# Color Texture Image Complexity--EEG-Sensed Human Brain Perception vs. Computed Measures
## 7 Experimental Results
### Image Complexity Measures vs. Subjective Evaluation--Correlation Analysis  
The natural images exhibit a complexity measure comprised between 7.33 and 16.37 for color entropy (Figure 2a), and in the range 1.89-3.98 for color fractal dimension (Figure 2b), with a Pearson correlation coefficient between CE and CFD of \(\rho=0.44\), expressing no significant correlation (also by non-linear measures: [PERSON]'s Tau \(\tau=0.27\) and [PERSON]'s rank \(\rho_{\text{\tiny{T}}}=0.37\)), which is confirmed by the disperse distribution of points, as seen in Figure 3a. The fractal images contain between 16.45 and 17.84 CE values (Figure 4a) and between 2.03 and 4.12 CFD (Figure 4b), with a significant CE-CFD non-linear correlation of \(\tau=0.63\) and \(\rho_{\text{\tiny{T}}}=0.8\) (Figure 3b), such as CFD increases, as with an increase of CE, indicating that more texture colors increases the complexity.  
These facts can be easier understood if we look over some texture examples, as, for example, in Figure 5, the CE and CFD values are gradually increasing together as with a higher level of complexity for both natural and fractal textures, however this is not a general rule, as seen in Figure 5d-g, where, for some _Nat_ image structures, when CE increases CFD varies differently. Therefore, not only the color amount influence complexity, but also the distribution of the elements, which is an important distinction to note between the random generated synthetic fractal structures for color fractal images and the natural occurring structure arrangements for color natural images. On this line, entropy is not a sufficient measure taken alone when expressing complexity, as also shown in [36]. That being said, when aiming to complexity by mathematical measures, contributions from both CE and CFD should be considered with appropriate weighting, depending on the content of the texture.  
Figure 3: Color Entropy versus Color Fractal Dimension for (**a**) _Nat_ and (**b**) _Frac_ textures in terms of [PERSON], [PERSON]’s Tau, and Spearman’s rank correlation coefficients.  
Figure 2: Color Entropy Histogram (**a**) and Color Fractal Dimension (**b**) for _Nat_ images regarding complexity levels. Adapted from Ref. [48].  
Figure 4: Color Entropy Histogram (**a**) and Color Fractal Dimension (**b**) for _Frac_ images regarding complexity levels. Adapted from Ref. [48].  
Figure 5: Texture complexity examples: natural textures (_Nat_) on first two rows (**a**–**g**) and synthetic fractal textures (_Frac_) last two bottom rows (**h**–**n**).  
In the following, we investigate the correlations between the CE and CFD levels versus participants scoring. For significance, we refer to the Pearson Correlation Table of Critical Values [67], in relation to the respective amount of data points (97 _Nat_ images and 99 _Frac_ images). Therefore, we consider the threshold of \(\rho=\pm 0.2\) for correlation, with a significance level of 5%, \(\alpha=0.05\)[68; 69]. For a viable comparison with participants answers on complexity levels (1--low, 2--medium, 3--high), we consider three levels of complexity equally divided based on CE values and separately on CFD values for _Nat_ and _Frac_ images, as shown in the table below (Table 2).