As mentioned in Chapter 4, there are several steps in stereo matching, each step there are several candidate methods. A combination of the selected method for each step is referred to as an approach. In this thesis, the name of approaches is composed of the name of constituent methods. The approaches that are compared in this thesis are as follows.
1. SAD+MAA+WTA+LRV: This approach uses SAD to compute pixel-matching costs, MAA to aggregate matching costs, WTA to compute disparities, and LRV to validate the left and the right disparity map of stereo pairs.
Chapter 6. Experimental Results and Discussions 111 2. SAD+MAA+DP: This approaches uses Dynamic Programming to compute disparities instead of WTA. Both Approach 1 and 2 are preferred in Intel- ligent Transportation Systems because of its simplification in the computa- tion.
3. SAD+EGA+WTA+LRV: This approach replaces MAA in Approach 1 by the proposed method, i.e. EGA, to demonstrate that SAD is not suitable for being combined with EGA.
4. XCS+EGA+WTA+LRV: This approach demonstrates the robustness of XCS and EGA in stereo matching.
5. XCS+EGA+GCP-DP: This approach demonstrates the robustness of GCP- DP with WTA and DP.
Both of the artificial and the real sequence are used to compare the five approaches given above, the parameters that are used in the computation of disparity images are shown in Table 6.2. The comparison is organized into qualitative and quan- titative sections. In qualitative comparison, we compute disparity maps for both of the sequences by the five methods given above, and these maps are arranged adjacently for being compared qualitatively. In quantitative comparison, the den- sity of valid disparities as well as the averaged absolute mean errors are compared for the artificial sequence because ground-truth images are available. However, in the case of the real sequence for which ground-truth images are not available, the quantitative comparison is done only by the density of valid disparities.
Table 6.2: Parameters used to compute disparity images.
Method The artificial sequence The real sequence MAA Window Size: 11×11 Window Size: 11×111
EGA Window Size: 21×501 Window Size: 11×181 Edge Detector: LoG Edge Detector: LoG
α= 0.2 α= 0.2
DP αe = 5; αne= 30
GCP-DP Tsc = 0.1;Tpro = 2 αe= 0.1;αne = 0.5
Chapter 6. Experimental Results and Discussions 112
6.3.1 Qualitative Comparisons
Several examples of output disparity images computed by the five compared ap- proaches are shown in FIGURE6.5. The first row is for the artificial sequence, the other rows are for the real sequence. The first column of all rows shows the left image of stereo pairs. The other columns, from the left to the right side, shows dis- parity images computed by the approaches as follows: SAD+MAA+WTA+LRV, SAD+MAA+DP, SAD+EGA+WTA+LRV, XCS+EGA+WTA+LRV, and XCS+
EGA+GCP-DP.
As shown in the first row of FIGURE6.5, disparity images for all of the stereo pairs in the artificial sequence can be computed by any approach in the five compared approaches except SAD+EGA+WTA+LRV. This result is due to the fact that the artificial sequence as synthesized in such a way that textures are well-distributed in stereo pairs. The results in the first row of FIGURE 6.5 also demonstrate that XCS+EGA+WTA+LRV is a reliable approach because it can produce a large number of valid pixels and can preserve depth-discontinued boundaries of vehicles.
The preservation of depth-discontinued boundaries can be explained as follows. As mentioned in Chapter4, boundaries which are computed by edge maps define ho- mogenous regions in stereo images, and only pixels in the homogeneous regions are assumed to have the same disparity. On the other hand, only a change from XCS to SAD in XCS+EGA+WTA+LRV, Approach SAD+EGA+WTA+LRV produces low quality disparity maps. This result is the fact that SAD can not be combined with EGA because it is sensitive to image noises.
In contrast with the artificial sequence, almost of stereo pairs in the real sequence are textureless, so the classical and simple approaches, i.e. SAD+MAA+WTA+LRV and SAD+WTA+DP, produce too many noisy disparities, as shown in the last three rows in FIGURE 6.5. FIGURE 6.5 also demonstrates that only the dispar- ities of pixels of strong edges in the images are reliable enough for being used in further steps, for example, ground plane estimation and vehicle detection. Hence, sparse disparity maps computed for pixels of strong edges are used in many re- search works in ground plane estimation and vehicle detection [103]. Similar to the experiment for the artificial sequence presented above, SAD can not be combined with EGA, especially in the case of using wide aggregation windows.
Finally, as shown in FIGURE6.5, both of XCS+EGA+WTA+LRV and XCS+EGA+
GCP-DP are reliable approaches for computing disparity images from stereo pairs
Chapter 6. Experimental Results and Discussions 113 in the artificial or the real sequence, or from stereo pairs having well-distributed textures or lack of textures.
6.3.2 Quantitative Comparisons
Two types of quantitative comparisons done for the artificial sequence are the mean of absolute errors (MAE) and the density of valid disparities. MAEs are computed for the five compared approaches by comparing their output disparity maps with corresponding ground-truth images, by Equation2.6. As shown in FIGURE 6.6, in the case of having no vehicles, i.e., Stereo Pair 1-49 and 89- 200, XCS+EGA+GCP-DP produces the smallest MAEs among the five compared approaches, but it and SAD+MMA+DP create high errors in the case of having vehicles. This phenomenon is due to the effect of using Dynamic Programming that may over smooths output disparity maps. On the other hand, the figure shows that XCS+EGA+WTA+LRV is a reliable approach because its MAEs are smallest in the case of having on-road vehicles and because its MAEs are higher than XCS+EGA+GCP-DP’s but are not so different to the smallest errors in the case of having no vehicles.
In the case of the density comparison for the artificial sequence, the density of valid disparity is computed for SAD+MAA+WTA+LRV and XCS+EGA+WTA+LRV.
These two approaches are selected for the density comparison because we would like to compare EGA with MAA. The density comparison for the artificial sequence is shown in FIGURE6.7(a). FIGURE6.6and FIGURE6.7(a) are together shows that XCS+EGA+WTA+LRV can produce larger number of valid disparities with almost smaller errors then SAD+MAA+WTA+LRV. Finally, XCS+EGA+WTA+
LRV and XCS+EGA+GCP-DP are more robustness than the other approaches.
The density comparison for the real sequence is shown in FIGURE 6.7 (b), which shows that XCS+EGA+WTA+LRV produces more number of valid disparities than SAD+MAA+WTA+LRV does. In combination with the qualitative com- parison, XCS+EGA+WTA+LRV is highly recommended for being used in further steps like ground plane estimation and vehicle detection.
Chapter 6. Experimental Results and Discussions 114
Figure6.5:Qualitativecomparisons.Columns(lefttoright):LeftImages,SAD+MAA+WTA+LRV,SAD+MAA+DP,SAD +EGA+WTA+LRV,XCS+EGA+WTA+LRV,andXCS+EGA+GCP-DP.
Chapter 6. Experimental Results and Discussions 115
Figure 6.6: Quantitative comparisons for the artificial sequence: Averaged Absolute Mean Errors.