Corrado Caudek

Depth perception in motion parallax and stereokinesis

Perceived depth in the stereokinetic effect (SKE) illusion and in the monocular derivation of depth from motion parallax were compared. Motion parallax gradients of velocity can be decomposed into 2 components: object- and observer-relative transformations. SKE displays present only the object-relative component. Observers were asked to estimate the magnitude and near-far order of depth in motion parallax and SKE displays. Monocular derivation of depth magnitude from motion parallax is fully accounted for by the perceptual response to the SKE, and observer-relative transformations absent in the SKE are of perceptual utility only as determinants of the near-far signing of perceived sequential depth. The amount of depth and rigidity perceived in motion parallax and SKE displays covaries with the projective size of the stimuli. The monocular derivation of depth from motion is mediated by a perceptual heuristic of which the SKE is symptomatic.

Stereo and motion information are not independently processed by the visual system.

Many visual tasks are carried out by using multiple sources of sensory information to estimate environmental properties. In this paper, we present a model for how the visual system combines disparity and velocity information. We propose that, in a first stage of processing, the best possible estimate of the affine structure is obtained by computing a composite score from the disparity and velocity signals. In a second stage, a maximum likelihood Euclidean interpretation is assigned to the recovered affine structure. In two experiments, we show that human performance is consistent with the predictions of our model. The present results are also discussed in the framework of another theoretical approach of the depth cue combination process termed Modified Weak Fusion.

3-D structure perceived from dynamic information: a new theory

Image movement provides one of the most potent two-dimensional cues for depth. From motion cues alone, the brain is capable of deriving a three-dimensional representation of distant objects. For many decades, theoretical and empirical investigations into this ability have interpreted these percepts as faithful copies of the projected 3-D structures. Here we review empirical findings showing that perceived 3-D shape from motion is not veridical and cannot be accounted for by the current models. We present a probabilistic model based on a local analysis of optic flow. Although such a model does not guarantee a correct reconstruction of 3-D shape, it is shown to be consistent with human performance.

Misperceptions of angular velocities influence the perception of rigidity in the kinetic depth effect

Accuracy in discriminating rigid from nonrigid motion was investigated for orthographic projections of three-dimension rotating objects. In 3 experiments the hypothesis that magnitudes of angular velocity are misperceived in the kinetic depth effect was tested, and in 4 other experiments the hypothesis that misperceiving angular velocities leads to misperceiving rigidity was tested. The principal findings were (a) the magnitude of perceived angular velocity is derived heuristically as a function of a property of the first-order optic flow called deformation and (b) perceptual performance in discriminating rigid from nonrigid motion is accurate in cases when the variability of the deformations of the individual triplets of points of the stimulus displays favors this interpretation and not accurate in other cases.

Visuomotor adaptation changes stereoscopic depth perception and tactile discrimination.

Perceptual judgments of relative depth from binocular disparity are systematically distorted in humans, despite in principle having access to reliable 3D information. Interestingly, these distortions vanish at a natural grasping distance, as if perceived stereo depth is contingent on a specific reference distance for depth-disparity scaling that corresponds to the length of our arm. Here we show that the brains representation of the arm indeed powerfully modulates depth perception, and that this internal calibration can be quickly updated. We used a classic visuomotor adaptation task in which subjects execute reaching movements with the visual feedback of their reaching finger displaced farther in depth, as if they had a longer arm. After adaptation, 3D perception changed dramatically, and became accurate at the “new” natural grasping distance, the updated disparity scaling reference distance. We further tested whether the rapid adaptive changes were restricted to the visual modality or were characteristic of sensory systems in general. Remarkably, we found an improvement in tactile discrimination consistent with a magnified internal image of the arm. This suggests that the brain integrates sensory signals with information about arm length, and quickly adapts to an artificially updated body structure. These adaptive processes are most likely a relic of the mechanisms needed to optimally correct for changes in size and shape of the body during ontogenesis.

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.

Perceived orientation of axis of rotation in structure-from-motion

Perceived orientation of axis of rotation and accuracy in discriminating fixed-axis from nonfixed-axis rotations were investigated for orthographic projections of three-dimensional rotating objects. The principal findings were (a) the slant of the axis of rotation was systematically misperceived; (b) in both two-view and multiview displays, the perceived slant of the axis of rotation was well-predicted by the ratio between the deformation (a property of the first-order optic flow) and the component parallel to the image plane of the global velocity vector; (c) if this ratio was kept constant in each frame transition of the stimulus sequence (or it was varied), then the stimuli tended to be judged as fixed-axis rotations (or as nonfixed-axis rotations), regardless of whether they simulated a fixed-axis rotation or not; and (d) the tilt of the axis of rotation was perceived in two-view displays with a very small error.

Temporal integration in structure from motion.

A temporal integration model is proposed that predicts the results reported in 4 psychophysical experiments. The main findings were (a) the initial part of a structure-from-motion (SFM) sequence influences the orientation evoked by the final part of that sequence (an effect lasting for more than 1 s), and (b) for oscillating SFM sequences, perceived slant is affected by the oscillation frequency and by the sign of the final gradient. For contracting optic flows (i.e., rotations away from the image plane), the sequence with the lowest oscillation frequency appeared more slanted; for expanding optic flows (i.e., rotations toward the image plane), the sequence with the highest oscillation frequency appeared more slanted.

The Intrinsic Constraint Model for Stereo-Motion Integration

How the visual system integrates the information provided by several depth cues is central for vision research. Here, we present a model for how the human visual system combines disparity and velocity information. The model provides a depth interpretation to a subspace defined by the covariation of the two signals. We show that human performance is consistent with the predictions of the model, and compare them with those of another theoretical approach, the modified weak-fusion model. We discuss the validity of each approach as a model for human perception of 3-D shape from multiple cues to depth.

Temporal integration of motion and stereo cues to depth.

In three experiments, we investigated the integration of three-dimensional information provided over time by different depth cues. In the first experiment, we found that the perceptual derivation of surface orientation from the optic flow was affected by the prior presentation of static stereo information in the same spatial location. This bias weakened as the length of the motion sequence increased, but it was still present after 800 msec. In the second experiment, conversely, we found that the perceived orientation of a stereo-specified surface was not influenced by the prior presentation of a static stereo surface. In a third experiment, we found that two surfaces defined by identical disparity fields did not elicit the same perceived depth if, previously, one of them had been specified by a conjunction of stereo and motion information. This effect was found to last for at least 400msec. Taken together, these findings indicate that interactions exist among different sources of depth information, even when they are provided at different moments of time.