# Reduction of Image Complexity Explains Aesthetic Preference for Symmetry

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

^{−k}, where k is a scalar parameter [23,24,25]. That is, on log-log coordinates, the relationship between the amplitude and spatial frequency is a straight line with a slope −k. Graham and Field [26,27] showed that the amplitude spectrum of paintings also decreases with spatial frequency. Furthermore, the value of slope k for the paintings, which were created for aesthetic purposes, is greater than randomly sampled nature images [26,27]. The implication is that the aesthetic value of an image may be related to the spectrum slope.

## 2. Method

#### 2.1. Stimuli

^{k}where k varied from 0 to 4. That is, there could be 1, 2, 4, 8 or 16 axes in a symmetric pattern. For patterns with 1 or 2 axes of symmetry, we also measured the effect of axis orientation offset. There were four possible axis orientations for the one-axis patterns: z = 0 (horizontal), π/4 (right diagonal), π/2 (vertical) and 3/4π (left diagonal). There were two possible axis orientation offsets for the two-axis patterns: z = 0 (or “+” type, with one vertical and one horizontal axis), and π/4 (“x” type, with two diagonal axes.) We used patterns with different orientations because it is easier to detect vertical symmetry [28]. We thus tested whether this vertical advantage persists in preference. In addition to mirror symmetric patterns, we also used point symmetry patterns where L(r, θ) = L(r, θ + π).

^{4}+ y

^{4})/σ

^{4}) where the scale constant σ was 3.47°. The purpose of the Gaussian window was to avoid sharp edges at the borders of the image and the resulting high spatial frequency ripples in the power spectrum. All were also scaled to have the same mean luminance and contrast energy.

#### 2.2. Procedure

## 3. Result

## 4. Discussion

#### 4.1. Comparison between Preference and Detection Performance

#### 4.2. Theoretic Implications

^{−k}, where k is a scalar parameter. Our images also showed the same property. We fit this function to the amplitude spectrum of each image between 4 cycles per image and the Nyquist limit of the horizontal dimension to get the amplitude slope on log-log coordinates.

^{n}

^{+1}axes can be considered to be a combination of two 2

^{n}-axis symmetric patterns each, times a square wave with a radial frequency π/2

^{n}of opposite phase. Hence, as axis number increases, the radial frequency of the square wave also increases. As a result, an image with a high number of axes has more high frequency content and its amplitude does not decrease with spatial frequency as fast as an image with fewer axes. Thus, it is likely that the observers preferred images with a shallow spectrum slope only because they have more axes.

## 5. Conclusion

## Acknowledgement

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**Figure 1.**Examples of stimuli: (

**a**) a phase scrambled image; (

**b**) a symmetric pattern with four axes; (

**c**) a repetitive pattern with eight axes; (

**d**) An anti-symmetric pattern with 16 axes; (

**e**) an interleaved pattern with four axes; and (

**f**) point symmetry.

**Figure 2.**The preference rating for one- and two-axis patterns with different orientation offset. The first bar dashed line denotes the preference level for phase scrambled image. The second to the fifth bars denotes the preference level for the one-axis patterns and the sixth and seventh, the two-axis patterns. The error bar denotes 1 standard error of measurement.

**Figure 3.**The preference rating for the symmetric (blue closed circles and solid lines), repetitive (Green open circles and dashed lines), anti-symmetric (red closed squares and dash-dot lines) and interleaved (open squares and solid lines) patterns. The cyan triangle denotes the preference rating for the point symmetry patterns. The dashed straight lines denote the preference level for phase scrambled image. The error bar denotes 1 standard error of measurement.

**Figure 4.**The relationship between preference and spectrum slope. Each dot represents one type of pattern at one axis number. A linear regression analysis (R

^{2}= 0.47) can account for this effect with preference = 9.52 + 4.5 × (spectrum slope).

**Figure 6.**The relationship between normalized preference and spectrum slope. Each dot represents one type of pattern at one axis number. Once the axis number effect is excluded, there is little correlation between preference and spectrum slope. The R

^{2}for the linear regression analysis was only 0.01.

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**MDPI and ACS Style**

Chen, C.-C.; Wu, J.-H.; Wu, C.-C.
Reduction of Image Complexity Explains Aesthetic Preference for Symmetry. *Symmetry* **2011**, *3*, 443-456.
https://doi.org/10.3390/sym3030443

**AMA Style**

Chen C-C, Wu J-H, Wu C-C.
Reduction of Image Complexity Explains Aesthetic Preference for Symmetry. *Symmetry*. 2011; 3(3):443-456.
https://doi.org/10.3390/sym3030443

**Chicago/Turabian Style**

Chen, Chien-Chung, Jo-Hsuan Wu, and Chia-Ching Wu.
2011. "Reduction of Image Complexity Explains Aesthetic Preference for Symmetry" *Symmetry* 3, no. 3: 443-456.
https://doi.org/10.3390/sym3030443