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.     

Recovering three-dimensional shape from perspective translations and orthographic rotations.

Perceived orientation in depth and 3-dimensional (3D) shape was investigated for perspective projections of translations and orthographic projections of rotations of 3D dihedral angles. The principal findings were that (1) perceived orientation in depth depends on the sign of the velocity gradient, even in the case of orthographic projections; (2) the relationship between perceived orientation and the sign of the velocity gradient is greater for shallower gradients in orthographic projections of rotations, consistent with previous findings for perspective translations; (3) the magnitudes of simulated dihedral angles were underestimated (relative depth overestimated) for orthographic projections of rotations but were overestimated for perspective projections of translations; and (4) the judged magnitude of the dihedral angle depends on the velocity ratio and on image compression; it cannot be predicted from the velocity ratio or the velocity gradient alone. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

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. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

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.     

Kinetic depth effect and identification of shape.

We introduce an objective shape-identification task (SIT) for measuring the kinetic depth effect (KDE). A rigidly rotating surface consisting of hills and valleys on an otherwise flat ground was defined by 300 randomly positioned dots. On each trial, Ss identified 1 of 53 shapes and its direction of rotation. Identification accuracy was an objective measure of Ss' perceptual ability to extract 3D structure from 2D motion via KDE. Objective accuracy data were consistent with previous subjective rating judgments of depth and coherence. Along with motion cues, rotating real 3D dot-defined shapes produced a cue of changing dot density. Shortening dot lifetimes to control dot density showed that changing density was neither necessary nor sufficient to account for accuracy; motion alone sufficed. Our SIT was solvable with motion cues from the 6 most relevant locations. We used the dots from these locations in a simplified 2D direction-labeling motion task with 6 perceptually flat flow fields. Ss' performance in the 2D and 3D tasks was equivalent, indicating that the information processing capacity of KDE is not unique. Our proposed structure-from-motion algorithm for the SIT finds relative minima and maxima of local velocity and then assigns 3D depths proportional to velocity. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

How to study the kinetic depth effect experimentally.

G. Sperling et al (see record 1990-06589-001) proposed an objective 3D shape identification task with 2D artifactual cues removed and with full feedback (FB) to the subjects to measure kinetic depth effect (KDE) and to circumvent algorithmically equivalent KDE-alternative computations and artifactual non-KDE processing. (1) The 2D velocity flow-field was necessary and sufficient for true KDE. (2) Only the first-order (Fourier-based) perceptual motion system could solve our task because the second-order (rectifying) system could not simultaneously process more than two locations. (3) To ensure first-order motion processing, KDE tasks must require simultaneous processing at more than two locations. (4) Practice with FB is essential to measure ultimate capacity (aptitude) and, thereby, to enable comparisons with ideal observers. Experiments without FB measure ecological achievement—the ability of subjects to extrapolate their past experience to the current stimuli. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Perceived orientation of axis 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 (1) the slant of the axis of rotation was systematically misperceived; (2) 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; (3) 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 (4) the tilt of the axis of rotation was perceived in two-view displays with a very small error. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The relationship of vertical and horizontal velocity gradients in the perception of shape, rotation, and rigidity

Perceived shape, rotation, and rigidity were investigated in displays with linear velocity gradients in the vertical and horizontal directions. Different temporal relationships between these gradients simulated perspective projections of frontally oriented or rotated translating dihedral angles, orthographic projections of rotating dihedral angles, or nonrigid motion. Displays with nonzero horizontal gradients were judged to represent greater angle magnitudes (less relative depth) than displays with 0 horizontal gradients. The temporal relationship between the vertical and horizontal gradients did not influence judged shape but did affect rotation and rigidity judgments; rigid rotations were judged to rotate most, and nonrigid displays were rated as least rigid. These results indicate that the visual system integrates information from more than 1 velocity field. Possible integration methods based on first-order optic flow analysis are discussed.     

The interaction between stereoscopic and luminance motion

An interaction in apparent motion between perceived three-dimensional forms defined by stereopsis and local luminous elements is reported. Vertical stripes of cyclopean square gratings were simulated by random-dot stereograms. Alternation of two-frame stereograms whose phases differed by 90 deg caused two kinds of percepts, planes' motion in depth (first-order stereoscopic motion, first-order SM) or lateral motion of gratings (higher-order stereoscopic motion, higher-order SM). Experiment 1 explored the conditions under which higher-order SM frequently arose, as opposed to local luminance-based in-depth motion (first-order SM). The results show that, when the spatial arrangements of two-frame random dots were correlated, higher-order SM dominated for long ISI conditions (ISI > 73 msec). When they were uncorrelated, higher-order SM dominated even under zero ISI conditions. Subjects reported that, when higher-order SM was seen, dots were attached to the surfaces of the moving cyclopean figure (motion capture). Experiment 2 tested which factor caused the domination of higher-order SM under uncorrelated conditions in Experiment 1, the larger distance of dot jump or the varied directions of the dots' motion. The results show that, when the distance of dot jump is large or when the directions of dots' motion are incoherent, higher-order SM arises more frequently. When local first-order motion signals are weakened by appropriate temporal and spatial conditions or by incoherent motion directions, higher-order SM dominates and it captures the motion of dots.     

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.     

Swagger, sway, and sexuality: Judging sexual orientation from body motion and morphology.

People can accurately judge the sexual orientation of others, but the cues they use have remained elusive. In 3 studies, the authors examined how body shape and motion affect perceived sexual orientation. In 2 studies, participants judged the sexual orientation of computer-generated animations in which body shape and motion were manipulated. Gender-typical combinations (e.g., tubular body moving with shoulder swagger or hourglass body moving with hip sway) were perceived generally to be heterosexual; gender-atypical combinations were perceived generally to be homosexual. These effects were stronger for male targets. Body shape affected perceived sexual orientation of women, but motion affected perceived sexual orientation of both men and women. Study 3 replicated and extended these findings. Participants judged dynamic outlines of real people (men and women, both gay and straight) in which body shape and motion were measured. Again, gender-atypical body motion affected perceived sexual orientation and, importantly, affected accuracy as well. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

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.     

Methodologic aspects of sodium appetite: an addendum

Investigated the relative effects of pattern cues and target-motion cues on time to detect linear targets embedded in static noise. A within-S factorial design was employed with 8 paid 18-22 yr olds who were instructed to detect targets in a simulated time-compressed radar display presented via a computer-controlled plasma panel equipped with a touch-sensitive response device. Two pattern-cue variables (number of target spots and target interspot distance) and 2 target-motion variables (rate of target advancement and target spot duration) were used, each at 3 levels. It was observed that each of the 4 target variables had a reliable effect on detection latency, but the number of target spots (a pattern cue) accounted for the largest proportion of variance. The more important of the 2 motion cues, target spot duration, primarily facilitated target detection when the number of target spots was reduced to 3, the lowest of the 3 target-spot levels investigated. It is concluded that pattern cues are the most critical feature in the present type of detection task. Implications of the findings for the design of operational time-compressed radar systems are considered. (16 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Temporal frequency modulates reaction time responses to first-order and second-order motion.

This study investigated the effect of temporal frequency and modulation depth on reaction times for discriminating the direction of first-order (luminance-defined) and second-order (contrast-defined) motion, equated for visibility using equal multiples of direction-discrimination threshold. Results showed that reaction times were heavily influenced by temporal frequency, especially in the case of second-order motion. At 1 Hz, reaction times were faster for first-order compared with second-order motion. As temporal frequency increased, reaction times for first-order motion decreased slightly, but those for second-order motion decreased more rapidly. At 8 Hz, reaction times for second-order motion were, in many cases, faster than those for first-order motion. Reaction times decreased as stimulus modulation depth increased at approximately the same rate for both motion types. The findings demonstrate that behavioral response latencies to first-order and second-order motion are dependent on specific stimulus parameters and may, in some cases, be shorter in response to second-order compared with first-order motion. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Second-order motions contribute to vection

First- and second-order motions differ in their ability to induce motion aftereffects (MAEs) and the kinetic depth effect (KDE). To test whether second-order stimuli support computations relating to motion-in-depth we examined the vection illusion (illusory self motion induced by image flow) using a vection stimulus (V, expanding concentric rings) that depicted a linear path through a circular tunnel. The set of vection stimuli contained differing amounts of first- and second-order motion energy (ME). Subjects reported the duration of the perceived MAEs and the duration of their vection percept. In Experiment 1 both MAEs and vection durations were longest when the first-order (Fourier) components of V were present in the stimulus. In Experiment 2, V was multiplicatively combined with static noise carriers having different check sizes. The amount of first-order ME associated with V increases with check size. MAEs were found to increase with check size but vection durations were unaffected. In general MAEs depend on the amount of first-order ME present in the signal. Vection, on the other hand, appears to depend on a representation of image flow that combines first- and second-order ME.     

Guidance of locomotion on foot uses perceived target location rather than optic flow

What visual information do we use to guide movement through our environment? Self-movement produces a pattern of motion on the retina, called optic flow. During translation, the direction of movement (locomotor direction) is specified by the point in the flow field from which the motion vectors radiate - the focus of expansion (FoE) [1-3]. If an eye movement is made, however, the FoE no longer specifies locomotor direction [4], but the 'heading' direction can still be judged accurately [5]. Models have been proposed that remove confounding rotational motion due to eye movements by decomposing the retinal flow into its separable translational and rotational components ([6-7] are early examples). An alternative theory is based upon the use of invariants in the retinal flow field [8]. The assumption underpinning all these models (see also [9-11]), and associated psychophysical [5,12,13] and neurophysiological studies [14-16], is that locomotive heading is guided by optic flow. In this paper we challenge that assumption for the control of direction of locomotion on foot. Here we have explored the role of perceived location by recording the walking trajectories of people wearing displacing prism glasses. The results suggest that perceived location, rather than optic or retinal flow, is the predominant cue that guides locomotion on foot.     

Processing of first- and second-order motion signals by neurons in area MT of the macaque monkey

Extrastriate cortical area MT is thought to process behaviorally important visual motion signals. Psychophysical studies suggest that visual motion signals may be analyzed by multiple mechanisms, a "first-order" one based on luminance, and a "second-order" one based upon higher level cues (e.g. contrast, flicker). Second-order motion is visible to human observers, but should be invisible to first-order motion sensors. To learn if area MT is involved in the analysis of second-order motion, we measured responses to first- and second-order gratings of single neurons in area MT (and in one experiment, in area V1) in anesthetized, paralyzed macaque monkeys. For each neuron, we measured directional and spatio-temporal tuning with conventional first-order gratings and with second-order gratings created by spatial modulation of the flicker rate of a random texture. A minority of MT and V1 neurons exhibited significant selectivity for direction or orientation of second-order gratings. In nearly all cells, response to second-order motion was weaker than response to first-order motion. MT cells with significant selectivity for second-order motion tended to be more responsive and more sensitive to luminance contrast, but were in other respects similar to the remaining MT neurons; they did not appear to represent a distinct subpopulation. For those cells selective for second-order motion, we found a correlation between the preferred directions of first- and second-order motion, and weak correlations in preferred spatial frequency. These cells preferred lower temporal frequencies for second-order motion than for first-order motion. A small proportion of MT cells seemed to remain selective and responsive for second-order motion. None of our small sample of V1 cells did. Cells in this small population, but not others, may perform "form-cue invariant" motion processing (Albright, 1992).     

The processing of first- and second-order motion in human visual cortex assessed by functional magnetic resonance imaging (fMRI)

We have examined the activity levels produced in various areas of the human occipital cortex in response to various motion stimuli using functional magnetic resonance imaging (fMRI) methods. In addition to standard luminance-defined (first-order) motion, three types of second-order motion were used. The areas examined were the motion area V5 (MT) and the following areas that were delineated using retinotopic mapping procedures: V1, V2, V3, VP, V3A, and a new area that we refer to as V3B. Area V5 is strongly activated by second-order as well as by first-order motion. This activation is highly motion-specific. Areas V1 and V2 give good responses to all motion stimuli, but the activity seems to be related primarily to the local spatial and temporal structure in the image rather than to motion processing. Area V3 and its ventral counterpart VP also respond well to all our stimuli and show a slightly greater degree of motion specificity than do V1 and V2. Unlike V1 and V2, the response in V3 and VP is significantly greater for second-order motion than for first-order motion. This trend is evident, but less marked, in V3A and V3B and absent in V5. The results are consistent with the hypothesis that first-order motion sensitivity arises in V1, that second-order motion is first represented explicitly in V3 and VP, and that V5 (and perhaps also V3A and V3B) is involved in further processing of motion information, including the integration of motion signals of the two types.     

2D motion aliasing yielding 3D ambiguity. A study with variants of a Necker cube

The 2D projection of a rotating Necker cube yields an ambiguous 3D interpretation based on both 2D shape and kinetic depth information. The present study shows that the alternation rate of the two 3D interpretations is constant with the rotation speed up to some critical value (around 25 turns/min for a cube whose sides subtend 2.5 deg) and increases monotonically thereafter. It is proposed that the additional perceptual reversals (PRs) observed at high rotation speeds are due to the increased frequency of the crossovers of the cube's edges. These crossovers yield 2D motion "aliasing" (or discontinuity) and "veridical" (or continuity) motion components. The motion aliasing (or crossover) hypothesis states that, in addition to the inherent ambiguity of the dynamic 2D projection of 3D objects, perceptual motion/perspective reversals will occur any time the discontinuity speed takes over the continuity speed. It is proposed that the relative strengths of the two components depend on the linear speed of the projected edges and that the discontinuity components take over the continuity one in the speed range where contrast sensitivity (or, above threshold, efficiency) is a decreasing function of speed. The motion aliasing hypothesis was tested and supported in a series of independent experiments showing that, for rotation speeds higher than 25 turns/min the PR rate increases with the crossover frequency at a constant speed, with linear speed at a constant crossover frequency and with the similarity of the crossing bars in terms of their orientation, polarity and spatial overlap. In addition, some of these experiments suggest that 2D shape and kinetic depth 3D-cues combine in such a way that the average PR rate they yield together is the same as the PR rate yielded by each of them independently. In the Discussion section we elaborate on issues related to the perceptual combination of ambiguous shape and kinetic depth, 3D cues.     

Monocular motion adaptation affects the perceived trajectory of stereomotion.

Perceived stereomotion trajectory was measured before and after adaptation to lateral motion in the dominant or nondominant eye to assess the relative contributions of 2 cues: changing disparity and interocular velocity difference. Perceived speed for monocular lateral motion and perceived binocular visual direction (BVD) was also assessed. Unlike stereomotion trajectory perception, the BVD of static targets showed an ocular dominance bias, even without adaptation. Adaptation caused equivalent biases in perceived trajectory and monocular motion speed, without significantly affecting perceived BVD. Predictions from monocular motion data closely match trajectory perception data, unlike those from BVD sources. The results suggest that the interocular velocity differences make a significant contribution to stereomotion trajectory perception. (PsycINFO Database Record (c) 2010 APA, all rights reserved)