Inconsistency of perceived 3D shape.

Internal consistency of local depth, slant, and curvature judgments was studied by asking participants to match two 3D surfaces rendered by different mixtures of 3D cues (velocity, texture, and shading). We found that perceptual judgments were not consistent with each other, with cue-specific distortions. Adding multiple cues did not eliminate the inconsistencies of the judgments. These results can be predicted by the Intrinsic Constraint (IC) model according to which the perceptual metric local estimates are a monotonically increasing function of the Signal-to-Noise Ratio of the optimal combination of direct information of 3D shape (Domini, Caudek, & Tassinari, 2006).

Segmentation in structure from motion: modeling and psychophysics.

Much work has been done on the question of how the visual system extracts the three-dimensional (3D) structure and motion of an object from two-dimensional (2D) motion information, a problem known as 'Structure from Motion', or SFM. Much less is known, however, about the human ability to recover structure and motion when the optic flow field arises from multiple objects, although observations of this ability date as early as Ullman's well-known two-cylinders stimulus [The interpretation of visual motion (1979)]. In the presence of multiple objects, the SFM problem is further aggravated by the need to solve the segmentation problem, i.e. deciding which motion signal belongs to which object. Here, we present a model for how the human visual system solves the combined SFM and segmentation problems, which we term SSFM, concurrently. The model is based on computation of a simple scalar property of the optic flow field known as def, which was previously shown to be used by human observers in SFM. The def values of many triplets of moving dots are computed, and the identification of multiple objects the image is based on detecting multiple peaks in the histogram of def values. In five experiments, we show that human SSFM performance is consistent with the predictions of the model. We compare the predictions of our model to those of other theoretical approaches, in particular those that use a rigidity hypothesis, and discuss the validity of each approach as a model for human SSFM.

Perceiving surface slant from deformation of optic flow.

Perceived surface orientation and angular velocity were investigated for orthographic projections of 3-D rotating random-dot planes. It was found that (a) tilt was accurately perceived and (b) slant and angular velocity were systematically misperceived. It was hypothesized that these misperceptions are the product of a heuristic analysis based on the deformation, one of the differential invariants of the first-order optic flow. According to this heuristic, surface attitude and angular velocity are recovered by determining the magnitudes of these parameters that most likely produce the deformation of the velocity field, under the assumption that all slant and angular velocity magnitudes have the same a priori probability. The results of the present investigation support this hypothesis. Residual orientation anisotropies not accounted for by the proposed heuristic were also found.

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

Four experiments related human perception of depth-order relations in structure-from-motion displays 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.

Discriminating constant from variable angular velocities in structure from motion.

We investigated accuracy in discriminating between constant and variable angular velocities for orthographic projections of three-dimensional rotating objects. The reported judgments of "constant" or "variable" angular velocity were only slightly influenced by the projected angular velocities, but they were greatly affected by the variations of the deformation, a first-order component of the optic flow. When viewing either a rotating ellipsoidal volume or a planar surface that accelerated and decelerated over the course of rotation, observers' tendencies to report a variable angular velocity were increased when the temporal phase of the acceleration pattern increased the range of variation of the median deformation; the tendencies were decreased when the same acceleration pattern was used to decrease the range of variation of the median deformation. These results provide evidence contrary to the hypothesis that the visual system performs a mathematically correct analysis of the 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.

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.

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.