# Evolutionary Optimization for Robust Epipolar-Geometry Estimation and Outlier Detection
## 5 Experimental Results and Discussion
### Experiments on Real Data  
The proposed algorithm of robust estimation and inlier detection was compared with other RANSAC-like techniques for 15 stereo pairs (Table 3). These examples were chosen to cover various cases, such as close-range and aerial photography, narrow and wide baselines, degenerate configurations, scale variation, multi-platform photography and highly contaminated data. The first seven pairs and their putative matches were gathered from [40]. For these data, the percentages of true inliers in the dataset (\(\epsilon\)) were manually determined in the reference article. For the 8 th, the 9 th and the 10 th stereo pairs, we used signalized targets to provide ground control data when acquiring the images. The reference fundamental matrices were calculated from these control points. The 11 th stereo pair belongs to the ISPRS datasets for urban classification www2.isprs.org/commissions/comm3/wg4/detection-and-reconstruction.html. The 14 th stereo pair belongs to the ISPRS benchmark for multi-platform photogrammetry [[http://www2.isprs.org/commissions/comm1/icwg15b/benchmark_main.html](http://www2.isprs.org/commissions/comm1/icwg15b/benchmark_main.html)]([http://www2.isprs.org/commissions/comm1/icwg15b/benchmark_main.html](http://www2.isprs.org/commissions/comm1/icwg15b/benchmark_main.html)) [55]. For these last two pairs, the exterior and interior orientation parameters provided by ISPRS were used as reference values for evaluation. For the last five stereo pairs, SIFT key points were detected and matched using the VIFeat www.vlfeat.org feature-based matching library. For the second and the 12 th stereo pairs, we could not apply Multi-GS, since the low inlier ratio and a high number of correspondences made that algorithm too slow to be executable.  
It can be noticed from the results that our algorithm generally yielded solutions that were compatible with the ground-truth in terms of either inlier-detection accuracy or estimation accuracy. For the eight and the ninth images, a dominant plane existed in the scene. Therefore, most of the algorithms ended up with a degenerate solution. However, the degeneracy could be avoided quite efficiently by our algorithm. This was mainly due to the guided sampling based on the spatial distribution of matches. Finally, it was noticed that the algorithm had good performance in challenging cases such as multi-platform photography.  
Figure 10: Performance of the proposed algorithm with varying GA population size. The graph at the bottom of each surface-plot represents the average of the respective performance criterion versus the population size.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Image Pairs** & **Coineria** & **Our Algorithm** & **RANSAC** & **MSAC** & **LO-RANSAC** & **Con-RANSAC** & **SuLSAC** & **Multi-GS-RANSAC** \\ \hline \multirow{4}{*}{} & \(\mu=38\%\), \(\kappa=1088\) & \(\mu=2823\) & 3201 & 16,088 & 503 & 160,8188 & 2465 \\  & \(\mu=\) & **34.0** & 32.0 & 32.0 & 34.2 & 1.1 & 43.2 & 42.8 \\  & \(\mu=\) & 0.163 & **0.111** & 0.092 & 0.228 & 24.916 & 6.026 & 28.593 \\ \hline \multirow{4}{*}{} & \(\mu=22\%\), \(\kappa=1516\) & \(\mu=208\) & 46,329 & 50,000 & 500,000 & 505 & 112,200 & \multirow{4}{*}{} \\  & \(\mu=\) & **21.6** & 8.0 & 20.6 & 6.9 & 0.7 & 14.9 & \multirow{4}{*}{} \\  & \(\mu=\) & 0.163 & 0.208 & **0.074** & 0.655 & 139,683 & 15,881 & \\ \hline \multirow{4}{*}{} & \(\mu=38\%\), \(\kappa=1088\) & \(\mu=27\) & 1044 & 1857 & 503 & 91,638 & 198 \\  & \(\mu=\) & 31.8 & 32.7 & 33.4 & **34.8** & 2.6 & 49.5 & 100.0 \\ \cline{1-1}  & \(\mu=\) & 0.199 & **0.115** & 0.170 & 0.194 & 154,981 & 46,196 & 4911 \\ \hline \multirow{4}{*}{} & \(\mu=65\%\), \(\kappa=1110\) & \(\mu=27\) & **78** & 964 & 1100 & 2547 & 502 & 52,692 & 1259 \\  & \(\mu=\) & **44.1** & 42.3 & 40.5 & 43.0 & 1.4 & 59.5 & 44.7 \\  & \(\mu=\) & 0.179 & 0.102 & **0.100** & 0.250 & 0.614 & 32