## 3 Results and Discussion
### Evaluation of the Robustness to the Illumination and Exposure of Our Cost Computation Method  
To verify the effectiveness of our proposed cost computation method, we used six pairs of stereo images with ground truth: Aloe, Baby1, Bowling1, Cloth1, Flowerpots, and Rocks 1, provided by Middlebury 2006 datasets [32] which have three illuminations (1, 2, 3) and three different exposure settings (0, 1, 2). Figure 7 shows the left image of the aloe data under three different illuminations  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline \(\lambda_{GRAD}\) & 25 & \(\lambda_{CTg}\) & 15 \\ \(\tau_{1}\) & 30 & \(L_{1}\) & 31 \\ \(\tau_{2}\) & 6 & \(L_{2}\) & 80 \\ \(d_{Lim}\) & 9 & \(\varepsilon\) & 0.012  \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameter settings of the proposed algorithm.  
(no exposure variation) and with three different exposure settings (no illumination change). In this paper, three widely used cost computation methods were considered for comparison, including a function combining the sum of absolute difference (SAD) and gradient [6], a function combining absolute difference (AD) with census transform [14] and a combination of absolute difference, gradient, and Census transform [15]. To highlight the preference of cost computation function, all disparity maps were computed with the same cost aggregation algorithm proposed in Section 2.2 and no further refinement was applied.  
Figures 8 and 9 show two pairs of the left and right images, the ground truth maps, and the disparity maps obtained by our proposed cost function and other three common combined cost methods under various illuminations and with different exposure settings, respectively. In Figure 8, the left images are captured under Illumination 1, the right images are captured under Illumination 3, and both are with the same Exposure 1. In Figure 9, the left images are taken with Exposure 0, while the right images are taken with Exposure 2. Furthermore, both the left image and right image are under the same Illumination 2. Comparing Figure 8g with Figure 8d-f, the disparity maps in Figure 8g are better than the disparity maps in Figure 8d-f, which indicates that the proposed cost computation method is more robust to illumination variation for these textureless stereo images. Comparing Figure 9g with Figure 9d,f, the disparity maps in Figure 9g are better than the disparity maps in Figure 9d,f, which indicates that the proposed cost computation method is more robust to exposure variation than cost combined SAD with gradient and cost combined AD, gradient and census. The disparity maps in Figure 9g and the disparity maps in Figure 9d have no significant differences.  
The average percentage of bad pixels of disparity maps via these four different cost measurements under three radiometric conditions are shown in Tables 2 and 3. As a reference, we also computed the disparity maps without any illumination changes (Illumination 1) and exposure changes (Exposure 1) and the result is shown in Table 4. In Table 2, the proposed cost computation method achieved smallest  
Figure 8: Disparity maps under different illumination conditions of Aloe and Baby1. (**a**) Left image under Illumination 1; (**b**) right image under Illumination 3; (**c**) ground truth; (**d**) cost combined sum of absolute difference (SAD) with gradient; (**e**) cost combined absolute difference (AD) with census transform; (**f**) combination of AD, gradient and census; (**g**) the proposed cost function.  
Figure 7: The left image of the aloe data under three different illuminations (with the same exposure 1) and with three different exposure settings (under the same Illumination 1). (**a**) Illumination 1; (**b**) Illumination 2; (**c**) Illumination 3; (**d**) Exposure 0; (**e**) Exposure 1; (**f**) Exposure 2.