# Evolutionary Optimization for Robust Epipolar-Geometry Estimation and Outlier Detection
## 5 Experimental Results and Discussion
### Performance under Various Outlier Ratios  
To assess the performance of the overall algorithm under different ratios of outliers, the Multiview dataset was used. In the following experiments, the stall generation of the GA was set to 60. The upper  
Figure 7: Inlier thresholds determined by (**a**) our adaptive thresholding method; (**b**) the median-based algorithm and (**c**) the covariance-based algorithm.  
bound to the standard deviation of image noise (\(\sigma_{\text{max}}\)) was set to three pixels. The GA population size was set to 27. The parameter \(n^{*}\) was set to \(n/10\) in all of our experiments. The algorithm was implemented in the MATLAB environment directly without using its optimization toolbox. The average of the results over all of the stereo pairs versus the outlier ratios are presented in Figure 8.  
The results can clearly illustrate the performance of the proposed algorithm. For instance, to reach 95% accuracy in inlier detection from a dataset with 70% outliers, at least 45,658 sample sets must be drawn in random sample consensus. However, the proposed algorithm reached 95% accuracy by drawing only 2100 sample sets. Similarly, our algorithm achieved 78% accuracy over the 80% contaminated dataset with only 1440 hypotheses, while 591,455 random sample sets would be theoretically required to reach that accuracy. There was a combination of reasons caused by the evolutionary search and the sampling strategy that boosted this improvement. Furthermore, for all of the outlier ratios, the number of GA iterations was lower than other algorithms (average _Itr_ of 93). However, it should be noted that any iteration of GA corresponds to the maximum of 27 hypothesis generation. In the case of data with a low percentage of outliers, there are many correct solutions that each can be slightly fitter; such slightly fitter solutions may violate the termination criterion mentioned in Section 4.3. Therefore, an additional condition based on the rate of improvement achieved by the new elites must be considered to avoid unnecessary iterations. One can use the following method; whenever the elite solutions of two generations have fitness values within 10% of one another, then the fitter solution should duplicate itself, and the less fit solution should be removed to ensure a low standard deviation over the stall generations.  
From the accuracy point of view, the proposed algorithm was more robust to outliers in comparison with other algorithms, especially when the outlier percentage grew over 40%. On average, the proposed technique achieved 91% \(\pm\) 6% accuracy for inlier detection. The considerably high estimation accuracy (average \(\mu_{d}\cdot CP\) of 0.376) confirmed this, as well. The improvement obtained by  
Figure 8: Performance of different algorithms under various percentages of outliers for the Multiview dataset. In the graphs, the x-axis represents the percentage of synthetic outliers in the dataset.  
the proposed algorithm was also evident regarding the true negative rate (average _TNR_ of 94%), which showed the efficiency of the algorithm to distinguish outliers from inliers. Figure 8 also indicates that LMedS performs robustly for outlier ratios less than 50%. However, model estimation and, particularly, inlier detection for higher outlier rates is the bottleneck of this algorithm. The Cov-RANSAC resulted in better _TNR_ compared to our algorithm. However, the spatial configuration and the level of noise in the sampled points are ignored in this method. As a result, the estimation of model uncertainty becomes impractically too large or too small. Consequently, the number of inliers is usually over- or under-estimated. That is why this technique resulted in very low _TPR_..