Recovery of 3-D shape from deforming contours

Three experiments were conducted to examine the accuracy of 3-D shape recovery from deforming-contour displays. The displays simulated silhouettes of ellipsoids rotating about a vertical axis. Subjects judged the horizontal cross-section of the ellipsoids. The shape of the ellipsoid, the position of the axis of rotation, and the type of projection were manipulated in Experiment 1. The results indicated relatively accurate shape recovery when the major axis of the ellipsoid was small. In Experiment 2, the shape of the ellipsoid and the velocity and curvature of the contour were manipulated. When the rate of deformation of curvature was decreased, more eccentric shapes were reported. In Experiment 3, the shape of the object and the amount of simulated rotation were manipulated. Subjects made both shape and extent of rotation judgments. The results showed that eccentricity of shape responses could be accurately predicted from rotation responses, suggesting that the recovery of 3-D shape from smooth, deforming contours is dependent on the perceived extent of rotation.     

Optic-flow-based perception of two-dimensional trajectories and the effects of a single landmark

Human observers can detect their heading direction on a short time scale on the basis of optic flow. We investigated the visual perception and reconstruction of visually travelled two-dimensional (2-D) trajectories from optic flow, with and without a landmark. As in our previous study, seated, stationary subjects wore a head-mounted display in which optic-flow stimuli were shown that simulated various manoeuvres: linear or curvilinear 2-D trajectories over a horizontal plane, with observer orientation either fixed in space, fixed relative to the path, or changing relative to both. Afterwards, they reproduced the perceived manoeuvre with a model vehicle, whose position and orientation were recorded. Previous results had suggested that our stimuli can induce illusory percepts when translation and yaw are unyoked. We tested that hypothesis and investigated how perception of the travelled trajectory depends on the amount of yaw and the average path-relative orientation. Using a structured visual environment instead of only dots, or making available additional extra-retinal information, can improve perception of ambiguous optic-flow stimuli. We investigated the amount of necessary structuring, specifically the effect of additional visual and/or extra-retinal information provided by a single landmark in conditions where illusory percepts occur. While yaw was perceived correctly, the travelled path was less accurately perceived, but still adequately when the simulated orientation was fixed in space or relative to the trajectory. When the amount of yaw was not equal to the rotation of the path, or in the opposite direction, subjects still perceived orientation as fixed relative to the trajectory. This caused trajectory misperception because yaw was wrongly attributed to a rotation of the path: path perception is governed by the amount of yaw in the manoeuvre. Trajectory misperception also occurs when orientation is fixed relative to a curvilinear path, but not tangential to it. A single landmark could improve perception. Our results confirm and extend previous findings that, for unambiguous perception of ego-motion from optic flow, additional information is required in many cases, which can take the form of fairly minimal, visual information.     

Tactile recognition of mirror images by children: intermanual transfer and rotation of the palm

In order to evaluate the importance of the axis of stimulus presentation, inter- and intramanual recognition of mirror pairs was studied with the stimulus materials aligned along the front/back axis (whereas in previous work the mirror pairs were aligned along the left/right axis). Children were allowed to feel shapes with the whole hand, with only four fingers (excluding the thumb), or with only the index finger. After learning with one hand, recognition was tested in experiment 1 with the other hand; after learning with one orientation of the hand (palm down or up), recognition was tested in experiment 2 with the other orientation (palm up or down) of the same hand; after learning with one coronal alignment of the hand (to the left or right), recognition was tested in experiment 3 with the other alignment (to the right or left), but without rotation, of the same hand. Significantly fewer intermanual recognition errors were made on mirror pairs with the materials oriented along the front/back axis than in previous work when oriented along the left/right axis. This supports the suggestion that such errors arise when the stimuli are oriented along the left/right axis during formation of the memory trace. The same trend was unexpectedly obtained for intramanual recognition errors (after rotation of the hand). These errors (after hand rotation) are largely due to coding with respect to the hand; they are reduced when the hand is not aligned with the body axis, since then coding can also occur in relation to the environment.     

Perceiving shape from profiles

Four experiments related human perception of shape from profiles to current theoretical predictions. In Experiment 1, judgments of structure and motion were obtained for single- and dualellipsoid displays rotating about various axes. Ratings were highest when the axis of rotation was in the image plane and were influenced by the number of ellipsoids and the orientation of a single ellipsoid. The subsequent experiments explored the effect of orientation on shape judgments of a single ellipsoid. The results of Experiments 2 and 3 suggested that the effect of orientation found in Experiment 1 was not due to either the inability of certain orientations to be perceived as three-dimensional objects or to two-dimensional artifacts. It was thus argued that this effect of orientation was due to points of correspondence in relative motion that arise when the major axis is not perpendicular to the axis of rotation. In Experiment 4, subjects provided judgments of both shape and angular velocity. The elevated ellipsoids that were judged as larger were also judged as rotating more slowly. The inverse relationship between size and angular velocity is consistent with current theories. The connection between theory and data was further demonstrated by applying a shape-recovery algorithm to the stimuli used in Experiment 4 and finding a similar tradeoff between angular velocity and shape.     

Analyzing the kinematics of hand movements in catching tasks—An online correction analysis of movement toward the target’s trajectory

Free, 3-D interceptive movements are difficult to visualize and quantify. For ball catching, the endpoint of a movement can be anywhere along the target’s trajectory. Furthermore, the hand may already have begun to move before the subject has estimated the target’s trajectory, and the subject may alter the targeted position during the initial part of the movement. We introduce a method to deal with these difficulties and to quantify three movement phases involved in catching: the initial, non-goal-directed phase; the goal-directed phase, which is smoothly directed toward the target’s trajectory; and the final, interception phase. Therefore, the 3-D movement of the hand was decomposed into a component toward the target’s trajectory (the minimal distance of the hand to the target’s parabolic [MDHP] trajectory) and a component along this trajectory. To identify the goal-directed phase of the MDHP trajectory, we employed the empirical finding that goal-directed trajectories are minimally jerky. The second component, along the target’s trajectory, was used to analyze the interaction of the hand with the ball. The method was applied to two conditions of a ball-catching task. In the manipulated condition, the initial part of the ball’s flight was occluded, so the visibility of the ball was postponed. As expected, the onset of the smooth part of the movement shifted to a later time. This method can be used to quantify anticipatory behavior in interceptive tasks, allowing researchers to gain new insights into movement planning toward the target’s trajectory.     

Eye-hand coupling during closed-loop drawing: evidence of shared motor planning?

Previous paradigms have used reaching movements to study coupling of eye-hand kinematics. In the present study, we investigated eye-hand kinematics as curved trajectories were drawn at normal speeds. Eye and hand movements were tracked as a monkey traced ellipses and circles with the hand in free space while viewing the hand's position on a computer monitor. The results demonstrate that the movement of the hand was smooth and obeyed the 2/3 power law. Eye position, however, was restricted to 2-3 clusters along the hand's trajectory and fixed approximately 80% of the time in one of these clusters. The eye remained stationary as the hand moved away from the fixation for up to 200 ms and saccaded ahead of the hand position to the next fixation along the trajectory. The movement from one fixation cluster to another consistently occurred just after the tangential hand velocity had reached a local minimum, but before the next segment of the hand's trajectory began. The next fixation point was close to an area of high curvature along the hand's trajectory even though the hand had not reached that point along the path. A visuo-motor illusion of hand movement demonstrated that the eye movement was influenced by hand movement and not simply by visual input. During the task, neural activity of pre-motor cortex (area F4) was recorded using extracellular electrodes and used to construct a population vector of the hand's trajectory. The results suggest that the saccade onset is correlated in time with maximum curvature in the population vector trajectory for the hand movement. We hypothesize that eye and arm movements may have common, or shared, information in forming their motor plans.     

Interpolation across surface discontinuities in structure from motion Asad Satdpour

Interpolation across orientation discontinuities in simulated three-dimensional (3-D). surfaces was studied in three experiments with the use of structure-from-motion (SFM). displays. The displays depicted dots on two slanted planes with a region devoid of dots (a gap). between them. If extended through the gap at constant slope, the planes would meet at a dihedral edge. Subjects were required to place an SFM probe dot, located within the gap, on the perceived surface. Probe dot placements indicated that subjects perceived a smooth surface connecting the planes rather than a surface with a discontinuity. Probe dot placements varied with slope of the planes, density of the dots, and gap size, but not with orientation (horizontal or vertical). of the dihedral edge or of the axis of rotation. Smoothing was consistent with models of 2-D interpolation proposed by Ullman (1976). and Kellman and Shipley (1991). and with a model of 3-D interpolation proposed by Grimson (1981).     

Comparing derived and acquired acceleration profiles: 3-D optical electronic data analyses

Advances in technology in the last century have provided the opportunity to observe human behavior in one, two, and three dimensions with higher recording frequencies and greater spatial accuracy. Consequently, detailed analyses of individual trials and composite measures of multiple movement trajectories are possible. However, 3-D data have often been analyzed by performing independent analyses of the limb trajectory along each axis. Essentially, analyses of individual axes are often inappropriate as movement in each axis can contribute to the overall trajectory. Employing such methods can compound error throughout the analysis process. The purpose of this study was to determine appropriate post hoc and real-time 3-D optoelectronic data reduction procedures for manual aiming movements. Rapid goal-directed movements were recorded using an Optotrak and triaxial accelerometer. Data were separately subjected to second order Butterworth filters employing low-cut frequencies of 6-24 Hz in 2 Hz increments. Subsequently, acceleration profiles were derived by double differentiating the individual position profiles and then calculating the resultant acceleration profile. In addition, acceleration profiles were also calculated by finding the resultant position and the total distance traveled each frame prior to double differentiation. Root mean square error between the derived and acquired profiles was employed as our main dependent measure. Trajectories reduced with the total distance procedure produced the lowest root mean square error. The results are important for experimenters analyzing 3-D data post hoc and those implementing real-time manipulations.     

How do Motor Systems Deal with the Problems of Controlling Three-Dimensional Rotations?

Rotations are fundamental to motor control, not only for orienting to stimuli but also in the joint articulations that underlie translational movements. Studying three-dimensional (3-D) rotations of the simplest joint system, the eye, has provided general insights into the neural control of movement. First, in selecting one 3-D eye orientation for each two-dimensional (2-D) gaze direction, the oculomotor system generates a behavior called Listing's law that constrains eye position to a 2-D plane, Listing's plane. This selection is made internally by an inverse kinematic transformation called the Listing's law operator. Second, the oculomotor system incorporates the inherent multiplicative relationship between rotational velocity and position to generate the 3-D movement and position commands required by Listing's law. Finally, the coordinate systems for these commands appear to align with Listing's plane rather than with anatomic structures. Recent investigations have revealed similar behavioral constraints in the orientations of the head and arm, suggesting that the neural mechanisms for Listing's law may have analogues in many motor systems.     

Lateral interception II: predicting hand movements

D. M. Jacobs and C. F. Michaels (2006) concluded that aspects of hand movements in lateral catching were predicted by the ratio of lateral optical velocity to expansion velocity. Their conclusions were based partly on a modified version of the required velocity model of catching (C. E. Peper, R. J. Bootsma, D. R. Mestre, & F. C. Bakker, 1994). The present article considers this optical ratio in detail and asks whether it, together with a control law, predicts the (often curious) hand trajectories observed in lateral interception. The optical ratio was used to create a succession of target-position inputs for the vector integration to endpoint model of hand movements (D. Bullock & S. Grossberg, 1988). The model used this succession, initial hand position, and model parameters (fit to 60 trials) to predict hand trajectories on each trial. Predicted trajectories were then compared with observed hand trajectories. Hand movements were predicted accurately, especially in the binocular condition, and were superior to predictions based on lateral ball position, the input variable of the required velocity model. The authors concluded, as did C. E. Peper et al. (1994), that perceivers continuously couple movements to optics.     

The role of surface attraction in perceiving volumetric shape

Rock [1973, Orientation and Form (New York: Academic Press)] showed that form perception generally depends more on the orientation of a stimulus in world coordinates than on its orientation in retinal coordinates. He suggested that the assignment of an object's 'environmental orientation' depends on gravity, visual frame of reference, and the observer's ability to impose orientation along one axis or another. This paper shows that the assignment of environmental orientation and perceived 3-D form also depends on the relationship between an object and retinally adjacent surfaces in the scene to which it might be attached. Whereas previous examples have demonstrated effects of orientation on 2-D form, we show that orientation can affect the perceived intrinsic 3-D shape of a volume.     

Effects of different motion characteristics on perceived motion in depth

Abstract.— The effect of different velocity characteristics on type of perceived motion were tested with three different stimulus patterns, each representing a certain case of relative motion vectors derived from a vector model for perceived motion in space. The oscilloscope generated patterns, displayed onto a translucent screen, consisted of two dots moving back and forth in their motion paths. The subjects described the perceived motion verbally. The reports were classified into four response categories, i.e. perceived translation in depth, rotation in depth, translation and rotation in depth, and finally, perceived motion in a frontoparallel plane. It was found, first, that no type of relative motion vectors consistently yielded the same distribution of responses for the different velocity conditions. Second, there were no main effects of type of velocity functions (sinusoidal, hyperbolical, and constant) on perceived motion. Third, the position of maximum velocity of the dots affected perceived motion, maximum velocity at the center of the motion path favoring perceived rotation in depth and maximum velocity at the end points of the paths favoring perceived translation in depth. Finally, patterns with continuously repeated motion cycles favored perceived rotation in depth. When the continuity was broken down by pauses at the center and the end points of the motion paths and a small spatial gap at the center of the path, perceived translation in depth was favored.     

Representational momentum and event course anticipation in the perception of implied periodical motions.

After viewing an object in an implied rotation, subjects' short-term visual memory for the object's position is distorted in the direction of rotation. Previous accounts of this representational momentum effect have emphasized the analogy to physical momentum. This study provides a more general perspective: Position memory is influenced by anticipatory processes related to the future event course. In Experiment 1, subjects are presented with an implied periodical event in which a rectangle rotates back and forth. When a direction change in the implied rotation can be anticipated, memory distortion size drops back to zero. Experiment 2 rejects an alternative explanation for the findings of Experiment 1 in terms of enhanced position memory caused by repeated presentations of the memory pattern orientation within the same trial. In Experiment 3, the periods of the implied event are marked by changes in velocity rather than direction. The anticipation of a sudden velocity increase leads to a larger memory shift. We conclude that the perceptual system anticipates the event course on the basis of a representation of the higher order event structure rather than the local motion characteristics.     

Multiple 3-D interpretations in a classic stereokinetic effect

It is known that a flat ellipse rotating in the frontoparallel plane sooner or later appears as a rigid circular disc tilting in 3-D space. An experiment is reported in which prolonged exposure to the same flat pattern produces a second previously unnoticed 3-D percept: an elongated egg slanted in 3-D space, which points towards the observer and the end parts of which describe a circular trajectory in the frontal plane. It is shown that the achievement of this alternative percept is not affected by the particular shape of the ellipse, although the time needed to reach it increases with an ellipse with a 2:3 axis ratio.     

Visual search for simple volumetric shapes.

Five experiments measured reaction time (RT) to detect the presence or absence of a simple volumetric shape (target) dependent on the number of display items (distractors) and their depicted three-dimensional (3-D) orientation. Experiments 1-4 examined every pairwise combination of two different simple volumetric shapes in two 3-D orientations. Conditions exhibiting "pop-out" could be predicted by differences in their two-dimensional (2-D) features. Conditions in which search was slower support previously found search asymmetries for particular 2-D features. When the distractors were a mixture of the other shapes in the same 3-D orientation, search was serial, except when the target had a curved principal axis (Experiment 5). The results suggest that these simple volumetric shapes are not processed preattentively.     

Visual search for simple volumetric shapes

Five experiments measured reaction time (RT) to detect the presence or absence of a simple volumetric shape (target) dependent on the number of display items (distractors) and their depicted three-dimensional (3-D) orientation. Experiments 1–4 examined every pairwise combination of two different simple volumetric shapes in two 3-D orientations. Conditions exhibiting “pop-out” could be predicted by differences in their two-dimensional (2-D) features. Conditions in which search was slower support previously found search asymmetries for particular 2-D features. When the distractors were a mixture of the other shapes in the same 3-D orientation, search was serial, except when the target had a curved principal axis (Experiment 5). The results suggest that these simple volumetric shapes are not processed preattentively.