# No-Reference Quality Assessment of Transmitted Stereoscopic Videos Based on Human Visual System
## 3 Materials and Methods
### Proposed Method
#### 3.2.1 Dissimilarity Measure Based on Disparity Index  
Firstly, stereo-matching with a block-based technique [39] is constructed to create a matrix of error energy for extracting disparity information from a pair of stereoscopic frames, based on which an intermediary disparity map [40] is generated from the two views. An averaging filter for eliminating unreliable disparity estimates is applied for enhancing the disparity map's reliability. We denote \(L_{v}(i,j,c)\) as the left-view RGB format, \(R_{v}(i,j,c)\) the right-view RGB format and error energy in an RGB format. The error energy \(E_{eng}(i,j,d)\) for a block size of \(p\times q\), can be expressed as  
\[E_{eng}(i,j,d)=\frac{1}{3 pq}\sum_{x=i}^{i+p}\sum_{y=j}^{i+q}\sum_{c=1}^{3}(L_{v }(x,y+d,c)-R_{v}(x,y,c))^{2} \tag{2}\]  
Here, \(d\) is the disparity and \(c\) has value of \(1,2,3\) which correspond to the RGB color space's red, green, and blue components, respectively. The error energy matrix \(E_{eng}(i,j,d)\) is smoothed for the predefined difference search range \(S\left(d=1\ to\ S\right)\) by applying averaging filters multiple times and eliminating very abrupt energy changes that may correspond to incorrect matching, with its recurring use uncovering global trends in error energy. The \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Experimental S3D Videos** & **Name** & **Disparity** & **Video Characteristics** \\ \hline  & & & \\ \hline  & & & Low contrast, \\  & & & high object motion \\ \hline  & & & \\ \hline  & & & Low contrast, \\  & & & low object motion \\ \hline  & & & \\ \hline  & & & \\ \hline  & & & \\ \hline \hline  & & & High Contrast, \\  & & & random object motion \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Experimental video datasets. whole process makes this algorithm a region-based approach. The averaging filtering of the \(E_{eng}(i,j,d)\) is described as follows for a \(p\times q\) window size. \[E_{eng}(i,j,d)=\frac{1}{3 pq}\sum_{x=i}^{i+p}\sum_{y=j}^{j+q}E_{eng}(x,y,d) \tag{3}\]  
Applying the averaging filter iteratively to the error energy matrix for each disparity, the disparity (\(D\)) with the minimum error energy of \(E_{eng}(i,j,d)\) is selected as the best disparity estimation of pixel \((i,j)\), of the disparity map as shown in Figure 4. The process can be summarized as follows: firstly, estimate the error energy matrix for every disparity D in the search range. Figure 4: Estimation of the disparity map from the minimum of smoothed error energy. Figure 3: Block diagram of a QA metric for 3D video. The average error energy obtained from the stereoscopic images is utilized to remove unreliable disparity estimates from the disparity map \(D(i,j)\), which is also calculated by the similar block-matching approach as shown in Equation (2). Apply the averaging filter iteratively to every error matrix for every disparity value, and finally, for each pixel \((i,j)\), assign the minimum error energy \(Min[E_{eng}(i,j,d)]\) to its disparity \(D(i,j)\) in the disparity map. These estimates are for points around object boundaries, resulting from object occlusion in images which may be recognized by examining the high error energy \(D_{ne}(i,j)\) in \(E_{eng}(i,j)\). The \(d\) is omitted from the rest of the equations since the average is taken from a disparity search range \(S\left(d=1\ \ to\ S\right)\). To increase the confidence of \(D(i,j)\), a simple threshold is applied to filter out unreliable difference estimates and obtain a new disparity map. \[\widetilde{D}(i,j)= \begin{cases}D(i,j)&,E_{eng}(i,j)\leq Th_{eng}(i,j)\\ D_{ne}(i,j)=0&,E_{eng}(i,j)>Th_{eng}(i,j)\end{cases}  \tag{4}\]  
where \(D_{ne}(i,j)\) represents the unestimated high-energy value of block mismatch due to errors in comparing pairs of views or unreliable parallax estimation.