# Improvement of the Cross-Scale Multi-Feature Stereo Matching Algorithm
## 3 Experimental Results and Analysis  
To validate the effectiveness of improvements in the proposed algorithm, we conducted experiments using calibrated image pairs from the Middlebury 3.0 benchmark [24]. The algorithmic framework was implemented in C++ with the OpenCV computer vision library, adhering to the standardized evaluation protocol for stereo matching. The proposed algorithm was comparatively evaluated against the SGM algorithm [25] and the conventional AD-Census [26] cost metric. The following evaluation metrics were employed to assess matching accuracy improvements:  
1. Non-occluded region error rate
2. All-region error rate  
The mismatch rate \(M\) is formally defined as:  
\[M=\frac{1}{N}|d_{c}(x,y)-d_{r}(x,y)|>T_{d}, \tag{11}\]  
Here, \(d_{r}(x,y)\) is the true disparity value of the image, \(d_{c}(x,y)\) is the disparity value obtained by the improved algorithm, and \(N\) represents the total number of pixels in non-occluded regions or across all regions. The main experimental parameters of the proposed algorithm are listed in Table 1. In the experiments, the disparity threshold was set to 1 pixel--this means that when the experimental data were compared with the ground-truth disparity map, a pixel would be identified as a mismatched point if its error exceeded 1 pixel. Three standard stereo image pairs (Teddy, Conces, and Venus) from the Middlebury3.0 platform were selected for the experiments. The mismatch rates in both non-occluded regions and all regions were calculated for each image set. Experimental results obtained using three distinct cost-computation methods are presented in Tables 2 and 3. An analysis of the experimental results in the figures above demonstrates that the proposed algorithm achieves higher-quality disparity maps when processing weakly textured regions compared to the other two algorithms. Furthermore, parameter adjustments \begin{table}
\begin{tabular}{c c c c c c} \hline
**Parameter** & \(\mathbf{\omega_{k}}\) & \(\mathbf{T_{d}}\) & \(\mathbf{\alpha}\) & \(\mathbf{s}\) & \(\mathbf{\lambda}\) \\ \hline Value & 9 & 1 & 0.7 & 4 & 0.9 \\ \hline \end{tabular}
\end{table} 
Table 1: Key parameter settings of the proposed algorithm in this study. \begin{table}
\begin{tabular}{c c c c c} \hline
**Algorithm** & **Teddy** & **Cones** & **Venus** & **Average** \\ \hline Census & 6.34 & 3.49 & 0.36 & 3.40 \\ SGM & 7.23 & 3.71 & 0.79 & 3.91 \\ Proposed & 5.94 & 2.71 & 0.31 & 2.99 \\ \hline \end{tabular}
\end{table} 
Table 2: Mismatch rates of different cost algorithms in non-occluded regions. \begin{table}
\begin{tabular}{c c c c c} \hline
**Algorithm** & **Teddy** & **Cones** & **Venus** & **Average** \\ \hline Census & 10.4 & 9.43 & 0.53 & 6.79 \\ SGM & 11.2 & 9.07 & 0.91 & 7.06 \\ Proposed & 11.4 & 8.36 & 0.48 & 6.75 \\ \hline \end{tabular}
\end{table} 
Table 3: Mismatch rates of different cost algorithms in all regions. A comparison between the experimental results in Figure 8 and the ground-truth disparity map demonstrates that the improved algorithm produces globally smoother disparity maps, achieving a satisfactory performance in both disparity discontinuity regions and flat areas. As illustrated by the mechanical parts comparison in Figure 9, the enhanced algorithm exhibits a superior capability in preserving the contour information of mechanical components. However, residual mismatch artifacts persist in the disparity maps, necessitating further refinement in subsequent research. A quantitative analysis reveals that in non-occluded regions of the low-texture Wood images, the average mismatch rate of the SGM algorithm measures 14.7%, while the proposed algorithm achieves 11.2%, demonstrating a 3.5% reduction. Furthermore, for mechanical component images, the proposed algorithm attains an average mismatch rate of 13.3% in non-occluded areas, representing a 4.1% improvement over the SGM algorithm's 17.4%. Collectively, the proposed method achieves an average mismatch rate of 12.25% across both datasets.