# No-Reference Quality Assessment of Transmitted Stereoscopic Videos Based on Human Visual System
## 3 Materials and Methods
### Proposed Method
#### 3.2.2 Edge-Based Perceptual Difference Measure  
Considering the human visual system, edges are the most essential perceptual elements. They record key events and changes in the features of an image, such as discontinuities in depth and surface orientations and fluctuations in scene illumination. The losses of edge magnitudes in visually relevant parts of an image are calculated in this subsection. Because of its minimal computing complexity and excellent efficiency for recognizing edges, we employ a Sobel filter [41] to find edge regions of a given video frame \(A\). As indicated in Equation (8), the operator constructs derivative approximations using two \(3\times 3\) kernels convoluted with the original image--one for horizontal and one for vertical changes. If we consider \(A\) to be the source picture, and \(Gx\) and \(Gy\) to be two images that comprise the horizontal and vertical derivative estimates at each position, the computations are as follows:\[G_{x}= \begin{bmatrix}-1&0&+1\\ -2&0&+2\\ -1&0&+1\end{bmatrix} *A\,\ G_{y}= \begin{bmatrix}+1&+2&+1\\ 0&0&0\\ -1&-2&-1\end{bmatrix} *A \tag{8}\]  
Here, \(*\) denotes the convolution operation for the two-dimensional signal processing. We can combine the resulting gradient approximations to get the gradient magnitude for the current frame (\(G_{c}\)) as follows:  
\[  
Using Equation (6), the disparity index (\(D_{n}\)) calculated from the reliable disparity measured between the left and right frames of the Bicycle Riding video was 4.155, a frame-by-frame comparison approach which continued for the entire video sequence. It was observed that the disparity indices remained relatively constant throughout a sequence assuming that there was no scene cut, with any error or distortion in either view reducing the value of \(D_{n}\). To verify this observation, different kinds of errors, i.e., packet losses, distortions, and manual errors, were applied in one of the two views. Then, based on variations in the error energy, the disparity index was calculated from the left and right views. In Figure 5, the intermediate calculations and the corresponding maps are shown. Using Equation (6), the disparity index (\(D_{n}\)) is calculated again from the reliable disparity between the distorted left and original right views of the Bicycle Riding video which was 3.497 and was less than the actual disparity index of 4.15 for two undistorted frames. Further examples of simulated packet losses and distortions are shown in Figures 6 and 7. Figure 5: Steps for calculating disparity index from left and right frames of the Bicycle Riding video. In Figures 6 and 7, different error mechanisms and artifacts induced in the frames can be seen, with the resultant disparity indices varying depending on the types of errors. In our experiment, packet losses were simulated using the JM H.264 reference software and, for various artifacts, the disparity indices were less than for those in undistorted frames. To verify that the left and right frames in a 3D video maintain a constant rate of disparity for proper viewing, we simulated different errors in 75 frames of the Bicycle Riding video sequence, with a graph of the disparity indices presented in Figure 8.  
Figure 6: Different error scenarios induced in left views of 3D Video (part-1). Figure 8: Disparity indices with respect to frames for the Bicycle Riding 3D video. Figure 7: Different error scenarios induced in left views of 3D Video (part-2). For a packet loss, due to the dissimilarity, the views result in a deteriorated disparity (in frames 50 to 75). Further, for each distorted artifact (in frames 20 to 30), the value of the index decreased and then increased back to its previous value for the original undistorted frame in both views. On that occasion, \(S_{m}\) of the current frame is measured by collating it with the previous frame indices of disparity using Equation (7). Different numbers of previous frames could be selected as reference ones by selecting different values of \(P\).