated more strongly by the load than the heavier arm. The jaw was decelerated strongly but briefly, <30 ms during jaw closing, indicating that muscle force increased before the onset of reflex activity. Apparently, the force-velocity properties of the jaw muscles have a stabilizing effect on the jaw and have this effect before sensory induced responses occur. The symmetrical responses in biceps and triceps indicate similar motor control of both arm muscles. The differences in reflex activity between masseter and digastric muscle indicate fundamental differences in sensory feedback to the jaw-closing muscle and jaw-opening muscle.

The influence of large scanning eye movements on stereoscopic slant estimation of large surfaces.

The results of several experiments demonstrate that the estimated magnitude of perceived slant of large stereoscopic surfaces increases with the duration of the presentation. In these experiments, subjects were free to make eye movements. A possible explanation for the increase is that the visual system needs to scan the stimulus with eye movements (which take time) before it can make a reliable estimate of slant. We investigated the influence of large scanning eye movements on stereoscopic slant estimation of large surfaces. Six subjects estimated the magnitude of slant about the vertical or horizontal axis induced by large-field stereograms of which one half-image was transformed by horizontal scale, horizontal shear, vertical scale, vertical shear, divergence or rotation relative to the other half-image. The experiment was blocked in three sessions. Each session was devoted to one of the following fixation strategies: central fixation, peripheral (20 deg) fixation and active scanning of the stimulus. The presentation duration in each of the sessions was 0.5, 2 or 8 s. Estimations were done with and without a visual reference. The magnitudes of estimated slant and the perceptual biases were not significantly influenced by the three fixation strategies. Thus, our results provide no support for the hypothesis that the time used for the execution of large scanning eye movements explains the build-up of estimated slant with the duration of the stimulus presentation.

Peripheral vision and oculomotor control during visual search.

The present study concerns the dynamics of multiple fixation search. We tried to gain insight into: (1) how the peripheral and foveal stimulus affect fixation duration; and (2) how fixation duration affects the peripheral target selection for saccades. We replicated the non-corroborating results of Luria and Strauss (1975) ('Eye movements during search for coded and uncoded targets', Perception and Psychophysics 17, 303-308) (saccades were selective), and Zelinsky (1996) (Using eye movements to assess the selectivity of search movements. Vision research 36(14), 2177-2187) (saccades were not selective), by manipulating the critical features for peripheral selection and discrimination separately. We found search to be more selective and efficient when the selection task was easy or when fixations were long-lasting. Remarkably, subjects did not increase their fixation durations when the peripheral selection task was more difficult. Only the discrimination task affected the fixation duration. This implies that the time available for peripheral target selection is determined mainly by the discrimination task. The results of the present experiment suggest that, besides the difficulty of the peripheral selection task, fixation duration is an important factor determining the selection of potential targets for eye movements.

Relation between torque history, firing frequency, decruitment levels and force balance in two flexors of the elbow.

By means of intramuscular electromyographic recordings, we studied the firing frequencies and recruitment/decruitment thresholds of individual motor units in two elbow flexors, the biarticular biceps brachii muscle and the monoarticular brachioradialis muscle. Subjects had to perform isometric contractions with increasing elbow flexion torque until a specific peak torque level was reached. The torque level was kept constant for 6 s during which firing frequencies were measured. Then the torque was decreased to a lower level and, after 3 s, firing frequencies were again measured for 6 s. By repeating this procedure, the torque level was decreased stepwise until the motor unit under study stopped firing. The last level before the unit stopped firing was considered to be the decruitment torque level. We measured the firing frequency at recruitment and decruitment, the torque-frequency relationship and the recruitment and decruitment torque thresholds after various levels of peak torque. In the biceps, both the firing frequencies at a specific torque level and the decruitment torque level itself were independent of the peak torque. In the brachioradialis, however, firing frequencies at a specific torque level decreased and decruitment torque levels increased after subjects generated higher peak torques. Thus, in this muscle firing frequencies as well as decruitment thresholds show hysteresis effects. The result indicates a shift of force from the brachioradialis muscle during recruitment to the biceps muscle during decruitment. This shift is smaller than was concluded from previous studies in which decruitment threshold levels for the brachioradialis muscle were assumed to be independent of force history. Moreover, we found that in both muscles decruitment firing frequencies were lower than recruitment frequencies and they were independent of the peak torque level. In order to analyse the effect of the peak torque level on the distribution of force over the two muscles, we performed a model study in which we simulated the activation-frequency relation of two elbow flexors: a biceps-like and brachioradialis-like muscle, each contributing equally to the elbow torque during recruitment. In addition, we analysed how the different behaviour of the biceps and the brachioradialis during decruitment alters their contribution to the total torque production and how this redistribution is caused. The model study shows that the shift in contribution to the total torque is not constant during the relaxation phase and is not caused by a simple mechanism like a shift of activation from one muscle to another. Furthermore, changes limited to the muscle in which hysteresis is present do not seem to be sufficient to explain the experimental results.

A computational model of depth perception based on headcentric disparity.

It is now well established that depth is coded by local horizontal disparity and global vertical disparity. We present a computational model which explains how depth is extracted from these two types of disparities. The model uses the two (one for each eye) headcentric directions of binocular targets, derived from retinal signals and oculomotor signals. Headcentric disparity is defined as the difference between headcentric directions of corresponding features in the left and right eye's images. Using Helmholtz's coordinate systems we decompose headcentric disparity into azimuthal and elevational disparity. Elevational disparities of real objects are zero if the signals which contribute to headcentric disparity do not contain any errors. Azimuthal headcentric disparity is a 1D quantity from which an exact equation relating distance and disparity can be derived. The equation is valid for all headcentric directions and for all binocular fixation positions. Such an equation does not exist if disparity is expressed in retinal coordinates. Possible types of errors in oculomotor signals (six) produce global elevational disparity fields which are characterised by different gradients in the azimuthal and elevational directions. Computations show that the elevational disparity fields uniquely characterise both the type and size of the errors in oculomotor signals. Our model uses a measure of the global elevational disparity field together with local azimuthal disparity to accurately derive headcentric distance throughout the visual field. The model explains existing data on whole-field disparity transformations as well as hitherto unexplained aspects of stereoscopic depth perception.

Adjustment of fixation duration in visual search.

To investigate whether fixation durations are adjusted to the duration of a foveal analysis task, we designed a search task in which each stimulus element yielded information about the position of the target. We asked subjects to look for the target by making eye movements in the direction indicated by each stimulus element. We explicitly asked the subjects to make the eye movements in the correct direction, but they did not always do this. They made only 65-80% of the eye movements in directions indicated by the stimulus elements. From these results we conclude that fixation durations are not solely determined by the immediate visual stimulus and that subjects encounter difficulties when trying to increase fixation durations to values that would enable them to direct saccades accurately. In a second experiment we shortened the presentation time in order to provide an incentive for the subjects to speed up search. Shortening the presentation time did not affect fixation duration. Therefore, we suggest that fixation duration is controlled by a mechanism that uses estimations of the foveal analysis time of previous fixated stimulus elements.

A comparison of curvatures of left and right hand movements in a simple pointing task.

Human arm movements towards visual targets are remarkably reproducible in several tasks and conditions. Various authors have reported that trajectories of unconstrained point-to-point movements are slightly curved, smooth and have bell-shaped velocity profiles. The hand paths of such movements show small - but significant - curvatures throughout the workspace. The cause of these curvatures is still obscure. Traditionally this curvature is explained as the result of an optimisation process or is ascribed to mechanical or dynamic properties of the effector system. Recently, however, it has been suggested that these curvatures are due at least partly, to the visual misperception of straight lines. To evaluate the latter hypothesis, we compared unconstrained, self-paced point-to-point movements that subjects made with their right and left hand. We assume that the visual misperception may depend on the position in the workspace, subject, etc. but not on the hand used to make the movement. Therefore we argue that if curvature is caused by a visual misperception of straight lines, curvatures should be the same for movements made with the left and right hand. Our experiments cast strong doubt on the hypothesis that curvatures are the result of a visual distortion, because curvatures of the left hand trajectories, mirrored in the mid-sagittal plane, are found to be accurately described by trajectories of the right hand. Estimates of the effect of visual distortion on movement curvature show that, if present, this effect is very small compared with other sources that contribute to movement curvature. We found that curvatures depend strongly on the subject and on the direction and distance of the movement. Curvatures do not seem to be caused purely by the dynamic properties of the arm, since curvatures do not change significantly with increasing movement velocity. Therefore, we conclude that curvatures reflect an inherent property of the control of multi-joint arm movements.

Temporal aspects of stereoscopic slant estimation: an evaluation and extension of Howard and Kaneko's theory.

We investigated temporal aspects of stereoscopically perceived slant produced by the following transformations: horizontal scale, horizontal shear, vertical scale, vertical shear, divergence and rotation, between the half-images of a stereogram. Six subjects viewed large field stimuli (70 degrees diameter) both in the presence and in the absence of a visual reference. The presentation duration was: 0.1, 0.4, 1.6, 6.4 or 25.6 s. Without reference we found the following: rotation and divergence evoked considerable perceived slant in a number of subjects. This finding violates the recently published results of Howard and Kaneko. Slant evoked by vertical scale and shear was similar to slant evoked by horizontal scale and shear but was generally less. With reference we found the following: vertical scale and vertical shear did not evoke slant. Slant due to rotation and divergence was similar to slant due to horizontal scale and shear but was generally less. According to the theory of Howard and Kaneko, perceived slant depends on the difference between horizontal and vertical scale and shear disparities. We made their theory more explicit by translating their proposals into linear mathematical expressions that contain weighting factors that allow for both slant evoked by rotation or divergence, subject-dependent underestimation of slant and other related phenomena reported in the literature. Our data for all stimulus durations and for all subjects is explained by this 'unequal-weighting' extension of Howard and Kaneko's theory.

Dynamics of horizontal vergence movements: interaction with horizontal and vertical saccades and relation with monocular preferences.

We studied the dynamics of pure vergence shifts and vergence shifts combined with vertical and horizontal saccades. It is known from earlier studies that horizontal saccades accelerate horizontal vergence. We wanted to obtain a more complete picture of the interactions between version and vergence. Therefore we studied pure version (horizontal and vertical), pure vergence (divergence and convergence) and combinations of both in five adult subjects with normal binocular vision and little phoria (< 5 degrees). The visual targets were LED's in isovergence arrays presented at two distances (35 and 130 cm) in a dimly lit room. Two targets were continuously lit during each trial and gaze-shifts were paced by a metronome. The two subjects with a strong monocular preference made vergence eye movements together with small horizontal saccades during pure vergence tasks. The other subjects, who did not have a strong monocular preference, made pure vergence movements (without saccades). These findings, suggest that monocular preferences influence the oculomotor strategy during vergence tasks. Vergence was facilitated by both horizontal and vertical saccades but vergence peak-velocity during horizontal saccades was higher than during vertical saccades.

Gaze-shift dynamics in two kinds of sequential looking tasks.

Gaze-shift dynamics of unrestrained seated subjects were examined. The subjects participated in two tasks. In the first task, they tapped sequences of 3-D targets located on a table in front of them. In the second task, they only looked at similar sequences of targets. The purpose of the task (tapping vs only looking) affected the dynamics of gaze-shifts. Gaze and eye-in-head peak velocities were higher and gaze-shift durations were shorter during tapping than during looking-only. We conclude that task variables affect gaze-shift dynamics, altering characteristics of the so-called saccadic "main sequence".

Capture of the visual direction of monocular objects by adjacent binocular objects.

Investigations of binocular visual direction have concentrated mainly on stationary objects. Eye positions were generally not measured and binocular fixation was assumed to be perfect. During the viewing of stationary objects, vergence errors are not negligible but small. During the viewing of moving objects, however, errors in binocular fixation are much larger. Existing rules for binocular visual direction were examined under the latter, more demanding viewing conditions. Eye movements were measured objectively by the scleral coil technique. Subjects viewed a large stereogram in which the half-images oscillated in counterphase. The stereogram contained two square random-dot patterns placed side by side with a gap in between. A vertical line, visible only to one eye, oscillated in the gap. Subjects were asked to adjust the amplitude of line motion until the line was perceived to be stationary. In so doing, they set amplitudes equal to the amplitudes of half-image motion if the gap between the patterns was narrow. They set amplitudes significantly smaller in wider gaps. Subjects made considerable fixational errors in following the oscillations of the line and the random-dot patterns. The results of the settings and of the retinal errors together refute existing rules for binocular visual direction of monocular objects. Perceived directions of monocular objects cannot be specified by geometrical rules that include only the positions of the objects and of the two eyes. The results suggest that perceived directions of monocular objects are captured by the binocular visual directions of adjacent binocular objects. Capture of binocular visual direction was found to be effective for gaps as wide as 8 deg between the binocular objects. The phenomenon of binocular capture has negative consequences for the general use of nonius lines as indicators of eye position.