# Bilateral Symmetry Strengthens the Perceptual Salience of Figure against Ground

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Stimuli

^{2}. The phenomenally black inducers (RGB: 5, 5, 5) a luminance of 4 cd/m

^{2}, and the phenomenally white inducers (RGB: 240, 240, 240) a luminance of 98 cd/m

^{2}. The moduli from the subjective rating task (RGB: 135, 135, 135 for the phenomenally darker ones and RGB: 145, 145, 145 for the phenomenally lighter ones) had a luminance of 52 cd/m

^{2}or 58 cd/m

^{2}respectively. The line contour control configurations (RGB: 120, 120, 120) from the choice response time task had a luminance of 48 cd/m

^{2}. The physically specified contrast intensities with positive and negative signs may be calculated using the Weber Contrast (Weber Ratio, W) formula:

**W**= (

**L**

_{config}−

**L**

_{background})/

**L**

_{background}

#### 2.2. Presentation of Configurations

#### 2.3. Experimental Procedure

#### 2.4. Subjects

#### 2.5. Data Analysis

_{10}× Symmetry

_{2}× Orientation

_{4}× Polarity

_{4}, produced a total of 320 subjective ratings. These data were fed into a Three-Way ANOVA. Means, standard errors, effect sizes, and F statistics with probability limits were determined.

_{6}× Symmetry

_{2}× Polarity

_{3}× RepeatedMeasures

_{4}, produced a total of 144 choice data and a total of 144 response times. In the experimental design plan, the control configuration represents the third modality of the “polarity” factor, with the three factor levels “positive” or ‘+ + +’, “negative” or ‘− − −’, and “control”. The response times were fed into a Two-Way Repeated Measures ANOVA with individual data averaged over the four levels of the repetition factor R

_{4}and without the third level of the “polarity” factor, i.e., the analysis plan therefore reads Subject

_{6}× Symmetry

_{2}× Polarity

_{2}.

## 3. Results

#### 3.1. Subjective Magnitude Estimation Task

#### 3.2. Choice Response Time Task

## 4. Discussion

## Supplementary Materials

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Variations of the Kanizsa triangle with phenomenally black inducers on a grey background. The subjective strength of the triangular figure-ground percept emerging in the center of the configuration critically depends on the physically specified-to-total contour, or support ratio. Stronger surface percepts are produced by higher support ratios (

**top**). To test for effects of symmetry on the salience of figure-ground, configurations with bilateral symmetry (

**bottom left**) and without (

**bottom right**) were generated. All the configurations had identical support ratio and, therefore, identical area size. All physically specified elements in the configurations (inducers) were of identical size and contrast intensity.

**Figure 2.**The configurations from the subjective rating experiment (

**a**) The asymmetric Kanizsa triangles, with varying orientation and inducer contrast polarities; (

**b**) The Kanizsa triangles with axial symmetry; (

**c**) the moduli for benchmarking the subjective rating scale (0–10). Subjects were told to associate the moduli with a figure-ground strength rating of ‘11’, regardless of the direction of the perceived contrast.

**Figure 3.**The test and control configurations (“ghosts”) from the choice response time experiment. Six subjects were asked to judge as swiftly as possible whether the triangle displayed on the screen seemed to stand out as foreground against the grey general background, or to lie behind the general grey background.

**Figure 4.**Average magnitudes of figure-ground in terms of average subjective ratings with bars indicating +/− the standard error of the mean. Effects produced by symmetric and asymmetric configurations are plotted as a function of the orientation of configurations in the plane (

**top**), and as a function of inducer polarity (

**bottom**).

**Figure 5.**Average choice response times with bars indicating +/− the standard error of the mean as a function of configuration and inducer polarity.

**Figure 6.**An example of a configuration where effects of symmetry on visual perception cannot be tested independently from possible effects of shape interpretation. In the square version of the Kanizsa figure, breaking the symmetry of the classic square configuration (images on left) inevitably requires breaking the perpendicularity of the shape borders. This inevitably results in a new and qualitatively different shape geometry and shape interpretation. In other words, shape interpretation then becomes a confusion factor. In this case here a “shard” with qualitatively different 3D-like shape properties emerges (images in middle and on left). When shape orientation changes, the percept changes, again, qualitatively and a new visual object emerges (cf. on the importance of “objectness”, see Bertamini [31]). All configurations here above have roughly equivalent, albeit not strictly identical, support ratio and central area size. Variations in inducer texture, figure orientation, and background intensity are presented here for illustration only.

**Table 1.**Figure dimensions in centimeters (cm) with the overall support ratio and surface area as a function of configuration (symmetric versus asymmetric). The symmetry factor only varies systematically between configurations, the shape interpretation (“triangle”) is the same and so are all relevant physical parameters.

Symmetric | Asymmetric | |
---|---|---|

Triangle base (b) | 9 cm | 13 cm |

Triangle side 1 | 12 cm | 11 cm |

Triangle side 2 | 12 cm | 9 cm |

Triangle height (h) | 11 cm | 7.62 cm |

Triangle surface area (1/2bxh) | 49.5 cm | 49.5 cm |

Physical inducer radius | 2 cm | 2 cm |

Support ratio | 0.36 | 0.36 |

**Table 2.**Three-Way ANOVA results with the means (average subjective magnitudes), standard errors (SEM), and F statistics for effects of main factors and their interactions from the analysis of the subjective rating data.

Factor | Level | Mean | SEM | F |
---|---|---|---|---|

Symmetry (S_{2}) | asymmetric | 3.8 | 0.15 | F(1, 319) = 108.8; p < 0.001 |

symmetric | 6.1 | 0.13 | ||

Polarity (P_{4}) | − − − | 4.7 | 0.21 | F(3, 319) = 1.24; NS |

+ + + | 5.3 | 0.22 | ||

− − + | 4.8 | 0.20 | ||

+ + − | 4.7 | 0.19 | ||

Orientation (O_{4}) | vertical base bottom | 4.8 | 0.20 | F(3, 319) = 1.17; NS |

vertical base top | 5.2 | 0.23 | ||

sideways base left | 4.9 | 0.21 | ||

sideways base right | 4.7 | 0.22 | ||

Symmetry × Polarity | interaction | _ | _ | F(3, 319) = 1.83; NS |

Symmetry × Orientation | interaction | _ | _ | F(3, 319) = 0.41; NS |

Polarity × Orientation | interaction | _ | _ | F(9, 319) = 0.67; NS |

**Table 3.**Percentage of “foreground” responses from the choice response time task as a function of configuration and inducer contrast polarity.

Asymmetric | Symmetric | |
---|---|---|

White inducers | 88% | 98% |

Black inducers | 75% | 92% |

Control | 70% | 55% |

**Table 4.**Two-Way Repeated Measures ANOVA results with the means (in milliseconds), standard errors (SEM), and F statistics for effects of main factors and their interactions from the analysis of the choice response times.

Factor | Level | Mean | SEM | F |
---|---|---|---|---|

Symmetry (S_{2}) | asymmetric | 1518 | 73 | F(1, 23) = 36.69; p < 0.01 |

symmetric | 900 | 65 | ||

Polarity (P_{2}) | − − − | 1269 | 64 | F(1, 23) = 1.74; NS |

+ + + | 1150 | 62 | ||

Symmetry × Polarity | interaction | _ | _ | F(1, 23) = 1.21; NS |

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**MDPI and ACS Style**

Dresp-Langley, B.
Bilateral Symmetry Strengthens the Perceptual Salience of Figure against Ground. *Symmetry* **2019**, *11*, 225.
https://doi.org/10.3390/sym11020225

**AMA Style**

Dresp-Langley B.
Bilateral Symmetry Strengthens the Perceptual Salience of Figure against Ground. *Symmetry*. 2019; 11(2):225.
https://doi.org/10.3390/sym11020225

**Chicago/Turabian Style**

Dresp-Langley, Birgitta.
2019. "Bilateral Symmetry Strengthens the Perceptual Salience of Figure against Ground" *Symmetry* 11, no. 2: 225.
https://doi.org/10.3390/sym11020225