The Effect of Two-Dimensional and Three-Dimensional Distance on Apparent Motion

Perception ◽  
1983 ◽  
Vol 12 (3) ◽  
pp. 305-312 ◽  
Author(s):  
Kathleen Mutch ◽  
Isabel M Smith ◽  
Albert Yonas
Keyword(s):  
Motion Perception ◽  
Apparent Motion ◽  
Three Dimensional ◽  
Spatial Separation ◽  
Three Dimensions ◽  
Correspondence Problem ◽  
Two Dimensional ◽  
Motion Display ◽  
Specific Concern ◽  
Actual Depth

The problem of how the visual system matches corresponding inputs from one instant to the next to produce the perception of motion has been experimentally examined. The specific concern was whether this correspondence problem is solved prior to the interpretation of three-dimensional distance. Observers judged the degree of apparent motion between pairs of lights in a conflicting motion display. Spatial separation of the lights was varied in two and three dimensions in order to assess whether retinal distance, actual depth, or some combination of these provided critical information for correspondence. The results support Ullman's contention that only two-dimensional (retinal) distances are used in establishing correspondence in motion perception.

The Tactile Quartet: Comparing Ambiguous Apparent Motion in Tactile and Visual Stimuli

Perception ◽  
2019 ◽  
Vol 49 (1) ◽  
pp. 61-80 ◽  
Author(s):  
Harry H. Haladjian ◽  
Stuart Anstis ◽  
Mark Wexler ◽  
Patrick Cavanagh
Keyword(s):  
Motion Perception ◽  
Apparent Motion ◽  
Index Finger ◽  
Dimensional Space ◽  
Visual Stimuli ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Different Depths ◽  
Three Dimensional Space

In the visual quartet, alternating diagonal pairs of dots produce apparent motion horizontally or vertically, depending on proximity. Here, we studied a tactile quartet where vibrating tactors were attached to the thumbs and index fingers of both hands. Apparent motion was felt either within hands (from index finger to thumb) or between hands. Participants adjusted the distance between their hands to find the point where motion changed directions. Surprisingly, switchovers occurred when between-hand distances were as much as twice that of within-hand distances—a general bias that was also found for tactile judgments of static distances. This expansion of within-hand felt distances was again seen when lights were placed on the hands rather than vibrating tactors. Importantly, switchover points were similar when the hands were placed at different depths, indicating that representations governing tactile motion were in perceptual three-dimensional space, not retinal two-dimensional space. This was true whether the quartets were visual stimuli on the hands or were purely visual on a monitor, suggesting that proximity is generally determined in three-dimensional coordinates for motion perception. Finally, the similarity of visual and tactile results suggests a common computation for apparent motion, albeit with different built-in distance biases for separate modalities.

Two Dimensionality of the Correspondence Process in Apparent Motion

Perception ◽  
1978 ◽  
Vol 7 (6) ◽  
pp. 683-693 ◽  
Author(s):  
Shimon Ullman
Keyword(s):  
Motion Perception ◽  
Apparent Motion ◽  
Spatial Separation ◽  
Two Dimensional ◽  
Fundamental Process

A fundamental process underlying motion perception is the matching of corresponding elements in different views. In this correspondence process spatial separation between elements plays a major role. The relevant separation is shown by the current study to be the two-dimensional, uninterpreted distance, a finding that has an implication to the level at which the correspondence process is carried out. The current findings are compared with earlier results concerning ‘optimality’ of apparent motion to conclude that optimality cannot serve as a measure for the correspondence strength.

scholarly journals Illusory size determines the perception of ambiguous apparent motion

2020 ◽  
Vol 27 (6) ◽  
pp. 1230-1238
Author(s):  
Madeleine Y. Stepper ◽  
Cathleen M. Moore ◽  
Bettina Rolke ◽  
Elisabeth Hein
Keyword(s):  
Motion Perception ◽  
Apparent Motion ◽  
Apparent Depth ◽  
Correspondence Problem ◽  
Ambiguous Information ◽  
Depth Cues ◽  
Pictorial Depth ◽  
Retinal Input ◽  
Motion Display ◽  
Level Of Processing

AbstractThe visual system constructs perceptions based on ambiguous information. For motion perception, the correspondence problem arises, i.e., the question of which object went where. We asked at which level of processing correspondence is solved – lower levels based on information that is directly available in the retinal input or higher levels based on information that has been abstracted beyond the input directly available at the retina? We used a Ponzo-like illusion to manipulate the perceived size and separations of elements in an ambiguous apparent motion display. Specifically, we presented Ternus displays – for which the type of motion that is perceived depends on how correspondence is resolved – at apparently different distances from the viewer using pictorial depth cues. We found that the perception of motion depended on the apparent depth of the displays, indicating that correspondence processes utilize information that is produced at higher-level processes.

Mine Impact Burial Prediction From One to Three Dimensions

2008 ◽  
Vol 62 (1) ◽  
Author(s):  
Peter C. Chu
Keyword(s):  
Three Dimensional ◽  
Time History ◽  
Three Dimensions ◽  
Vertical Position ◽  
Burial Depth ◽  
Prediction Errors ◽  
Two Dimensional ◽  
Dimensional Model ◽  
One Dimensional ◽  
Dimensional Models

The Navy’s mine impact burial prediction model creates a time history of a cylindrical or a noncylindrical mine as it falls through air, water, and sediment. The output of the model is the predicted mine trajectory in air and water columns, burial depth/orientation in sediment, as well as height, area, and volume protruding. Model inputs consist of parameters of environment, mine characteristics, and initial release. This paper reviews near three decades’ effort on model development from one to three dimensions: (1) one-dimensional models predict the vertical position of the mine’s center of mass (COM) with the assumption of constant falling angle, (2) two-dimensional models predict the COM position in the (x,z) plane and the rotation around the y-axis, and (3) three-dimensional models predict the COM position in the (x,y,z) space and the rotation around the x-, y-, and z-axes. These models are verified using the data collected from mine impact burial experiments. The one-dimensional model only solves one momentum equation (in the z-direction). It cannot predict the mine trajectory and burial depth well. The two-dimensional model restricts the mine motion in the (x,z) plane (which requires motionless for the environmental fluids) and uses incorrect drag coefficients and inaccurate sediment dynamics. The prediction errors are large in the mine trajectory and burial depth prediction (six to ten times larger than the observed depth in sand bottom of the Monterey Bay). The three-dimensional model predicts the trajectory and burial depth relatively well for cylindrical, near-cylindrical mines, and operational mines such as Manta and Rockan mines.

Monkey superior colliculus represents rapid eye movements in a two-dimensional motor map

1993 ◽  
Vol 69 (3) ◽  
pp. 965-979 ◽  
Author(s):  
K. Hepp ◽  
A. J. Van Opstal ◽  
D. Straumann ◽  
B. J. Hess ◽  
V. Henn
Keyword(s):  
Eye Movements ◽  
Superior Colliculus ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Eye Position ◽  
Two Dimensional ◽  
Vestibular Nystagmus ◽  
Rapid Eye Movements ◽  
Q Model

1. Although the eye has three rotational degrees of freedom, eye positions, during fixations, saccades, and smooth pursuit, with the head stationary and upright, are constrained to a plane by ListingR's law. We investigated whether Listing's law for rapid eye movements is implemented at the level of the deeper layers of the superior colliculus (SC). 2. In three alert rhesus monkeys we tested whether the saccadic motor map of the SC is two dimensional, representing oculocentric target vectors (the vector or V-model), or three dimensional, representing the coordinates of the rotation of the eye from initial to final position (the quaternion or Q-model). 3. Monkeys made spontaneous saccadic eye movements both in the light and in the dark. They were also rotated about various axes to evoke quick phases of vestibular nystagmus, which have three degrees of freedom. Eye positions were measured in three dimensions with the magnetic search coil technique. 4. While the monkey made spontaneous eye movements, we electrically stimulated the deeper layers of the SC and elicited saccades from a wide range of initial positions. According to the Q-model, the torsional component of eye position after stimulation should be uniquely related to saccade onset position. However, stimulation at 110 sites induced no eye torsion, in line with the prediction of the V-model. 5. Activity of saccade-related burst neurons in the deeper layers of the SC was analyzed during rapid eye movements in three dimensions. No systematic eye-position dependence of the movement fields, as predicted by the Q-model, could be detected for these cells. Instead, the data fitted closely the predictions made by the V-model. 6. In two monkeys, both SC were reversibly inactivated by symmetrical bilateral injections of muscimol. The frequency of spontaneous saccades in the light decreased dramatically. Although the remaining spontaneous saccades were slow, Listing's law was still obeyed, both during fixations and saccadic gaze shifts. In the dark, vestibularly elicited fast phases of nystagmus could still be generated in three dimensions. Although the fastest quick phases of horizontal and vertical nystagmus were slower by about a factor of 1.5, those of torsional quick phases were unaffected. 7. On the basis of the electrical stimulation data and the properties revealed by the movement field analysis, we conclude that the collicular motor map is two dimensional. The reversible inactivation results suggest that the SC is not the site where three-dimensional fast phases of vestibular nystagmus are generated.(ABSTRACT TRUNCATED AT 400 WORDS)

Local-Level and Global-Level Form Characteristics in Apparent-Motion Correspondence

Perception ◽  
1995 ◽  
Vol 24 (11) ◽  
pp. 1233-1245 ◽  
Author(s):  
Terry Palmer ◽  
Ovid J L Tzeng ◽  
Sheng He
Keyword(s):  
Apparent Motion ◽  
Motion Detection ◽  
Local Level ◽  
The Other ◽  
Correspondence Problem ◽  
Global Level ◽  
Global Precedence ◽  
Detection Mechanism ◽  
Motion Display ◽  
Motion Correspondence

This study addressed the ‘correspondence’ problem of apparent-motion (AM) perception in which parts of a scene must be matched with counterparts separated in time and space. Given evidence that AM correspondence can be mediated by two distinct processes—one based on a low-level motion-detection mechanism (the Reichardt process), the other involving the tracking of objects by visual attention (the attention-based process)—the present study explored how these processes interact in the perception of apparent motion between hierarchically structured figures. In three experiments, hierarchical figures were presented in a competition motion display so that, across frames, figures were identical at either the local or the global level. In experiment 1 it was shown that AM occurred between locally identical figures. Furthermore, with the Reichardt AM component eliminated in experiments 3 and 4, no preference was obtained for either level. While evidence from previous studies suggests that form extraction for hierarchically structured figures proceeds from the global to the local level, the present results indicate the irrelevance of such a global precedence in AM correspondence. In addition, it is suggested that Reichardt AM correspondence between local elements constrains attention-based AM correspondence between global figures so that both components move in the same direction. It is argued that this constraining process represents an elegant means of achieving AM correspondence between objects undergoing complex transformations.

Bringing Dynamic Geometry to Three Dimensions

2015 ◽  
pp. 68-99
Author(s):  
Nicholas H. Wasserman
Keyword(s):  
Teaching And Learning ◽  
Spatial Reasoning ◽  
Mathematics Classroom ◽  
Three Dimensional ◽  
Dynamic Geometry ◽  
State Standards ◽  
Three Dimensions ◽  
Two Dimensional ◽  
The Common ◽  
K 12

Contemporary technologies have impacted the teaching and learning of mathematics in significant ways, particularly through the incorporation of dynamic software and applets. Interactive geometry software such as Geometers Sketchpad (GSP) and GeoGebra has transformed students' ability to interact with the geometry of plane figures, helping visualize and verify conjectures. Similar to what GSP and GeoGebra have done for two-dimensional geometry in mathematics education, SketchUp™ has the potential to do for aspects of three-dimensional geometry. This chapter provides example cases, aligned with the Common Core State Standards in mathematics, for how the dynamic and unique features of SketchUp™ can be integrated into the K-12 mathematics classroom to support and aid students' spatial reasoning and knowledge of three-dimensional figures.

scholarly journals The magnetorotational instability prefers three dimensions

2020 ◽  
Vol 476 (2233) ◽  
pp. 20190622
Author(s):  
Jeffrey S. Oishi ◽  
Geoffrey M. Vasil ◽  
Morgan Baxter ◽  
Andrew Swan ◽  
Keaton J. Burns ◽  
...  
Keyword(s):  
Shear Rate ◽  
Angular Velocity ◽  
Laboratory Experiments ◽  
Three Dimensional ◽  
Linear Instability ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Magnetorotational Instability ◽  
Dynamo Action ◽  
Wide Range

The magnetorotational instability (MRI) occurs when a weak magnetic field destabilizes a rotating, electrically conducting fluid with inwardly increasing angular velocity. The MRI is essential to astrophysical disc theory where the shear is typically Keplerian. Internal shear layers in stars may also be MRI-unstable, and they take a wide range of profiles, including near-critical. We show that the fastest growing modes of an ideal magnetofluid are three-dimensional provided the shear rate, S , is near the two-dimensional onset value, S c . For a Keplerian shear, three-dimensional modes are unstable above S  ≈ 0.10 S c , and dominate the two-dimensional modes until S  ≈ 2.05 S c . These three-dimensional modes dominate for shear profiles relevant to stars and at magnetic Prandtl numbers relevant to liquid-metal laboratory experiments. Significant numbers of rapidly growing three-dimensional modes remainy well past 2.05 S c . These finding are significant in three ways. First, weakly nonlinear theory suggests that the MRI saturates by pushing the shear rate to its critical value. This can happen for systems, such as stars and laboratory experiments, that can rearrange their angular velocity profiles. Second, the non-normal character and large transient growth of MRI modes should be important whenever three-dimensionality exists. Finally, three-dimensional growth suggests direct dynamo action driven from the linear instability.

scholarly journals On the Measure-Preserving Mappings with Three-Dimensions

1993 ◽  
Vol 132 ◽  
pp. 73-89
Author(s):  
Yi-Sui Sun
Keyword(s):  
Fixed Point ◽  
Invariant Manifolds ◽  
Three Dimensional ◽  
Invariant Curve ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Kolmogorov Entropy ◽  
Numerical Exploration ◽  
Area Preserving ◽  
Dimensional Mapping

AbstractWe have systematically made the numerical exploration about the perturbation extension of area-preserving mappings to three-dimensional ones, in which the fixed points of area preserving are elliptic, parabolic or hyperbolic respectively. It has been observed that: (i) the invariant manifolds in the vicinity of the fixed point generally don’t exist (ii) when the invariant curve of original two-dimensional mapping exists the invariant tubes do also in the neighbourhood of the invariant curve (iii) for the perturbation extension of area-preserving mapping the invariant manifolds can only be generated in the subset of the invariant manifolds of original two-dimensional mapping, (iv) for the perturbation extension of area preserving mappings with hyperbolic or parabolic fixed point the ordered region near and far from the invariant curve will be destroyed by perturbation more easily than the other one, This is a result different from the case with the elliptic fixed point. In the latter the ordered region near invariant curve is solid. Some of the results have been demonstrated exactly.Finally we have discussed the Kolmogorov Entropy of the mappings and studied some applications.

An Intrinsically Three-Dimensional Fractal

2014 ◽  
Vol 24 (06) ◽  
pp. 1430017 ◽  
Author(s):  
M. Fernández-Guasti
Keyword(s):  
Bifurcation Diagram ◽  
Chaotic Behavior ◽  
Logistic Map ◽  
Three Dimensional ◽  
Periodic Points ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Hyperbolic Numbers ◽  
Self Similar ◽  
One To One

The quadratic iteration is mapped using a nondistributive real scator algebra in three dimensions. The bound set S has a rich fractal-like boundary. Periodic points on the scalar axis are necessarily surrounded by off axis divergent magnitude points. There is a one-to-one correspondence of this set with the bifurcation diagram of the logistic map. The three-dimensional S set exhibits self-similar 3D copies of the elementary fractal along the negative scalar axis. These 3D copies correspond to the windows amid the chaotic behavior of the logistic map. Nonetheless, the two-dimensional projection becomes identical to the nonfractal quadratic iteration produced with hyperbolic numbers. Two- and three-dimensional renderings are presented to explore some of the features of this set.

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