Home  ›  Psc 131 How Could This Model Explain Why We See Apparent Motion as Continuous Motion

Psc 131 How Could This Model Explain Why We See Apparent Motion as Continuous Motion

Written By Saturday, October 15, 2022 Add Comment Edit

May 2007

Volume 7, Issue 8

  • Issue

Figure 1

Perceptual equilibrium in apparent motion. (A) A stimulus for ambiguous apparent motion is depicted in two spatial coordinates (x, y) and one temporal coordinate. The spatial projection of the stimulus is shown in the inset. Element o has two potential matches: a (giving rise to motion path ma) and b (giving rise to motion path mb). Each motion path has two parameters: temporal distance (Ta or Tb) and spatial distance (Sa or Sb). (B) In the distance plot, each motion path is represented by a point {Ti, Si}. We constrain the parameters such that Ta and Sa are fixed and Tb = 2Ta. The spatial distance Sb is allowed to vary to determine the point of perceptual equilibrium where the competing motions are equally likely to be seen (Figure 2). Note that the distance plot does not represent information about the direction (and, therefore, about velocity) of motion.

Perceptual equilibrium in apparent motion. (A) A stimulus for ambiguous apparent motion is depicted in two spatial coordinates (x, y) and one temporal coordinate. The spatial projection of the stimulus is shown in the inset. Element o has two potential matches: a (giving rise to motion path ) and b (giving rise to motion path ). Each motion path has two parameters: temporal distance (T a or T b) and spatial distance (S a or S b). (B) In the distance plot, each motion path is represented by a point {T i , S i }. We constrain the parameters such that T a and S a are fixed and T b = 2T a. The spatial distance S b is allowed to vary to determine the point of perceptual equilibrium where the competing motions are equally likely to be seen (Figure 2). Note that the distance plot does not represent information about the direction (and, therefore, about velocity) of motion.

Figure 2

Hypothetical conditions of perceptual equilibrium between two paths of apparent motion, m a and m b, in Figure 1. The temporal and spatial distances { T a, S a } between successive elements in m a are represented by Point 1, which is fixed. The temporal distance of m b is also held constant at T b = 2 T a. We vary the spatial distance S b to determine its value when m b is in equilibrium with m a, that is, p( μ a) = p( μ b) = 0.5. Space–time tradeoff occurs whenever S b < S a, in the dark gray region (e.g., at Point 2). Space–time coupling occurs whenever S b > S a, in the light gray region (e.g., at Point 4). Time independence—or

Hypothetical conditions of perceptual equilibrium between two paths of apparent motion, m a and m b , in Figure 1. The temporal and spatial distances { T a, S a } between successive elements in m a are represented by Point 1, which is fixed. The temporal distance of m b is also held constant at T b = 2 T a. We vary the spatial distance S b to determine its value when m b is in equilibrium with m a , that is, p( μ a) = p( μ b) = 0.5. Space–time tradeoff occurs whenever S b < S a, in the dark gray region (e.g., at Point 2). Space–time coupling occurs whenever S b > S a, in the light gray region (e.g., at Point 4). Time independence—or "shortest spatial path"—occurs at S b = S a (Point 3).

Figure 3

Data reconstructed from Korte (1915). The rows contain data for different observers; and the columns, for different interstimulus intervals (ISI). The highest rating corresponds to good motion. To maintain the experience of good motion, the temporal distance between successive stimuli and their spatial distance should be both increased or both decreased.

Data reconstructed from Korte (1915). The rows contain data for different observers; and the columns, for different interstimulus intervals (ISI). The highest rating corresponds to good motion. To maintain the experience of good motion, the temporal distance between successive stimuli and their spatial distance should be both increased or both decreased.

Figure 4

Stimulus of Burt and Sperling (1981). (A) A horizontal row of dots is flashed sequentially while it is displaced horizontally and downward. The rows of unfilled dots are occupied by the row of dots across time: Every row is occupied once, at time Ti, designated on the right. Under appropriate conditions, one perceives a flow of motion along a path pi. The three paths marked by arrows are most likely. (B) Removing every second dot in the row affects the spatial and temporal parameters of paths p2 and p3, but not of path p1.

Stimulus of Burt and Sperling (1981). (A) A horizontal row of dots is flashed sequentially while it is displaced horizontally and downward. The rows of unfilled dots are occupied by the row of dots across time: Every row is occupied once, at time T i , designated on the right. Under appropriate conditions, one perceives a flow of motion along a path p i . The three paths marked by arrows are most likely. (B) Removing every second dot in the row affects the spatial and temporal parameters of paths p2 and p3, but not of path p1 .

Figure 5

Empirical and theoretical equivalence classes. The format of both panels is similar to that of Figure 2, except that the two axes are logarithmic. (A) Human isosensitivity contours. Each contour is a spatiotemporal isosensitivity curve. The color of each curve corresponds to the normalized magnitude of sensitivity, as explained in the color bar on the right. (B) Theoretical equivalence contours predicted by the normative theory of Gepshtein et al. (2007). The roughly hyperbolic curve connects conditions expected to be optimal for speed estimation across speeds. The colored curves connect conditions equally suboptimal for motion measurement and hence expected to be equally preferable: The warmer the color, the more resources should be allocated to the corresponding contour and the higher sensitivity is expected. The pairs of connected circles in Panels A and B demonstrate that the regimes of coupling (at a high speed) and tradeoff (at a lower speed) are expected from normative considerations (in Panel B) and are consistent with data on human spatiotemporal sensitivity (in Panel A). The vertical arrows correspond to the arrow in Figure 1B; they illustrate the procedure we use to reveal the regimes of coupling and tradeoff.

Empirical and theoretical equivalence classes. The format of both panels is similar to that of Figure 2, except that the two axes are logarithmic. (A) Human isosensitivity contours. Each contour is a spatiotemporal isosensitivity curve. The color of each curve corresponds to the normalized magnitude of sensitivity, as explained in the color bar on the right. (B) Theoretical equivalence contours predicted by the normative theory of Gepshtein et al. (2007). The roughly hyperbolic curve connects conditions expected to be optimal for speed estimation across speeds. The colored curves connect conditions equally suboptimal for motion measurement and hence expected to be equally preferable: The warmer the color, the more resources should be allocated to the corresponding contour and the higher sensitivity is expected. The pairs of connected circles in Panels A and B demonstrate that the regimes of coupling (at a high speed) and tradeoff (at a lower speed) are expected from normative considerations (in Panel B) and are consistent with data on human spatiotemporal sensitivity (in Panel A). The vertical arrows correspond to the arrow in Figure 1B; they illustrate the procedure we use to reveal the regimes of coupling and tradeoff.

Figure 6

The design of a six-stroke motion lattice M6. (A) The six successive frames of M6 are shown superimposed in space. Gray levels indicate time. (B) The time course of M6. To differentiate dots from different frames, in this illustration (but not in the actual stimulus), they are shown in different shades of gray. The three most likely motions—along m1, m2, and m3—can occur because dots in frame fi can match dots in either frame fi+1 or frame fi+2. (C–D) Conditions in which different motion paths dominate: m1 in Panel C and m3 in Panel D. (In all our experiments, we chose conditions in which m2 would never dominate.)

The design of a six-stroke motion lattice M6. (A) The six successive frames of M6 are shown superimposed in space. Gray levels indicate time. (B) The time course of M6. To differentiate dots from different frames, in this illustration (but not in the actual stimulus), they are shown in different shades of gray. The three most likely motions—along m1, m2, and m3—can occur because dots in frame f i can match dots in either frame f i+1 or frame f i+2. (C–D) Conditions in which different motion paths dominate: m1 in Panel C and m3 in Panel D. (In all our experiments, we chose conditions in which m2 would never dominate.)

Figure 7

Single frames of motion lattices (not to scale). Only the filled dots appear in the actual frames; the open dots are shown in the figure to indicate the locations of dots in other frames. The frames in Panels A and B correspond to conditions in Panels C and D in Figure 6, respectively. Four animated demonstrations of motion lattices are available in the Appendix.

Single frames of motion lattices (not to scale). Only the filled dots appear in the actual frames; the open dots are shown in the figure to indicate the locations of dots in other frames. The frames in Panels A and B correspond to conditions in Panels C and D in Figure 6, respectively. Four animated demonstrations of motion lattices are available in the 1.

Figure 8

Results of Experiment 1. (A) Computation of a single equilibrium point r 31*. Perceptual equilibrium holds when the competing percepts μ 3 and μ 1 are equiprobable, that is, when the log-odds of corresponding probabilities (the ordinate L) is zero. To find r 31*, we performed a linear interpolation (oblique solid line) between the data points that straddle L = 0 (filled circles). The equilibrium point is marked by the vertical red line. (B) Equilibrium points plotted as a function of spatial scale for six observers. We observe equilibrium points in the tradeoff region ( r 31* < 1) and the coupling region ( r 31* > 1). The vertical bars (visible only where they are larger than the data symbols) correspond to ±1 SE. The plots for observers S.G., T.K., and C.C. contain only four equilibrium points because at the smallest spatial scale, they always saw μ 1 more often than μ 3 (i.e., L < 0).

Results of Experiment 1. (A) Computation of a single equilibrium point r 31*. Perceptual equilibrium holds when the competing percepts μ 3 and μ 1 are equiprobable, that is, when the log-odds of corresponding probabilities (the ordinate L) is zero. To find r 31*, we performed a linear interpolation (oblique solid line) between the data points that straddle L = 0 (filled circles). The equilibrium point is marked by the vertical red line. (B) Equilibrium points plotted as a function of spatial scale for six observers. We observe equilibrium points in the tradeoff region ( r 31* < 1) and the coupling region ( r 31* > 1). The vertical bars (visible only where they are larger than the data symbols) correspond to ±1 SE. The plots for observers S.G., T.K., and C.C. contain only four equilibrium points because at the smallest spatial scale, they always saw μ 1 more often than μ 3 (i.e., L < 0).

Figure 9

Results of Experiment 2. (A) Equilibrium points r 31* (averaged across observers) plotted against spatial scale. The four curves were derived from the fitted linear models in Figure 10A. (B) When equilibrium points are plotted against speed, they follow one function. The solid curve is a fit by the statistical model in Figure 10B. The model accounts for 98% of the variability in the data. The dashed curve corresponds to the dashed line in Figure 10B.

Results of Experiment 2. (A) Equilibrium points r 31* (averaged across observers) plotted against spatial scale. The four curves were derived from the fitted linear models in Figure 10A. (B) When equilibrium points are plotted against speed, they follow one function. The solid curve is a fit by the statistical model in Figure 10B. The model accounts for 98% of the variability in the data. The dashed curve corresponds to the dashed line in Figure 10B.

Figure 10

Results of Experiment 2. (A) When equilibrium points are plotted against reciprocal spatial scale, they follow linear functions. (B) When equilibrium points are plotted against reciprocal speed (slowness), the data fall on a single linear function. The dashed line is a fit to all the data; the solid line excludes two outliers (the two leftmost black dots) at the two largest spatial scales for τ = 27 ms.

Results of Experiment 2. (A) When equilibrium points are plotted against reciprocal spatial scale, they follow linear functions. (B) When equilibrium points are plotted against reciprocal speed (slowness), the data fall on a single linear function. The dashed line is a fit to all the data; the solid line excludes two outliers (the two leftmost black dots) at the two largest spatial scales for τ = 27 ms.

Figure 11

Results of Experiment 2 and the empirical equivalence sets in the space–time plot. The thin lines on the background are the empirical equivalence sets we reconstructed from the results of Experiment 2 using the linear model in Figure 10. The pairs of red connected circles represent the measured equilibrium points; each pair corresponds to a data point in Figure 10. The slopes of both the empirical equivalence sets and the lines connecting the circles gradually change across the plot, indicating a gradual change from tradeoff to coupling, as do the slopes of isosensitivity contours measured for continuous motion at the threshold of visibility ( Figure 5A). The oblique thick line indicates the boundary speed of 12°/s.

Results of Experiment 2 and the empirical equivalence sets in the space–time plot. The thin lines on the background are the empirical equivalence sets we reconstructed from the results of Experiment 2 using the linear model in Figure 10. The pairs of red connected circles represent the measured equilibrium points; each pair corresponds to a data point in Figure 10. The slopes of both the empirical equivalence sets and the lines connecting the circles gradually change across the plot, indicating a gradual change from tradeoff to coupling, as do the slopes of isosensitivity contours measured for continuous motion at the threshold of visibility ( Figure 5A). The oblique thick line indicates the boundary speed of 12°/s.

Figure 12

An illustration of how the size of spatiotemporal frequency band of visual stimulus affects the shapes of equivalence contours. We simulated the effect of frequency band by averaging empirical estimates of spatiotemporal sensitivity ( Figure 5A; Kelly, 1979) across a range of spatial and temporal frequencies; this range grows across the panels, from left to right. The equivalence contours grow shallower as the averaging range increases.

An illustration of how the size of spatiotemporal frequency band of visual stimulus affects the shapes of equivalence contours. We simulated the effect of frequency band by averaging empirical estimates of spatiotemporal sensitivity ( Figure 5A; Kelly, 1979) across a range of spatial and temporal frequencies; this range grows across the panels, from left to right. The equivalence contours grow shallower as the averaging range increases.

Demonstrations of Motion Lattices (M 6)

MOVIE 1: All lattice locations visible.

MOVIE 2: Lattice Locations hidden.

MOVIE 3: All lattice locations visible.

MOVIE 4: Lattice Locations hidden.

© 2007 ARVO

johnsongingee.blogspot.com

Source: https://jov.arvojournals.org/article.aspx?articleid=2122193

0 Response to "Psc 131 How Could This Model Explain Why We See Apparent Motion as Continuous Motion"

Post a Comment

Subscribe to: Post Comments (Atom)

Iklan Atas Artikel

Iklan Tengah Artikel 1

Iklan Tengah Artikel 2

Iklan Bawah Artikel