# Human Symmetry Uncertainty Detected by a Self-Organizing Neural Network Map

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Original Images

#### 2.2. Experimental Display

#### 2.3. Choice Response Time Test

#### 2.4. Neural Network (SOM) Analysis

_{i}of n-dimension is associated with each element in the SOM. Vector m

_{i}is a model and the SOM is therefore an array of models. Assuming a general distance measure between x and m

_{i}given by d(x,m

_{i}), the map of an input vector x on the SOM array is defined as the array element m

_{c}that best matches x yielding the smallest d(x,m

_{i}). During the learning process, an input vector x is compared with all the m

_{i}to identify m

_{c}. The Euclidean distances ||x-m

_{i}|| define m

_{c}. Models topographically close in the map up to a certain geometric distance, indicated by h

_{ci}, will activate each other to learn from their joint input x. This results in a local relaxation or smoothing effect on the models in this neighborhood, which in continuous learning leads to global ordering. Learning is represented by

_{ci}(t) denotes the neighborhood function—a smoothing kernel defined across the map points which converges towards zero with time—$\alpha \left(t\right)$ is the learning rate, which also converges towards zero with time and affects the amount of learning in each model. At the end of a winner-take-all learning process in the SOM, each image input vector x is matched to its best matching model within the map m

_{c}. The difference between x and m

_{c}, ||x − m

_{c}||, is a measure indicating how close a final SOM value is to the original input value; it is reflected by the quantization error, QE. The average QE of all x (X) within a given image is determined by

## 3. Results

_{4}) associated with the colors BLUE and RED, and two levels (1,2) of “Appearance” (A

_{2}) associated with the multiple color case termed MULTICOL here. The three color conditions, blue, red, and multicolor, describe three operational levels of a second factor termed “Color” (C

_{3}) herein. In a first step, two separate two-way analyses of variance (ANOVA) were run to test for significant effects of the factors “Appearance” and “Color”. The first ANOVA compares between four levels of “Appearance” (1,2,3,4) in two levels (BLUE, RED) of the “Color” factor. The second ANOVA compares between two levels of “Appearance” in three levels (BLUE, RED, MULTICOL) of the “Color” factor.

#### 3.1. Two-Way ANOVA on Choice Response Times

#### 3.1.1. A_{4} × C_{2} × 15

_{4}× C

_{2}× 15, with four levels (1,2,3,4) of the “Appearance” factor and two levels (BLUE, RED) of the “Color” factor on the 15 individual average response times (RT), yielding a total number (N-1) of 119 degrees of freedom (DF). The results from this analysis are shown here below in the top part of Table 2.

#### 3.1.2. A_{2} × C_{3} × 15

_{2}× C

_{3}× 15, with two levels (1,2) of the “Appearance” factor and three levels (BLUE, RED, MULTICOL) of the “Color” factor on the 15 individual average response times (RT), yielding a total number (N-1) of 89 degrees of freedom. The results from this analysis are shown above in the bottom part of Table 2. They signal a statistically significant effect of the “Appearance” factor on the average RT and a statistically significant effect of the “Color” factor. A statistically significant interaction is not observed here. Statistical post-hoc comparisons (Holm–Sidak) reveal statistically significant differences between the factor levels MULTICOL and RED (t(1,1) = 14.44, p < 0.001) and between the factor levels MULTICOL and BLUE (t(1,1) = 12.60, p < 0.001), but not, as could be expected from the previous ANOVA, between the factor levels RED and BLUE (t(1,1) = 1.84, p < 0.09 NS). The “Color” effect here is reflected by the observation that shape pairs with multiple color elements yield significantly longer symmetry related RT compared with shape pairs composed of any of the two single colors here. This effect can be appreciated further by looking at the effect sizes for the different comparisons, which are visualized further in Figure 5 below.

#### 3.2. RT Effect Sizes

#### 3.3. SOM-QE Effect Sizes

#### 3.4. Linear Regression Analyses

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Schweisguth, F.; Corson, F. Self-Organization in Pattern Formation. Dev. Cell
**2019**, 49, 659–677. [Google Scholar] [CrossRef] [PubMed] - Carroll, S.B. Chance and necessity: The evolution of morphological complexity and diversity. Nature
**2001**, 409, 1102–1109. [Google Scholar] [CrossRef] [PubMed] - García-Bellido, A. Symmetries throughout organic evolution. Proc. Natl. Acad. Sci. USA
**1996**, 93, 14229–14232. [Google Scholar] [CrossRef] [Green Version] - Groves, J.T. The physical chemistry of membrane curvature. Nat. Chem. Biol.
**2009**, 5, 783–784. [Google Scholar] [CrossRef] - Hatzakis, N.S.; Bhatia, V.K.; Larsen, J.; Madsen, K.L.; Bolinger, P.Y.; Kunding, A.H.; Castillo, J.; Gether, U.; Hedegård, P.; Stamou, D. How curved membranes recruit amphipathic helices and protein anchoring motifs. Nat. Chem. Biol.
**2009**, 5, 835–841. [Google Scholar] [CrossRef] [PubMed] - Holló, G. Demystification of animal symmetry: Symmetry is a response to mechanical forces. Biol. Direct
**2017**, 12, 11. [Google Scholar] [CrossRef] [Green Version] - Mach, E. On Symmetry. In Popular Scientific Lectures; Open Court Publishing: Lasalle, IL, USA, 1893. [Google Scholar]
- Arnheim, R. Visual Thinking, 1969; University of California Press: Oakland, CA, USA, 2004. [Google Scholar]
- Deregowski, J.B. Symmetry, Gestalt and information theory. Q. J. Exp. Psychol.
**1971**, 23, 381–385. [Google Scholar] [CrossRef] - Eisenman, R. Complexity–simplicity: I. Preference for symmetry and rejection of complexity. Psychon. Sci.
**1967**, 8, 169–170. [Google Scholar] [CrossRef] - Eisenman, R.; Rappaport, J. Complexity preference and semantic differential ratings of complexity-simplicity and symmetry-asymmetry. Psychon. Sci.
**1967**, 7, 147–148. [Google Scholar] [CrossRef] - Deregowski, J.B. The role of symmetry in pattern reproduction by Zambian children. J. Cross Cult. Psychol.
**1972**, 3, 303–307. [Google Scholar] [CrossRef] - Amir, O.; Biederman, I.; Hayworth, K.J. Sensitivity to non-accidental properties across various shape dimensions. Vis. Res.
**2012**, 62, 35–43. [Google Scholar] [CrossRef] [Green Version] - Bahnsen, P. Eine Untersuchung über Symmetrie und Asymmetrie bei visuellen Wahrnehmungen. Z. Für Psychol.
**1928**, 108, 129–154. [Google Scholar] - Wagemans, J. Characteristics and models of human symmetry detection. Trends Cogn. Sci.
**1997**, 9, 346–352. [Google Scholar] [CrossRef] - Sweeny, T.D.; Grabowecky, M.; Kim, Y.J.; Suzuki, S. Internal curvature signal and noise in low- and high-level vision. J. Neurophysiol.
**2011**, 105, 1236–1257. [Google Scholar] [CrossRef] [PubMed] - Wilson, H.R.; Wilkinson, F. Symmetry perception: A novel approach for biological shapes. Vis. Res.
**2002**, 42, 589–597. [Google Scholar] [CrossRef] [Green Version] - Baylis, G.C.; Driver, J. Perception of symmetry and repetition within and across visual shapes: Part-descriptions and object-based attention. Vis. Cognit.
**2001**, 8, 163–196. [Google Scholar] [CrossRef] - Michaux, A.; Kumar, V.; Jayadevan, V.; Delp, E.; Pizlo, Z. Binocular 3D Object Recovery Using a Symmetry Prior. Symmetry
**2017**, 9, 64. [Google Scholar] [CrossRef] - Jayadevan, V.; Sawada, T.; Delp, E.; Pizlo, Z. Perception of 3D Symmetrical and Nearly Symmetrical Shapes. Symmetry
**2018**, 10, 344. [Google Scholar] [CrossRef] [Green Version] - Li, Y.; Sawada, T.; Shi, Y.; Steinman, R.M.; Pizlo, Z. Symmetry is the sine qua non of shape. In Shape Perception in Human and Computer Vision; Dickinson, S., Pizlo, Z., Eds.; Springer: London, UK, 2013; pp. 21–40. [Google Scholar]
- Pizlo, Z.; Sawada, T.; Li, Y.; Kropatsch, W.G.; Steinman, R.M. New approach to the perception of 3D shape based on veridicality, complexity, symmetry and volume: A mini-review. Vis. Res.
**2010**, 50, 1–11. [Google Scholar] [CrossRef] [Green Version] - Barlow, H.B.; Reeves, B.C. The versatility and absolute efficiency of detecting mirror symmetry in random dot displays. Vis. Res.
**1979**, 19, 783–793. [Google Scholar] [CrossRef] - Barrett, B.T.; Whitaker, D.; McGraw, P.V.; Herbert, A.M. Discriminating mirror symmetry in foveal and extra-foveal vision. Vis. Res.
**1999**, 39, 3737–3744. [Google Scholar] [CrossRef] [Green Version] - Machilsen, B.; Pauwels, M.; Wagemans, J. The role of vertical mirror symmetry in visual shape perception. J. Vis.
**2009**, 9, 11. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Dresp-Langley, B. Bilateral Symmetry Strengthens the Perceptual Salience of Figure against Ground. Symmetry
**2019**, 11, 225. [Google Scholar] [CrossRef] [Green Version] - Dresp-Langley, B. Affine Geometry, Visual Sensation, and Preference for Symmetry of Things in a Thing. Symmetry
**2016**, 8, 127. [Google Scholar] [CrossRef] [Green Version] - Sabatelli, H.; Lawandow, A.; Kopra, A.R. Asymmetry, symmetry and beauty. Symmetry
**2010**, 2, 1591–1624. [Google Scholar] [CrossRef] [Green Version] - Poirier, F.J.A.M.; Wilson, H.R. A biologically plausible model of human shape symmetry perception. J. Vis.
**2010**, 10, 1–16. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Giurfa, M.; Eichmann, B.; Menzl, R. Symmetry perception in an insect. Nature
**1996**, 382, 458–461. [Google Scholar] [CrossRef] - Krippendorf, S.; Syvaeri, M. Detecting symmetries with neural networks. Mach. Learn. Sci. Technol.
**2021**, 2, 015010. [Google Scholar] [CrossRef] - Toureau, V.; Bibiloni, P.; Talavera-Martínez, L.; González-Hidalgo, M. Automatic Detection of Symmetry in Dermoscopic Images Based on Shape and Texture. Inf. Process. Manag. Uncertain. Knowl. Based Syst.
**2020**, 1237, 625–636. [Google Scholar] - Shen, D.; Wu, G.; Suk, H.I. Deep Learning in Medical Image Analysis. Annu. Rev. Biomed. Eng.
**2017**, 19, 221–248. [Google Scholar] [CrossRef] [Green Version] - Hramov, A.E.; Frolov, N.S.; Maksimenko, V.A.; Makarov, V.V.; Koronovskii, A.A.; Garcia-Prieto, J.; Antón-Toro, L.F.; Maestú, F.; Pisarchik, A.N. Artificial neural network detects human uncertainty. Chaos
**2018**, 28, 033607. [Google Scholar] [CrossRef] - Dresp-Langley, B. Seven Properties of Self-Organization in the Human Brain. Big Data Cogn. Comput.
**2020**, 4, 10. [Google Scholar] [CrossRef] - Wandeto, J.M.; Dresp-Langley, B. Ultrafast automatic classification of SEM image sets showing CD4 + cells with varying extent of HIV virion infection. In Proceedings of the 7ièmes Journées de la Fédération de Médecine Translationnelle de l’Université de Strasbourg, Strasbourg, France, 25–26 May 2019. [Google Scholar]
- Dresp-Langley, B.; Wandeto, J.M. Unsupervised classification of cell imaging data using the quantization error in a Self-Organizing Map. In Transactions on Computational Science and Computational Intelligence; Arabnia, H.R., Ferens, K., de la Fuente, D., Kozerenko, E.B., Olivas Varela, J.A., Tinetti, F.G., Eds.; Advances in Artificial Intelligence and Applied Computing; Springer-Nature: Berlin/Heidelberg, Germany, in press.
- Wandeto, J.M.; Nyongesa, H.K.O.; Remond, Y.; Dresp-Langley, B. Detection of small changes in medical and random-dot images comparing self-organizing map performance to human detection. Inf. Med. Unlocked
**2017**, 7, 39–45. [Google Scholar] [CrossRef] - Wandeto, J.M.; Nyongesa, H.K.O.; Dresp-Langley, B. Detection of smallest changes in complex images comparing self-organizing map and expert performance. In Proceedings of the 40th European Conference on Visual Perception, Berlin, Germany, 27–31 August 2017. [Google Scholar]
- Wandeto, J.M.; Dresp-Langley, B.; Nyongesa, H.K.O. Vision-Inspired Automatic Detection of Water-Level Changes in Satellite Images: The Example of Lake Mead. In Proceedings of the 41st European Conference on Visual Perception, Trieste, Italy, 26–30 August 2018. [Google Scholar]
- Dresp-Langley, B.; Wandeto, J.M.; Nyongesa, H.K.O. Using the quantization error from Self-Organizing Map output for fast detection of critical variations in image time series. In ISTE OpenScience, collection “From data to decisions”; Wiley & Sons: London, UK, 2018. [Google Scholar]
- Wandeto, J.M.; Dresp-Langley, B. The quantization error in a Self-Organizing Map as a contrast and colour specific indicator of single-pixel change in large random patterns. Neural Netw.
**2019**, 119, 273–285, Special Issue in Neural Netw.**2019**, 120, 116–128.. [Google Scholar] [CrossRef] [PubMed] - Dresp-Langley, B.; Wandeto, J.M. Pixel precise unsupervised detection of viral particle proliferation in cellular imaging data. Inf. Med. Unlocked
**2020**, 20, 100433. [Google Scholar] [CrossRef] [PubMed] - Dresp-Langley, B.; Reeves, A. Simultaneous brightness and apparent depth from true colors on grey: Chevreul revisited. Seeing Perceiving
**2012**, 25, 597–618. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Dresp-Langley, B.; Reeves, A. Effects of saturation and contrast polarity on the figure-ground organization of color on gray. Front. Psychol.
**2014**, 5, 1136. [Google Scholar] [CrossRef] [Green Version] - Dresp-Langley, B.; Reeves, A. Color and figure-ground: From signals to qualia, In Perception Beyond Gestalt: Progress in Vision Research; Geremek, A., Greenlee, M., Magnussen, S., Eds.; Psychology Press: Hove, UK, 2016; pp. 159–171. [Google Scholar]
- Dresp-Langley, B.; Reeves, A. Color for the perceptual organization of the pictorial plane: Victor Vasarely’s legacy to Gestalt psychology. Heliyon
**2020**, 6, 04375. [Google Scholar] [CrossRef] - Bonnet, C.; Fauquet, A.J.; Estaún Ferrer, S. Reaction times as a measure of uncertainty. Psicothema
**2008**, 20, 43–48. [Google Scholar] - Brown, S.D.; Marley, A.A.; Donkin, C.; Heathcote, A. An integrated model of choices and response times in absolute identification. Psychol. Rev.
**2008**, 115, 396–425. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Luce, R.D. Response Times: Their Role in Inferring Elementary Mental Organization; Oxford University Press: New York, NY, USA, 1986. [Google Scholar]
- Posner, M.I. Timing the brain: Mental chronometry as a tool in neuroscience. PLoS Biol.
**2005**, 3, e51. [Google Scholar] [CrossRef] [Green Version] - Posner, M.I. Chronometric Explorations of Mind; Erlbaum: Hillsdale, NJ, USA, 1978. [Google Scholar]
- Hickw, E. Rate Gain Information. Q. J. Exp. Psychol.
**1952**, 4, 11–26. [Google Scholar] - Bartz, A.E. Reaction time as a function of stimulus uncertainty on a single trial. Percept. Psychophys.
**1971**, 9, 94–96. [Google Scholar] [CrossRef] - Jensen, A.R. Clocking the Mind: Mental Chronometry and Individual Differences; Elsevier: Amsterdam, The Netherland, 2006. [Google Scholar]
- Salthouse, T.A. Aging and measures of processing speed. Biol. Psychol.
**2000**, 54, 35–54. [Google Scholar] [CrossRef] - Kuang, S. Is reaction time an index of white matter connectivity during training? Cogn. Neurosci.
**2017**, 8, 126–128. [Google Scholar] [CrossRef] [PubMed] - Ishihara, S. Tests for Color-Blindness; Hongo Harukicho: Tokyo, Japan, 1917. [Google Scholar]
- Monfouga, M. Python Code for 2AFC Forced-Choice Experiments Using Contrast Patterns. 2019. Available online: https://pumpkinmarie.github.io/ExperimentalPictureSoftware/ (accessed on 8 January 2021).
- Dresp-Langley, B.; Monfouga, M. Combining Visual Contrast Information with Sound Can Produce Faster Decisions. Information
**2019**, 10, 346. [Google Scholar] [CrossRef] [Green Version] - Kohonen, T. Self-Organizing Maps. 2001. Available online: http://link.springer.com/10.1007/978-3-642-56927-2 (accessed on 8 January 2021).
- Kohonen, T. MATLAB Implementations and Applications of the Self-Organizing Map; Unigrafia Oy: Helsinki, Finland, 2014; p. 177. [Google Scholar]
- Nordfang, M.; Dyrholm, M.; Bundesen, C. Identifying bottom-up and top-down components of attentional weight by experimental analysis and computational modeling. J. Exp. Psychol. Gen.
**2013**, 142, 510–535. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Liesefeld, H.R.; Müller, H.J. Modulations of saliency signals at two hierarchical levels of priority computation revealed by spatial statistical distractor learning. J. Exp. Psychol. Gen.
**2020**, in press. [Google Scholar] [CrossRef] [PubMed] - Dresp, B.; Fischer, S. Asymmetrical contrast effects induced by luminance and color configurations. Percept. Psychophys.
**2001**, 63, 1262–1270. [Google Scholar] [CrossRef] [Green Version] - Dresp-Langley, B. Why the brain knows more than we do: Non-conscious representations and their role in the construction of conscious experience. Brain Sci.
**2012**, 2, 1–21. [Google Scholar] [CrossRef] [Green Version] - Dresp-Langley, B. Generic properties of curvature sensing by vision and touch. Comput. Math. Methods Med.
**2013**, 634168. [Google Scholar] [CrossRef] [PubMed] - Dresp-Langley, B. 2D geometry predicts perceived visual curvature in context-free viewing. Comput. Intell. Neurosci.
**2015**, 9. [Google Scholar] [CrossRef] [Green Version] - Gerbino, W.; Zhang, L. Visual orientation and symmetry detection under affine transformations. Bull. Psychon. Soc.
**1991**, 29, 480. [Google Scholar] - Batmaz, A.U.; de Mathelin, M.; Dresp-Langley, B. Seeing virtual while acting real: Visual display and strategy effects on the time and precision of eye-hand coordination. PLoS ONE
**2017**, 12, e0183789. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Dresp-Langley, B. Principles of perceptual grouping: Implications for image-guided surgery. Front. Psychol.
**2015**, 6, 1565. [Google Scholar] [CrossRef] [Green Version] - Martinovic, J.; Jennings, B.J.; Makin, A.D.J.; Bertamini, M.; Angelescu, I. Symmetry perception for patterns defined by color and luminance. J. Vis.
**2018**, 18, 4. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Treder, M.S. Behind the Looking-Glass: A Review on Human Symmetry Perception. Symmetry
**2010**, 2, 1510–1543. [Google Scholar] [CrossRef] - Spillmann, L.; Dresp-Langley, B.; Tseng, C.H. Beyond the classic receptive field: The effect of contextual stimuli. J. Vis.
**2015**, 15, 7. [Google Scholar] [CrossRef] [Green Version] - Tsogkas, S.; Kokkinos, I. Learning-Based Symmetry Detection in Natural Images. In Lecture Notes in Computer Science; Computer Vision—ECCV 2012; Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C., Eds.; Springer: Berlin/Heidelberg, Germany, 2012; Volume 7578. [Google Scholar]
- Liu, Y. Computational Symmetry in Computer Vision and Computer Graphics; Now Publishers Inc.: Norwell, MA, USA, 2009. [Google Scholar]
- Bakhshandeh, S.; Azmi, R.; Teshnehlab, M. Symmetric uncertainty class-feature association map for feature selection in microarray dataset. Int. J. Mach. Learn. Cyber.
**2020**, 11, 15–32. [Google Scholar] [CrossRef] - Radovic, M.; Ghalwash, M.; Filipovic, N.; Obradovic, Z. Minimum redundancy maximum relevance feature selection approach for temporal gene expression data. BMC Bioinform.
**2017**, 18, 9. [Google Scholar] [CrossRef] [Green Version] - Strippoli, P.; Canaider, S.; Noferini, F.; D’Addabbo, P.; Vitale, L.; Facchin, F.; Lenzi, L.; Casadei, R.; Carinci, P.; Zannotti, M.; et al. Uncertainty principle of genetic information in a living cell. Theor. Biol. Med. Model.
**2005**, 30, 40. [Google Scholar] [CrossRef] [PubMed] [Green Version]

**Figure 1.**Hick’s Law [53,54] postulates that, provided the error rate in the given psychophysical task is low, sensory system uncertainty (SU) increases linearly with the amount of transmitted information (I) in a set (

**top graph**). The law presumes a direct relationship between choice RT and sensory system uncertainty (SU) where RT increases linearly with amount of transmitted information/stimulus uncertainty (

**bottom graph**).

**Figure 2.**Copies of the test images, for illustration. Mirror symmetric shape pairs are displayed on a medium grey background. Visual symmetry uncertainty in the shape pairs was varied by giving shape elements variable amounts of color information resulting in variations in appearance. The condition with the highest amount of locally different color information is MULTICOL2.

**Figure 3.**Statistically significant differences in average RT (

**top**) for the comparison between BLUE and RED shape pairs with appearance levels 1 and 2. The corresponding Self-Organizing Map Quantization Error (SOM-QE) values (

**bottom**) from the neural network analysis are plotted in the graph below.

**Figure 4.**Statistically significant differences in average RT (

**top**) for the comparison between BLUE and RED shape pairs with appearance levels 1, 3 and 4. The corresponding SOM-QE values (

**bottom**) from the neural network analysis are plotted in the graph below. The difference in average RT between BLUE3 and BLUE4 is the only one here that is not statistically significant (see “Section 3.1.1.”).

**Figure 5.**Differences in average RT (

**top**) for the comparison between BLUE and RED shape pairs with appearance level 1 and the multicolored MULTICOL shape pairs with appearance levels 1 and 2. The differences between BLUE and RED shape pairs of any appearance level are not statistically significant (see “Section 3.1.1”). The differences between image conditions BLUE1 or RED1 and MULTICOL1 and between BLUE2 or RED2 and MULTICOL2 are highly significant, as is the difference between MULTICOL1 and MULTICOL2 (see “Section 3.1.2”). The corresponding SOM-QE values (

**bottom**) from the neural network analysis are plotted in the graph below.

**Figure 6.**The tight link between variations in RT reflecting different levels of human uncertainty and the variations in the SOM-QE metric from the neural network analyses is brought to the fore here under the light of linear regression analysis on the RT data for shape pairs with varying levels of appearance in BLUE, RED and MULTICOL shapes, and linear regression analysis on the SOM-QE data for exactly the same shape pairs.

Color | Hue | Saturation | Lightness | R-G-B | |
---|---|---|---|---|---|

“Strong” | BLUE | 240 | 100 | 50 | 0-0-255 |

RED | 0 | 100 | 50 | 255-0-0 | |

GREEN | 120 | 100 | 50 | 0-255-0 | |

MAGENTA | 300 | 100 | 50 | 255-0-255 | |

YELLOW | 60 | 100 | 50 | ||

“Pale” | BLUE | 180 | 95 | 50 | 10-250-250 |

RED | 0 | 100 | 87 | 255-190-190 | |

GREEN | 120 | 100 | 87 | 190-255-190 | |

MAGENTA | 300 | 25 | 87 | 255-190-255 | |

YELLOW | 600 | 65 | 67 | 255-255-190 |

**Table 2.**Results from the two-way analyses of variance with factor-specific degrees of freedom (DF), the corresponding F statistics, and their associated probability limits (p).

Factor | DF | F | p | |
---|---|---|---|---|

1st 2-way ANOVA | APPEARANCE | 3 | 68.42 | <0.001 |

COLOR | 1 | 0.012 | <0.914 NS | |

INTERACTION | 3 | 5.37 | <0.01 | |

2nd 2-way ANOVA | APPEARANCE | 1 | 8.20 | <0.01 |

COLOR | 2 | 123.56 | <0.001 | |

INTERACTION | 2 | 0.564 | <0.57 NS |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Dresp-Langley, B.; Wandeto, J.M.
Human Symmetry Uncertainty Detected by a Self-Organizing Neural Network Map. *Symmetry* **2021**, *13*, 299.
https://doi.org/10.3390/sym13020299

**AMA Style**

Dresp-Langley B, Wandeto JM.
Human Symmetry Uncertainty Detected by a Self-Organizing Neural Network Map. *Symmetry*. 2021; 13(2):299.
https://doi.org/10.3390/sym13020299

**Chicago/Turabian Style**

Dresp-Langley, Birgitta, and John M. Wandeto.
2021. "Human Symmetry Uncertainty Detected by a Self-Organizing Neural Network Map" *Symmetry* 13, no. 2: 299.
https://doi.org/10.3390/sym13020299