## 3 EEG Analysis
\[r(x)=\frac{\sqrt{n_{1}\cdot n_{2}}}{n_{1}+n_{2}}\frac{\mu_{i,1}-\mu_{i,2}}{ \sigma_{x,i}}\,,\] (3) where \(n_{1}\) and \(n_{2}\)--the numbers of samples in class 1 and class 2, respectively, \(\mu_{i,1}\) and \(\mu_{i,2}\) the class means and \(\sigma_{xi}\) the standard deviation, while the signed \(r^{2}\) values are sgn-\(r^{2}(x)=\) sign\((x)\cdot r(x^{2})\). It is a measure of how much variance of the joint distribution can be explained by class membership. 4. Event-Related (De)Synchronization, ERD/ERS analysis--The neural modulations in different frequency bands, such as the (de)synchronization (ERD/ERS) effects [43], are outlined by the modulation of the amplitudes in the temporal domain, such as the signals envelopes within specific chosen bands. We used the upper envelope computed based on the Hilbert Transform [65] and then smoothed with a moving average filter based on the Root Mean Square (RMS) with a 200 ms sliding window. The envelope is baseline corrected using an interval of 200 ms from the fixation period. 5. Power spectral density (PSD) analysis--The power spectrum from 3 to 40 Hz, is computed on the trial interval (0-1350 ms), based on the Fourier transform with Kaiser window ([PERSON], 1997) and the logarithmic spectral power is presented as \(10\cdot log_{10}(power)\). 6. Event-Related Spectral Perturbation (ERSP) analysis--In addition to the narrow-bands ERD curves, the Event-Related Spectral Perturbations (ERSPs) method allows the simultaneous investigation of the full spectrum [57; 66; 67; 68]. Computed here (with EEGLab) based Short-Time Fourier analysis using Morlet wavelet transform with three cycles wide windows at each 0.5 frequency, within 0-50 Hz, on the interval \(-\)550 ms to 1350 ms, relative to the baseline period (\(-\)200, 0 ms). 7. Inter-Trial Coherence, ITC--In contrast to ERSP, Inter-Trial Coherence (ITC) offer additional information over the local phase coherence across consecutive trials [69], since the ERD/ERS phenomena are time locked to a stimulus, not phase locked to an event [57; 70]. Classification--We are interested to investigate if the brain responses can be discriminated in accordance to the image perceived, namely the synthetic fractal texture, Frac, the natural texture Nat, or the reference image, Uni. The estimation is performed using single-trial classification, by Regularized Linear Discriminant Analysis [71], in multi-class form. The three class labels are given by the stimuli images: Uni, Nat or Frac. Spatio-temporal features (channels and time, extracted as in [30,64]) are considered from intervals with highest discriminations between classes based on the signed \(r^{2}\). Namely, the signed \(r^{2}\) discriminability is computed between Nat-Uni and Frac-Nat classes on the temporal signals (0-1200 ms) for all channels, and three short intervals of up to 150 ms are heuristically selected for each discrimination pair (Nat-Uni and Frac-Nat) where the discriminability is highest across all channels (see Section 4). The short temporal intervals detected are comprised within the 200-400 ms and 480-1200 ms ranges. The averaged value of the temporal signals within these short intervals considering each channel and each discrimination pair is further selected for each trial, giving a concatenated vector as spatio-temporal features of 6 \(\times\) 5 dimension: 3 averaged values for Nat-Uni pair, 3 for Frac-Nat pair, for all 5 channels and all trials. Separately, also multi-modal classification is investigated considering frequency features along with the temporal features (spatio-tempo-spectral features). Similarly, the spectral features are detected as averaged values of the power spectrum (0-30 Hz) within three frequency intervals with maximum signed \(r^{2}\) discriminability over the power spectrum (3-40 Hz) for Nat-Uni and Frac-Nat pairs. The frequency range intervals selected vary around 8-14 Hz and 17-39 Hz, consistent with the highest spectrum differences as observed in spectrum analysis in Section 4.