# On Alpha-Expansion-Based Graph-Cut Optimization for Decoder-Side Depth Estimation
## 4 Experimental Results
### Results  
First of all, we establish the performance of the hierarchical alpha-expansion (reference state-of-the-art method) by comparing it with the basic alpha-expansion. The results shown in Table 2 indicate that, on average, using hierarchical scheme with the optimization step equal to 2 decreases the time of decoding (which includes parsing the bitstream, depth estimation, and virtual view rendering) by almost 20%. On the other hand, the loss in the quality of estimated depth maps results in 5% of BD-rate loss in both reported quality metrics. When the optimization step is equal to 4, further decrease of runtime can be seen (by another 18%) as well as progressing BD-rate loss (Table 2). This indicates that in immersive video applications, the state-of-the-art hierarchical alpha-expansion used for depth estimation cannot be used to further decrease the complexity of a decoder--the quality losses become too significant to accept. The proposed second-cycle label offset, as presented in Table 3, overcomes the limitations of the state-of-the-art hierarchical alpha-expansion. If the optimization step is equal to 2, then the runtime is decreased by more than 40% and the quality is only negligibly decreased. For the step equal to 4 (Table 3), the quality loss becomes noticeable and the runtime is longer than in the previous configuration (as the refinement iterations have to be performed in this scheme). \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Sequence** & **Source** & **Type** & **Resolution** & **Views** \\ \hline Classroom Video & [25] & Equirectangular projection & Computer generated & 4096 \(\times\) 2048 & 15 \\ \hline Museum & [26] & Equirectangular projection & Computer generated & 2048 \(\times\) 2048 & 24 \\ \hline Chess & [27] & Equirectangular projection & Computer generated & 2048 \(\times\) 2048 & 10 \\ \hline Guitarist & [28] & Equirectangular projection & Computer generated & 2048 \(\times\) 2048 & 23 \\ \hline Hijack & [29] & Equirectangular projection & Mixed & 4096 \(\times\) 2048 & 10 \\ \hline Cyberpunk & [29] & Equirectangular projection & Mixed & 2048 \(\times\) 2048 & 10 \\ \hline Kitchen & [30] & Perspective, planar & Computer generated & 1920 \(\times\) 1080 & 25 \\ \hline Cadillac & [31] & Perspective, planar & Computer generated & 1920 \(\times\) 1080 & 15 \\ \hline Mirror & [32] & Perspective, planar & Computer generated & 1920 \(\times\) 1080 & 15 \\ \hline Fan & [33] & Perspective, planar & Computer generated & 1920 \(\times\) 1080 & 15 \\ \hline Group & [34] & Perspective, convergent & Computer generated & 1920 \(\times\) 1080 & 21 \\ \hline Dancing & [35] & Perspective, convergent & Computer generated & 1920 \(\times\) 1080 & 24 \\ \hline Painter & [36] & Perspective, planar & Natural content & 2048 \(\times\) 1088 & 16 \\ \hline Breakfast & [37] & Perspective, planar & Natural content & 1920 \(\times\) 1080 & 15 \\ \hline Barn & [38] & Perspective, planar & Natural content & 1920 \(\times\) 1080 & 15 \\ \hline Frog & [39] & Perspective, planar & Natural content & 1920 \(\times\) 1080 & 13 \\ \hline Carpark & [40] & Perspective, planar & Natural content & 1920 \(\times\) 1088 & 9 \\ \hline Street & [40] & Perspective, planar & Natural content & 1920 \(\times\) 1088 & 9 \\ \hline Fencing & [41] & Perspective, convergent & Natural content & 1920 \(\times\) 1088 & 9 \\ \hline CBABasketball & [42] & Perspective, convergent & Natural content & 1920 \(\times\) 1080 & 34 \\ \hline MartialArts & [43] & Perspective, convergent & Natural content & 1920 \(\times\) 1080 & 15 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: List of test sequences used. Nevertheless, turning on neighboring segment label examination (Table 4) significantly improves the quality, even over the configuration without hierarchical alpha-expansion (gain of 6.6% for IV-PSNR-based BD-rate). The results show that it is not optimal to examine all depth levels, as is done in hierarchical alpha-expansion with second-cycle label offset with step 2.