# Dynamic Cancellation of Perceived Rotation from the Venetian Blind Effect

^{1}

^{2}

^{*}

## Abstract

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## 1. Introduction

_{max}− L

_{min})/(L

_{max}+ L

_{min}) [1].) [2,3,4,5,6,7,8,9] than a geometrically-identical image shown to the other eye (Venetian blind effect). Blake and Cormack [10] failed to replicate the results of Fiorentini and Maffei [6].

#### 1.1. Venetian Blind Effect

^{2}bright region bordering a region of less than 1 cd/m

^{2}. von Helmholtz [11] did not discuss the Venetian blind effect, but his description of irradiation could be applied as a possible explanation for the effect. Again, an interocular difference in retinal illuminance would create a perceived geometric disparity due to the differential shift in the apparent location of the bar edges in the two eyes. Both theories would predict that, due to the increased apparent width of those bars in the higher-intensity image relative to that in the lower-intensity image, a square-wave grating viewed binocularly with an average luminance or contrast disparity would appear to have rotated bright bars [7].

#### 1.2. Rationale for Current Research

## 2. Materials and Methods

#### 2.1. Observers

#### 2.2. Apparatus

^{2}, respectively. As a result, the largest average luminance value that could be presented was 44 cd/m

^{2}and the maximum contrast value that could be presented was approximately 0.95. For experimental trials, the baseline average luminance value for each grating was set at 29 cd/m

^{2}with a baseline contrast of 0.325. The contrast or the luminance of the gratings (Figure 2) were either increased or decreased depending on experimental conditions. When the average luminance or contrast of the gratings were dynamically changed, the value of one quality (contrast or luminance) stayed constant while the other changed. For example, during a contrast condition, the average luminance of the grating viewed by each eye remained at 29 cd/m

^{2}while the contrast of the grating viewed by one eye was increased to a value of 0.546 and decreased to a value of 0.104 when viewed by the other eye. Similarly, for luminance conditions, the contrast of the gratings viewed by each eye remained at 0.325 while the average luminance of the grating viewed by one eye was increased to 48.72 cd/m

^{2}and the average of the grating viewed by the other eye was reduced to 9.28 cd/m

^{2}. Specific contrast, luminance, and geometric disparities were selected based on cancellation values determined by Hetley and Stine [8].

^{2}, which was equal to the luminance of the background, and an overall contrast of 0.325. Above and below each grating, 0.03° wide binocular fixation lines were placed to aid in the fusion of the two images. The center of each line contained a 0.137° by 0.515° vertical rectangle with the same luminance as each dark bar of the left grating.

#### 2.3. Procedure

^{2}for five minutes to adjust to the darkened room. After five minutes, a stimulus containing only binocular lines was presented for 10 s and then was replaced with an animated experimental stimulus that was presented for 10 s. After 10 s, the experimental stimulus was replaced with a blank gray screen, the observer was prompted to make a response, a response was made, and then the process began again (the five minute adaptation only occurred before the first trial).

## 3. Results

^{2}= 0.758, MSRES = 0.147; spread log (β): F(1, 15) = 8.316, Giesser-Greenhouse adjusted p = 0.0384, partial ω

^{2}= 0.454, MSRES = 0.758). Both the mean and standard deviation for the criterion power to perceive a jump was greater when a geometric disparity lead a contrast disparity than when a geometric disparity lead an average luminance disparity, or when either contrast or luminance disparities lead geometric disparities. Furthermore, there were differences among the observers with respect to the mean power required to detect a jump (F(2, 15) = 10.67, p = 0.0131, ρ

_{I}= 0.416, MSRES = 0.147). Other effects were not significant (see Appendix C). The adjusted coefficients of multiple determination were R

^{2}= 0.812 and R

^{2}= 0.520 for the mean and standard deviation criterion power, respectively [34]. Hence, to describe 16 psychometric functions measured for each observer, one mean and standard deviation are sufficient for the eight functions where contrast or luminance lead geometry, one mean and standard deviation when geometry leads contrast, and one mean and standard deviation when geometry leads average luminance (six parameters to describe 16 psychometric functions for each observer). Furthermore, the standard deviations do not differ among the observers even though the means do differ across observers (giving 16 parameters to describe 48 psychometric functions). In summary, the differences among the plots in Figure 3 may be fully described by differences in Laplace distribution means and standard deviations, which describe criterion effects in the model. Contrast has a slow onset, which creates larger means when contrast leads geometry, but a rapid offset, which gives means closer to zero when contrast leads the geometry. Both the mean and standard deviation for the criterion power to perceive a jump was greater when a geometric disparity led a contrast disparity than when a geometric disparity led an average luminance disparity or when either of the contrasts or luminance disparities led geometric disparities. The possibility of describing these differences with gain changes is discussed below.

## 4. Discussion

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. The Dynamic Models of the Venetian Blind Effect

#### Appendix A.1. Generalized Difference Model

_{max}= 27.4 imp/s is the maximum response rate for the cell, C is the contrast of a grating, σ

_{50}= 0.15 is the semi-saturation constant, or that contrast that gives a response for the cell that is half R

_{max}, M = 8.22 imp/s is the resting response rate of the cell, and n = 2.4. The perceived edge shift in response to a contrast disparity was modeled using a system of three differential equations [9] (System 1).

_{eye}(t), changes as a function of time, R(C

_{eye}(t)) is Equation (A1) and describes the steady-state response of a cell to contrast, f

_{eye}(t) describes the dynamic neural response to the contrast presented to a given eye, incorporating R(C

_{eye}(t)), τ is the time constant for the neural response to contrast for either eye, g(t) is the cyclopean perceived disparity of the particular edges of the bars composing the rectangular-wave grating, M is defined with respect to Equation (A1), gain is the parameter controlling the strength of the input from the generalized difference in a neural response to the grating pairs, and τ

_{cyc}is the time constant for the cyclopean response. One of the solutions to System (A2), g(t) (see Equation (3) in Dobias and Stine [9]), is used to calculate the perceived horizontal size ratio (Dobias and Stine [9], Equation (4)).

#### Appendix A.2. Gated Generalized Difference Model

_{eye}(t) for the left and right eyes with g(t),

## Appendix B. Predictions and Fits from the Dynamic Models

_{cyc}/100 (after Dobias and Stine [9]) coupled with, if appropriate, Equation (A4). Perceived rotation from the luminance or contrast disparity was modeled similarly, but using τ equal to 79.95 times that used for the geometric modulation (corresponding to the average measured by Dobias and Stine [9]). The relative phases of the disparity modulations were varied over the range used in the experiment. The Mathematica 8 routine NDSolve was used for the numerical simulations of System (A2). Again, details for choosing constants are outlined in Appendix B of Dobias and Stine [9].

## Appendix C. Analysis of Variance for the Laplace Parameter Estimates

^{−1/2}σ (RBF-242, [34], Ch. 10). A Holm’s sequentially rejected procedure based on the Šidák inequality [53] and [34] was used to hold the family-wise Type I error to α = 0.05 across the two dependent variables.

^{2}= 0.758, MSRES = 0.147; log (β): F(1, 15) = 8.316, Giesser-Greenhouse adjusted p = 0.0384, partial ω

^{2}= 0.454, MSRES = 0.758). Phase lag (log (μ): F(1, 15) = 8.544, Giesser-Greenhouse adjusted p > 0.05, MSRES = 0.147; log (β): F(1, 15) = 3.842, p > 0.05, MSRES = 0.758), modulation frequency (log (μ): F(1, 15) = 10.14, Giesser-Greenhouse adjusted p > 0.05, MSRES = 0.147, log (β): F(1, 15) = 1.788, p > 0.05, MSRES = 0.758), and modulation type (log (μ): F(1, 15) = 3.234, Giesser-Greenhouse adjusted p > 0.05, MSRES = 0.147, log (β): F(1, 15) = 7.548 × 10

^{−4}, p > 0.05, MSRES = 0.758) showed no effects for either dependent variable. There were differences among the observers for log (μ) (F(2, 15) = 10.67, p = 0.0131, ρ

_{I}= 0.416, MSRES = 0.147) but not log (β) (F(2, 15) = 3.514, p > 0.05, MSRES = 0.758).

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**Figure 1.**Predictions from the Generalized Difference Model (left) and the Gated Generalized Difference Model (right) when a geometric disparity modulation is used to cancel the perceived rotation induced by a contrast or average luminance disparity modulation. The probability of a jump corresponds to the probability of a brief rotation induced by one disparity before being cancelled by the second disparity. The details concerning the algorithm that was used to generate these predictions can be viewed in Appendix B.

**Figure 2.**Stereograms with binocular fixation lines of rectangular-wave gratings that have zero disparity (top left), a geometric disparity created by wider bars on the left side grating (bottom left), a contrast (top right), or a luminance (bottom right) disparity corresponding to a dichoptic contrast modulation of approximately 0.6. Either crossed or uncrossed fusion is appropriate. The bars of the zero disparity stimulus (top left) should appear to be in the fronto-parallel plane. For the other three stimuli that contain disparities (geometric, contrast, and luminance), the lighter bars of the static stimuli will appear to rotate with their right edges closer to the viewer. If crossed fusion is used, the lighter bars of the fused image will appear to rotate with their left edges closer to the viewer (see Reference [3] Figure 1 for a 100%-contrast example).

**Figure 3.**Data points with standard error bars describe the probability of reporting a “jump” for contrast (left) and luminance (right) disparity modulations for observer JJD (top), WWS (middle), and PCN (bottom). Standard errors are calculated using the score confidence interval (Agresti and Coull [32] (Equation (2)), Wilson, [33] with n = 20 and α = 0.318. Lines are the predicted probability of reporting a “jump” using the Gated Generalized Difference Model.

**Figure 4.**The parameters for the Laplace distributions represent response criteria to perceive a jump. The top row plots mean log (μ) and the bottom row mean log (σ) as a function of disparity modulation frequency with standard errors. The left column presents parameters for phase lags where contrast or average luminance disparities precede geometric disparity modulations and the right column where geometric modulations lead contrast or luminance modulations with standard errors.

**Table 1.**Coefficients of determination for modulations of contrast and luminance disparity for observers JJD, WWS, and PCN.

Observer | Modulation Type | R^{2} | Adjusted R^{2} |
---|---|---|---|

JJD | Contrast | 0.995 | 0.991 |

Luminance | 0.974 | 0.954 | |

WWS | Contrast | 0.994 | 0.989 |

Luminance | 0.984 | 0.973 | |

PCN | Contrast | 0.993 | 0.987 |

Luminance | 0.971 | 0.949 |

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**MDPI and ACS Style**

Dobias, J.J.; Stine, W.W.
Dynamic Cancellation of Perceived Rotation from the Venetian Blind Effect. *Vision* **2019**, *3*, 14.
https://doi.org/10.3390/vision3020014

**AMA Style**

Dobias JJ, Stine WW.
Dynamic Cancellation of Perceived Rotation from the Venetian Blind Effect. *Vision*. 2019; 3(2):14.
https://doi.org/10.3390/vision3020014

**Chicago/Turabian Style**

Dobias, Joshua J., and Wm Wren Stine.
2019. "Dynamic Cancellation of Perceived Rotation from the Venetian Blind Effect" *Vision* 3, no. 2: 14.
https://doi.org/10.3390/vision3020014