PERCEIVED DIRECTION OF MOTION VS. DETECTION OF GLOBAL FLOW IN RANDOM DOT CINEMATOGRAMS

A.B. Sekuler, R. Sekuler*, C. Penbeci

INTRODUCTION

€Question 1. What direction does global flow take? Researchers have assumed that perceived flow is in the mean of all directions present in the cinematogram (Williams & Brannan). This assumption sets strong constraints on the mechanisms responsible for global flow. Is perceived flow in the mean direction of a cinematogram, as always has been assumed?

€Question 2. How are direction and strength of global flow related to one another? The distribution of directions in a cinematogram governs the ease with which flow is seen. The same distribution presumably also governs the perceived direction of that flow. Can one framework account for both the ease of seeing global flow and the accuracy with which flow's direction tracks the overall distribution of directions?

€Question 3. What neural computations generate global flow? We evaluated two competing computational views of how the nervous system might process directional information to produce a single perceived direction of flow from a multivectoral stimulus: (1) Vector Averaging and (2) Winner-Take-All. Salzman &Newsome speculated that Vector Averaging might be responsible for the perception of global flow because a unified direction of motion is perceived; whereas the Winner-Take-All model might be responsible for motion perception under conditions in which more than one motion is perceived (e.g., transparency).

Demonstrations of ONE DOT undergoing motion with a distribution width of 0 deg, 90 deg, and 180 deg. These demonstrations require Netscape 2.0

Observers' Tasks and Dependent Measures.
€Direction Identification. Observers indicated perceived direction of motion by clicking on the perimeter of a circle surrounding the location of the cinematogram. Accuracy was indexed by the absolute difference between the direction response and the mean direction of the distribution.
€Signal vs. Noise Discrimination. Observers used a 6-point rating scale to judge signal vs. noise, and to express confidence in judgment (Signal Definitely, Signal Probably, Signal Maybe, Noise Maybe, Noise Probably, Noise Definitely). Sensitivity (strength of flow) was indexed by 2ArcsinˆP(A) ‹ a rating scale approximation to d'.

THE MODELS. In both models, directional information is represented by responses of 12 directionally-selective mechanisms. The idea of such a representation is supported by work on (i) motion metamers (Williams, Sekuler & Tweten), (ii) discrimination of global flow's direction (Watamaniuk & Sekuler), and (iii) statistical efficiency of motion perception (Watamaniuk). Mechanism n's response a cinematogram is given by the inner product between a vector containing the distribution of directions in the cinematogram, and a vector of the mechanism's sensitivity to motion in each direction.

NOISING UP THE CHANNELS. To bring the model into the domain of human observers' imperfect performance, we introduced random, Gaussian noise into the sensitivities of the 12 mechanisms. Each simulated trial used new, independent samples of Gaussian noise. We adjusted noise variance so that human and simulation accuracy matched with direction distribution width = 0. This noise level remained constant for all simulations, but the two models required different noise levels. Both models treated discriminability of signal from noise as a statistical decision based on [Rs-Rn] / sqrt[VARs+VARn], where Rs and Rn are the responses generated by a signal and noise cinematograms; and VARs and VARn are the variances of responses from signal and noise.

The next two figures illustrate the relative amount of noise introduced into directional channels for the VAvg and WTA models. Note that the VAVg model requires more noise than the WTA model to match human performance.

RESULTS OF SIMULATIONS. Both models give respectable, if imperfect, accounts of direction accuracy. VAvg also does well in predicting observers' discrimination of signal from noise; but WTA overpredicts discriminability. This overprediction arises from the very small values of VARs produced by WTA for broad direction distributions.

Symbols in the following 4 figures represent the mean results for observers. The solid lines in each represent the predictions of the VAvg or WTA models. The first two graphs show results for direction accuracy:

The next two graphs show results for sensitivity:

Take Home Message from Experiment 1: The Vector Averaging model provides a good fit for both accuracy and sensitivity. The Winner- Take-All model does not predict both sets of results. The visual system appears to rely on a neural computation like that of Vector Averaging when integrating disparate direction signals.

Question for Experiment 2: Does the visual system always rely on Vector Averaging?

EXPERIMENT 2

Cinematograms and Procedure
Stimuli and tasks were as in Experiment 1, except:
€Observers discriminated: (i) a signal distribution (with a gap centered around the mean direction) from the same distribution width with no gap (noise). The total number of dots was equal across gap and no-gap stimuli.
€Within each session, distribution width was constant (90, 135, or 180 deg), but gap size varied (from 0 to 135 deg, in 15 deg steps).

Results: Identification of Direction
€Errors in direction identification increased with gap width; the rate and extent of this increase varied among observers.
€WTA provided a better fit than VAvg for all observers with Distribution Width = 90, for ABS with DW = 135, and for MBS with DW = 180.
€Vavg provided a better fit than WTA for CP with Distribution Widths = 135 and 180, although in these cases the fits declined with increasing gap width.
€Neither model consistently performed well.

These figures show the accuracy (relative to the mean of the distribution) for perceived direction for Gap stimuli with Distribution widths of 90, 135, and 180 deg. In all figures, the lower line shows predictions of the VAvg model, and the upper line shows predictions of the WTA model.

Results: Discrimination of Gap vs. No-gap
€Discrimination of gap from non-gap cinematograms improved with increasing gap width, but the rate of improvement varied considerably among observers.
€Regardless of the cinematogram's overall width of direction distribution, a constant gap width produced a constant level of discriminability.
€Neither model predicted the obtained pattern of discrimination results.

The next three figures show sensitivity as a function of gap width for observers ABS, CP, and MBS.

The next two figures show the predictions of the VAvg and WTA models. Note that the scales have been altered significantly relative to observers.

The Bottom Line for Experiment 2: Neither the Vector Averaging nor the Winner-Take-All models consistently predict the accuracy and sensitity of observers. The introduction of a gap -- and of perceived transparency -- causes the visual system to use a neural computation other than Vector Averaging. However, contrary to previous predictions, the visual system does not use a Winner-Take-All strategy either.

GENERAL DISCUSSION

Ideal Behaviour
Sensitivity results from Experiment 2 suggest that observers can adapt their behaviour ideally. Regardless of distribution range, gap width was the primary predictor of sensitivity. This pattern is expected from an ideal observer, although neither the VAvg nor WTA models produce this result. Further research is required to determine the extent to which observers can control the strategies with which they perceive motion, or attend to specific aspect of a stimulus.

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Allison Sekuler:

Robert Sekuler: