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.     

Minimum points and views for the recovery of three-dimensional structure.

Mathematical analyses of motion perception have established minimum combinations of points and distinct views that are sufficient to recover three-dimensional (3D) structure from two-dimensional (2D) images, using such regularities as rigid motion, fixed axis of rotation, and constant angular velocity. To determine whether human subjects could recover 3D information at these theoretical levels, we presented subjects with pairs of displays and asked them to determine whether they represented the same or different 3D structures. Number of points was varied between two and five; number of views was varied between two and six; and the motion was fixed axis with constant angular velocity, fixed axis with variable velocity, or variable axis with variable velocity. Accuracy increased with views, decreased with points, and was greater with fixed-axis motion. Subjects performed above chance levels even when motion was eliminated, indicating that they exploited regularities in addition to those in the theoretical analyses. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Speed gradients and the perception of surface slant: analysis is two-dimensional not one-dimensional

Motion parallax provides cues to the three-dimensional layout of a viewed scene and, in particular, to surface tilt and slant. For example, as a textured surface, inclined around a horizontal axis, translates horizontally relative to an observer's view point, then, in the absence of head and eye movements, the observer's retinal flow will contain a one-dimensional (1D) vertical speed gradient. The direction of this gradient indicates the direction of surface tilt, and its magnitude and sign can be used in calculating the magnitude and sign of the surface slant. Alternatively, the same retinal flow contains a 1D translating component, plus a two-dimensional (2D) component of rotation (curl), and a 2D component of deformation (def). On this view, the direction of surface tilt is related to the orientation of def and the magnitude and sign of the surface slant is related to the magnitude and sign of def. We used computer generated random dot patterns as stimuli to determine whether the human visual system employs a 1D analysis (i.e. 1D speed gradients) or a 2D analysis (i.e. deformation) of surface slant from motion parallax. Using a matching technique we found compelling impressions of slant when we vector summed a translation field with (i) vertical shear, horizontal shear or deformation (made from vertical and horizontal shear), but not rotation; and (ii) vertical compression, horizontal compression or deformation (made from vertical and horizontal compression), but much less so for expansion. In both cases, the first three conditions contain def, but the fourth does not, and the last three conditions contain 1D speed gradients orthogonal to the perceived axis of inclination, but the first one does not. Therefore, the results from the first and fourth conditions distinguish between the two processing strategies. They support the idea that surface slant is coded by combining both horizontal and vertical speed gradients in a way similar to the 2D differential invariant def and oppose the view that surface slant is encoded by a 1D analysis of motion in a direction orthogonal to the perceived axis of inclination. In a further experiment, we found essentially no effect of reducing the field size from 18 to 9 deg.     

The transepicondylar axis approximates the optimal flexion axis of the knee

The traditional understanding of knee kinematics holds that no single fixed axis of rotation exists in the knee. In contrast, a recent hypothesis suggests that knee kinematics are better described simply as two simultaneous rotations occurring about fixed axes. Knee flexion and extension occurs about an optimal flexion axis fixed in the femur, whereas tibial internal and external rotations occur about a longitudinal rotation axis fixed in the tibia. No other translations or rotations exist. This hypothesis has been tested. Tibiofemoral kinematics were measured for 15 cadaveric knees undergoing a realistic loadbearing activity (simulated squatting). An optimization technique was used to identify the locations of the optimal flexion and longitudinal rotation axes such that simultaneous rotations about them could best represent the measured kinematics. The optimal flexion axis was compared with the transepicondylar axis defined by bony landmarks. The longitudinal rotation axis was found to pass through the medial joint compartment. The optimal flexion axis passed through the centers of the posterior femoral condyles. No significant difference was found between the optimal flexion and transepicondylar axes. To an average accuracy of better than 3.4 mm in translation, and 2.9 degrees in orientation, knee kinematics were represented successfully by simple rotations about the optimal flexion and longitudinal rotation axes. The optimal flexion axis is fixed in the femur and can be considered the true flexion axis of the knee. The transepicondylar axis axis, which is identified easily by palpation, closely approximates the optimal flexion axis.     

Determinants of the perception of rotational motion: Orientation of the motion to the object and to the environment.

The results of two experiments suggest that strong constraints on the ability to imagine rotations extend to the perception of rotations. Participants viewed stereographic perspective views of rotating squares, regular polyhedra, and a variety of polyhedral generalized cones, and attempted to indicate the orientation of the axis and planes of rotation in terms of one of the 13 canonical directions in 3D space. When the axis and planes of a rotation were aligned with principal directions of the environment, participants could indicate the orientation of the motion well. When a rotation was oblique to the environment, the orientation of the object to the motion made a very large difference to performance. Participants were fast and accurate when the object was a generalized cone about the axis of rotation or was elongated along the axis. Variation of the amount of rotation and reflection symmetry of the object about the axis of rotation was not powerful. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Three-dimensional organization of otolith-ocular reflexes in rhesus monkeys. I. Linear acceleration responses during off-vertical axis rotation

1. The dynamic properties of otolith-ocular reflexes elicited by sinusoidal linear acceleration along the three cardinal head axes were studied during off-vertical axis rotations in rhesus monkeys. As the head rotates in space at constant velocity about an off-vertical axis, otolith-ocular reflexes are elicited in response to the sinusoidally varying linear acceleration (gravity) components along the interaural, nasooccipital, or vertical head axis. Because the frequency of these sinusoidal stimuli is proportional to the velocity of rotation, rotation at low and moderately fast speeds allows the study of the mid-and low-frequency dynamics of these otolith-ocular reflexes. 2. Animals were rotated in complete darkness in the yaw, pitch, and roll planes at velocities ranging between 7.4 and 184 degrees/s. Accordingly, otolith-ocular reflexes (manifested as sinusoidal modulations in eye position and/or slow-phase eye velocity) were quantitatively studied for stimulus frequencies ranging between 0.02 and 0.51 Hz. During yaw and roll rotation, torsional, vertical, and horizontal slow-phase eye velocity was sinusoidally modulated as a function of head position. The amplitudes of these responses were symmetric for rotations in opposite directions. In contrast, mainly vertical slow-phase eye velocity was modulated during pitch rotation. This modulation was asymmetric for rotations in opposite direction. 3. Each of these response components in a given rotation plane could be associated with an otolith-ocular response vector whose sensitivity, temporal phase, and spatial orientation were estimated on the basis of the amplitude and phase of sinusoidal modulations during both directions of rotation. Based on this analysis, which was performed either for slow-phase eye velocity alone or for total eye excursion (including both slow and fast eye movements), two distinct response patterns were observed: 1) response vectors with pronounced dynamics and spatial/temporal properties that could be characterized as the low-frequency range of "translational" otolith-ocular reflexes; and 2) response vectors associated with an eye position modulation in phase with head position ("tilt" otolith-ocular reflexes). 4. The responses associated with two otolith-ocular vectors with pronounced dynamics consisted of horizontal eye movements evoked as a function of gravity along the interaural axis and vertical eye movements elicited as a function of gravity along the vertical head axis. Both responses were characterized by a slow-phase eye velocity sensitivity that increased three- to five-fold and large phase changes of approximately 100-180 degrees between 0.02 and 0.51 Hz. These dynamic properties could suggest nontraditional temporal processing in utriculoocular and sacculoocular pathways, possibly involving spatiotemporal otolith-ocular interactions. 5. The two otolith-ocular vectors associated with eye position responses in phase with head position (tilt otolith-ocular reflexes) consisted of torsional eye movements in response to gravity along the interaural axis, and vertical eye movements in response to gravity along the nasooccipital head axis. These otolith-ocular responses did not result from an otolithic effect on slow eye movements alone. Particularly at high frequencies (i.e., high speed rotations), saccades were responsible for most of the modulation of torsional and vertical eye position, which was relatively large (on average +/- 8-10 degrees/g) and remained independent of frequency. Such reflex dynamics can be simulated by a direct coupling of primary otolith afferent inputs to the oculomotor plant. (ABSTRACT TRUNCATED)     

Types of size disparity and the perception of surface slant

We examined (i) perceived slant of a textured surface about a vertical axis as a function of disparity magnitude for horizontal-size disparity, vertical-size disparity, and overall-size disparity; and (ii) interactions between patterns with various types and magnitudes of size disparity and superimposed or adjacent zero-disparity stimuli. Horizontal-size disparity produced slant which increased with increasing disparity, was enhanced by superimposed zero-disparity stimuli, and induced contrasting slant in superimposed or adjacent zero-disparity stimuli. Vertical-size disparity produced opposite slant (induced effect) which was reduced to near zero by a superimposed zero-disparity pattern and both patterns appeared as one surface. Adjacent vertical-size-disparity and zero-disparity patterns appeared as separate surfaces with a wide curved boundary. Overall-size disparity produced slant which was enhanced by a superimposed zero-disparity pattern and less so by a zero-disparity line, and induced more slant in a zero-disparity line than in a zero-disparity pattern. The results are discussed in terms of depth underestimation of isolated surfaces, depth enhancement, depth contrast, and the processing of deformation disparity.     

Transient hemifacial spasm associated with subarachnoid brainstem cysticercosis: a case report

The vestibulo-ocular reflex (VOR) and angular displacement perception were measured in 25 healthy humans in darkness before and after exposure to incoherent visual-vestibular stimulation (VVS): 45 min of repeated passive 180 degrees whole-body rotations around the vertical axis concurrent with only 90 degrees rotation in a visual virtual square room. Large inter-individual variability was observed for both VOR gain and turning estimates. The individual VOR gains were not correlated with perceived angles of rotation either before or after VVS. After VVS, the angular displacement perception decreased by 24+/-16% while the VOR gain did not change significantly. The results suggest that adaptive plasticity in turning perception and adaptive plasticity in VOR might be independent of one another.     

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

Mental rotation of objects retrieved from memory: A functional MRI study of spatial processing.

This functional MRI study examined how people mentally rotate a 3-dimensional object (an alarm clock) that is retrieved from memory and rotated according to a sequence of auditory instructions. We manipulated the geometric properties of the rotation, such as having successive rotation steps around a single axis versus alternating between 2 axes. The latter condition produced much more activation in several areas. Also, the activation in several areas increased with the number of rotation steps. During successive rotations around a single axis, the activation was similar for rotations in the picture plane and rotations in depth. The parietal (but not extrastriate) activation was similar to mental rotation of a visually presented object. The findings indicate that a large-scale cortical network computes different types of spatial information by dynamically drawing on each of its components to a differential, situation-specific degree. (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.     

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.     

The effect of foot structure on the three-dimensional kinematic coupling behavior of the leg and rear foot

BACKGROUND AND PURPOSE: Differences in foot structures have been reported to account for the large variability in findings in previous studies that have examined the relationship between foot structure and the interdependent rotations of the lower extremity. The purpose of this study was to determine, in individuals with radiographically distinct foot structures, the effect of foot structure on three-dimensional kinematic behavior of the leg and rear foot during running. SUBJECTS AND METHODS: Based on radiographic measurements, 10 recreational runners were assigned to a low rear-foot group and another 10 recreational runners were assigned to a high rear-foot group. Three-dimensional kinematic data were collected during treadmill running. Individual axis rotations and the "coupled" relationship between the leg and rear-foot segments were defined using a Cardan angle system of three ordered rotations. RESULTS: The predominant rotations suggest a combined subtalar and talocalcaneal joint axis to favor calcaneal eversion and inversion for the low rear-foot group and tibial medial and lateral rotation for the high rear-foot group. Group differences were also found for the coupling ratio, which described the proportion of calcaneal eversion and inversion transferred or coupled to tibial axial rotation. CONCLUSION AND DISCUSSION: The rotational patterns and coupling response unique to each foot group may enhance our understanding of lower-extremity injuries related to certain foot structures. An assessment of the coupling relationship in combination with traditional frontal-plane measurements may better guide decisions regarding selection of footwear and orthoses.     

Rotational and translational components of motion parallax: Observers' sensitivity and implications for three-dimensional computer graphics.

The motion of objects during motion parallax can be decomposed into 2 observer-relative components: translation and rotation. The depth ratio of objects in the visual field is specified by the inverse ratio of their angular displacement (from translation) or equivalently by the inverse ratio of their rotations. Despite the equal mathematical status of these 2 information sources, it was predicted that observers would be far more sensitive to the translational than rotational components. Such a differential sensitivity is implicitly assumed by the computer graphics technique billboarding, in which 3-dimensional (3-D) objects are drawn as planar forms (i.e., billboards) maintained normal to the line of sight. In 3 experiments, observers were found to be consistently less sensitive to rotational anomalies. The implications of these findings for kinetic depth effect displays and billboarding techniques are discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Visualizing 3D objects from 2D cross sectional images displayed in-situ versus ex-situ.

The present research investigates how mental visualization of a 3D object from 2D cross sectional images is influenced by displacing the images from the source object, as is customary in medical imaging. Three experiments were conducted to assess people’s ability to integrate spatial information over a series of cross sectional images in order to visualize an object posed in 3D space. Participants used a hand-held tool to reveal a virtual rod as a sequence of cross-sectional images, which were displayed either directly in the space of exploration (in-situ) or displaced to a remote screen (ex-situ). They manipulated a response stylus to match the virtual rod’s pitch (vertical slant), yaw (horizontal slant), or both. Consistent with the hypothesis that spatial colocation of image and source object facilitates mental visualization, we found that although single dimensions of slant were judged accurately with both displays, judging pitch and yaw simultaneously produced differences in systematic error between in-situ and ex-situ displays. Ex-situ imaging also exhibited errors such that the magnitude of the response was approximately correct but the direction was reversed. Regression analysis indicated that the in-situ judgments were primarily based on spatiotemporal visualization, while the ex-situ judgments relied on an ad hoc, screen-based heuristic. These findings suggest that in-situ displays may be useful in clinical practice by reducing error and facilitating the ability of radiologists to visualize 3D anatomy from cross sectional images. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Motional dynamics of residues in a beta-hairpin peptide measured by 13C-NMR relaxation

Structurally characterizing partially folded peptides is problematic given the nature of their transient conformational states. 13C-NMR relaxation data can provide information on the geometry of bond rotations, motional restrictions, and correlated bond rotations of the backbone and side chains and, therefore, is one approach that is useful to assess the presence of folded structure within a conformational ensemble. A peptide 12mer, R1GITVNG7KTYGR12, has been shown to partially fold in a relatively stable beta-hairpin conformation centered at NG. Here, five residues, G2, V5, G7, Y10, G11, were selectively 13C-enriched, and 13C-NMR relaxation experiments were performed to obtain auto- and cross-correlation motional order parameters, correlation times, bond rotation angular variances, and bond rotational correlation coefficients. Our results indicate that, of the three glycines, G7 within the hairpin beta-turn displays the most correlated phi(t),psi(t) rotations with its axis of rotation bisecting the angle defined by the H-C-H bonds. These positively correlated bond rotations give rise to "twisting" type motions of the HCH group. V5 and Y10 phi,psi bond rotations are also positively correlated, with their CbetaCalphaH groups undergoing similar "twisting" type motions. Motions of near-terminal residues G2 and G11 are less restricted and less correlated and are best described as wobbling-in-a-cone. V5 and Y10 side-chain motions, aside from being highly restricted, were found to be correlated with phi,psi bond rotations. At 303 K, where the hairpin is considered "unfolded," the peptide exists in a transient, collapsed state because backbone and side-chain motions of V5, G7, and Y10 remain relatively restricted, unlike their counterparts in GXG-based tripeptides. These results provide unique information toward understanding conformational variability in the unfolded state of proteins, which is necessary to solve the protein folding problem.     

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)     

Depth information and perceived self-motion during simulated gaze rotations

When presented with random-dot displays with little depth information, observers cannot determine their direction of self-motion accurately in the presence of rotational flow without appropriate extra-retinal information (Royden CS et al. Vis Res 1994;34:3197-214.). On theoretical grounds, one might expect improved performance when depth information is added to the display (van den Berg AV and Brenner E. Nature 1994;371:700-2). We examined this possibility by having observers indicate perceived self-motion paths when the amount of depth information was varied. When stereoscopic cues and a variety of monocular depth cues were added, observers still misperceived the depicted self-motion when the rotational flow in the display was not accompanied by an appropriate extra-retinal, eye-velocity signal. Specifically, they perceived curved self-motion paths with the curvature in the direction of the simulated eye rotation. The distance to the response marker was crucial to the objective measurement of this misperception. When the marker distance was small, the observers' settings were reasonably accurate despite the misperception of the depicted self-motion. When the marker distance was large, the settings exhibited the errors reported previously by Royden CS et al. Vis Res 1994;34-3197-3214. The path judgement errors observers make during simulated gaze rotations appear to be the result of misattributing path-independent rotation to self-motion along a circular path with path-dependent rotation. An analysis of the information an observer could use to avoid such errors reveals that the addition of depth information is of little use.     

The role of retinal versus perceived size in the effects of pitched displays on visually perceived eye level

Visually perceived eye level (VPEL) was measured while subjects viewed two vertical lines which were either upright or pitched about the horizontal axis. In separate conditions, the display consisted of a relatively large pair of lines viewed at a distance of 1 m, or a display scaled to one third the dimensions and viewed at a distance of either 1 m or 33.3 cm. The small display viewed at 33.3 cm produced a retinal image the same size as that of the large display at 1 m. Pitch of all three displays top-toward and top-away from the observer caused upward and downward VPEL shifts, respectively. These effects were highly similar for the large display and the small display viewed at 33.3 cm (ie equal retinal size), but were significantly smaller for the small display viewed at 1 m. In a second experiment, perceived size of the three displays was measured and found to be highly accurate. The results of the two experiments indicate that the effect of optical pitch on VPEL depends on the retinal image size of stimuli rather than on perceived size.     

Spatial coordination by descending vestibular signals. 2. Response properties of medial and lateral vestibulospinal tract neurons in alert and decerebrate cats

Spatial response properties of medial (MVST) and lateral (LVST) vestibulospinal tract neurons were studied in alert and decerebrate cats during sinusoidal angular rotations of the whole body in the horizontal and many vertical planes. Of 220 vestibulospinal neurons with activity modulated during 0.5-Hz sinusoidal rotations, 200 neurons exhibited response gains that varied as a cosine function of stimulus orientation and phases that were near head velocity for rotation planes far from the minimum response plane. A maximum activation direction vector (MAD), which represents the axis and direction of rotation that maximally excites the neuron, was calculated for these neurons. Spatial properties of secondary MVST neurons in alert and decerebrate animals were similar. The responses of 88 of 134 neurons (66%) could be accounted for by input from one semicircular canal pair. Of these, 84 had responses consistent with excitation from the ipsilateral canal of the pair (13 horizontal, 27 anterior, 44 posterior) and 4 with excitation from the contralateral horizontal canal. The responses of the remaining 46 (34%) neurons suggested convergent inputs. The activity of 38 of these was significantly modulated by both horizontal and vertical rotations. Twelve neurons (9%) had responses that were consistent with input from both vertical canal pairs, including 9 cells with MADs near the roll axis. Thirty-two secondary MVST neurons (24%) had type II yaw and/or roll responses. The spatial response properties of 18 secondary LVST neurons, all studied in decerebrate animals, were different from those of secondary MVST neurons. Sixteen neurons (89%) had type II yaw and/or roll responses, and 12 (67%) appeared to receive convergent canal pair input. Convergent input was more common on higher-order vestibulospinal neurons than on secondary neurons. These results suggest that MVST and LVST neurons and previously reported vestibulo-ocular neurons transmit functionally different signals. LVST neurons, particularly those with MADs close to the roll axis, may be involved in the vestibular-limb reflex. The combination of vertical and ipsilateral horizontal canal input on many secondary MVST neurons suggests a contribution to the vestibulocollic reflex. However, in contrast to most neck muscles, very few neurons had maximum vertical responses near pitch.