## 2 Proposed Method  
The block diagram for our blind S3D-IQM method is depicted in Figure 1. During the offline training phase, similarity scores and a weighted LBP histogram are generated from training S3D images; subsequently, a quality codebook is constructed. During the online testing phase, by implementing feature extraction for test S3D images, blind perceptual quality pooling can be easily achieved by a distance-based weighting scheme. Our method is described in detail as follows. _(1) Training dataset preparation:_ We select 12 reference S3D images collected from Mobile S3 DTV and MPEG (please refer to Figure 2) [19]. From each reference S3D image, we then generate distorted S3D images using four types of distortions, including JPEG2000 (JP2K), Gaussian blur (Gblur), white noise (WN), and JPEG. For each distortion, five quality levels are generated by controlling different parameters. Figure 1: Block diagram for our blind S3D-IQM. Figure 2: Left views of the training S3D images in this paper. _(2) Quality measurement of the training S3D images:_ Neuroscience has made rapid progress in comprehending the human visual mechanism and how S3D visual signals are transmitted to the human brain. BRR is a well-researched visual mechanism of competition in the visual cortex [20]. BRR is a human visual response whereby the binocular visual mechanism alternates between contradictory monocular images viewed by both eyes. Some findings in [20] showed that BRR can be strongly regulated by low-level sensory features, and a classic linear mathematical model is provided. Motivated by the above, 2D-Gabor is used for both views to simulate the rivalries. Consequently, BRR, which can be denoted by \(R_{bin}(x,y,\sigma)\), is defined as  
\[R_{bin}(x,y,\sigma)=W_{l}(x,y)\cdot M_{l}(x,y,\sigma)+W_{r}(x+d,y)\cdot M_{r}( x+d,y,\sigma) \tag{1}\]  
where \(d\) denotes a disparity value estimated using an S3D matching algorithm [21] (Reference [22] reports that similar performance is attained when using either the ground truth or the estimated disparity). Subscripts \"\(l\)\" and \"\(r\)\" are the left and right views, respectively. \(M_{l}(x,y,\sigma)\) and \(M_{r}(x,y,\sigma)\) are the monocular responses of both views, which can be obtained using a difference of Gaussian (DoG) filter  
\[h_{\sigma}(r,\sigma)=\frac{1}{2\pi\sigma^{2}}\exp(-\frac{r^{2}}{2\sigma^{2}}) -\frac{1}{2\pi k^{2}\sigma^{2}}\exp(-\frac{r^{2}}{2k^{2}\sigma^{2}}) \tag{2}\]  
where \(\sigma\) denotes the scales parameter and \(k\) is used to control the scales of the DoG. \(r\) denotes the \(l_{2}\) norm. In this study, scales \(\sigma\) of the DoG are set to 0, 1, 1.6, 2.56, and 4.096 (the same values as the filter used in [2]), with \(k=1.6\). \(W_{l}\) and \(W_{r}\) denote the weights for imitating the BRR. They are represented as \(W_{l}(x,y)=G_{l}(x,y)/(G_{l}(x,y)+G_{r}(x+d,y))\) and \(W_{r}(x+d,y)=G_{r}(x+d,y)/(G_{l}(x,y)+G_{r}(x+d,y))\), respectively, where \(G_{l}(x,y)\) and \(G_{r}(x,y)\) denote the respective 2D-Gabor responses of both views. The 2D Gabor filter can be defined as:  
\[G(x,y,\sigma_{x},\sigma_{y},\zeta_{x},\zeta_{y},\theta)=\frac{1}{2\pi\sigma_{ x}\sigma_{y}}e^{-(1/2)[((x\cos\theta+y\sin\theta)/\sigma_{x})^{2}+((y\cos \theta-\sin\theta)/\sigma_{y})^{2}]}e^{i(x\zeta_{x}+y\zeta_{y})} \tag{3}\]  
where \(\sigma_{x}\) and \(\sigma_{y}\) denote the standard deviations along the \(x\) and \(y\) axes, \(\zeta_{x}\) and \(\zeta_{y}\), and \(\theta\) denotes spatial frequencies and orients the filter. The design of the 2D-Gabor filter was based on the research conducted by [PERSON] et al. [23]. The similarity score between the BRRs of the original S3D image and distorted S3D images is defined as:  
\[S_{n}=\frac{1}{\Omega}\sum_{x,y}\left(\prod_{\sigma}\left(\frac{2\left\langle R _{0,n}(x,y,\sigma),R_{d,n}(x,y,\sigma)\right\rangle+T}{\left\|R_{0,n}(x,y, \sigma)\right\|_{2}\cdot\left\|R_{d,n}(x,y,\sigma)\right\|_{2}+T}\right)\right) \tag{4}\]  
where \(T\) is a small positive constant. In this study, we set \(T=0.085\) in our experiments.