## 3 Experiments
### Middlebury Dataset
MGM performs better than SGM4 and SGM8 because there are multiple paths between any two pixels, which strengthens the interactions of pixels in the local region. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Method** & **BF** & **GF** & **NL** & **ST** & **MGM** & **SGM4** & **SGM8** & **Ours** \\ \hline Aloe & 6.93\({}^{\prime}\) & 5.29\({}_{6}\) & 4.79\({}_{5}\) & 4.79\({}_{5}\) & 4.44\({}_{4}\) & 4.29\({}_{3}\) & 4.26\({}_{2}\) & 4.19\({}_{1}\) \\ Baby1 & 4.26\({}_{7}\) & 3.62\({}_{5}\) & 7.47\({}_{5}\) & 4.10\({}_{6}\) & 2.65\({}_{2}\) & 2.84\({}_{4}\) & 2.67\({}_{3}\) & 2.33\({}_{1}\) \\ Baby2 & 3.47\({}_{5}\) & 3.39\({}_{4}\) & 11.94\({}_{7}\) & 13.36\({}_{8}\) & 1.87\({}_{1}\) & 4.03\({}_{6}\) & 2.54\({}_{3}\) & 2.38\({}_{2}\) \\ Baby3 & 4.47\({}_{4}\) & 3.98\({}_{2}\) & 5.00\({}_{6}\) & 4.29\({}_{3}\) & 4.50\({}_{5}\) & 5.42\({}_{6}\) & 5.23\({}_{7}\) & 3.18\({}_{1}\) \\ Bowling1 & 10.38\({}_{3}\) & 9.36\({}_{2}\) & 19.49\({}_{8}\) & 19.44\({}_{7}\) & 11.20\({}_{4}\) & 13.64\({}_{5}\) & 14.79\({}_{6}\) & 7.56\({}_{1}\) \\ Bowling2 & 5.84\({}_{5}\) & 4.70\({}_{2}\) & 8.21\({}_{6}\) & 8.25\({}_{7}\) & 8.38\({}_{8}\) & 4.89\({}_{4}\) & 4.78\({}_{3}\) & 3.37\({}_{1}\) \\ Cloth1 & 3.19\({}_{8}\) & 1.20\({}_{7}\) & 0.62\({}_{1}\) & 0.63\({}_{2}\) & 0.96\({}_{5}\) & 0.73\({}_{4}\) & 0.67\({}_{3}\) & 1.15\({}_{6}\) \\ Cloth2 & 6.11\({}_{8}\) & 1.89\({}_{1}\) & 3.87\({}_{6}\) & 3.74\({}_{5}\) & 2.25\({}_{2}\) & 2.47\({}_{3}\) & 4.29\({}_{7}\) & 2.75\({}_{4}\) \\ Cloth3 & 3.39\({}_{8}\) & 1.70\({}_{1}\) & 2.39\({}_{6}\) & 2.57\({}_{7}\) & 1.92\({}_{2}\) & 2.09\({}_{4}\) & 2.06\({}_{3}\) & 2.35\({}_{5}\) \\ Cloth4 & 3.23\({}_{8}\) & 2.92\({}_{7}\) & 1.81\({}_{2}\) & 1.80\({}_{1}\) & 1.97\({}_{3}\) & 1.99\({}_{4}\) & 2.00\({}_{5}\) & 2.21\({}_{6}\) \\ Flowerpts & 8.33\({}_{4}\) & 7.52\({}_{1}\) & 13.56\({}_{8}\) & 10.13\({}_{7}\) & 4.21\({}_{1}\) & 12.17\({}_{7}\) & 11.21\({}_{6}\) & 7.84\({}_{3}  
After disparity refinement, our OmniSGM achieves the best results among these approaches. The error rates for non-occluded and all regions for final disparity image are decreased by 0.87% and 0.63% respectively, when compared with that of SGM8. The performance of ST and NL is inferior to those SGM-based methods for the overusing of piece-wise constant assumption. Figure 5 shows examples of disparity images for GF, SGM, MGM and our method. Our method generates better results than GF, SGM, and MGM. Disparities of all major structures are correctly predicted and reliable disparities propagate along the MST to recover that of _unstable_ pixels. GF utilizes information in a local window, and SGM only takes pixels on multiple scan lines into account, so that neither of them can effectively solve the ambiguity in the low textural area. Our method incorporates useful information from pixels in the whole image and successively improves the robustness of initial cost volume, since we achieve the best results among these methods. Stereo Pairs from Natural Conditions: Middlebury 2014 dataset [36] provides high-resolution stereo pairs with large label space under natural conditions. The 10 testing stereo pairs with ground truth are used to evaluate the effectiveness of typical cost aggregation methods. Here, we use _Census Transform_ (CT) in a 9 \(\times\) 9 window to compute matching cost, and normalize the matching cost to [0, 1.0] to avoid tremendous message. In order to fairly compare various cost aggregation methods, we perform evaluation of average error rate and average endpoint error for initial disparity images. Figure 6 shows the error rate and endpoint error of testing stereo pairs for GF, SGM, MGM and our method. We can see that our method outperforms GF, SGM and MGM almost on all testing images in both metrics. The superiority of our method is more  
Figure 5: Examples of disparity images for MGM, SGM and our method on Mibblebury dataset [9]. SGM4 and SGM8 corresponds to performing optimization along four and eight scan lines for SGM.